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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ESD</journal-id><journal-title-group>
    <journal-title>Earth System Dynamics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ESD</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Earth Syst. Dynam.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">2190-4987</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/esd-12-1115-2021</article-id><title-group><article-title>Taxonomies for structuring models for World–Earth systems analysis of the Anthropocene: subsystems, their interactions and social–ecological feedback loops</article-title><alt-title>Taxonomies for structuring models of World–Earth systems</alt-title>
      </title-group><?xmltex \runningtitle{Taxonomies for structuring models of World--Earth systems}?><?xmltex \runningauthor{J. F. Donges et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Donges</surname><given-names>Jonathan F.</given-names></name>
          <email>donges@pik-potsdam.de</email>
        <ext-link>https://orcid.org/0000-0001-5233-7703</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff3 aff4">
          <name><surname>Lucht</surname><given-names>Wolfgang</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Cornell</surname><given-names>Sarah E.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4367-1296</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Heitzig</surname><given-names>Jobst</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0442-8077</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff6">
          <name><surname>Barfuss</surname><given-names>Wolfram</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9077-5242</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff7 aff8">
          <name><surname>Lade</surname><given-names>Steven J.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9719-9826</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Schlüter</surname><given-names>Maja</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 106 91 Stockholm, Sweden</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Geography, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Integrative Research Institute on Transformations of Human-Environment Systems, Humboldt University <?xmltex \hack{\break}?>of Berlin, Unter den Linden 6, 10099 Berlin, Germany</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Complexity Science, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Department of Physics, Humboldt University of Berlin, Newtonstr. 15, 12489 Berlin, Germany</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>Fenner School of Environment and Society, The Australian National University, Building 141, Linnaeus way, Canberra, ACT 2601, Australia</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>Bolin Centre for Climate Research, Stockholm University, Geoscience Building at Frescati Campus Svante Arrhenius väg 8, 106 91 Stockholm Sweden</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Jonathan F. Donges (donges@pik-potsdam.de)</corresp></author-notes><pub-date><day>12</day><month>November</month><year>2021</year></pub-date>
      
      <volume>12</volume>
      <issue>4</issue>
      <fpage>1115</fpage><lpage>1137</lpage>
      <history>
        <date date-type="received"><day>26</day><month>April</month><year>2018</year></date>
           <date date-type="rev-request"><day>26</day><month>April</month><year>2018</year></date>
           <date date-type="rev-recd"><day>18</day><month>February</month><year>2021</year></date>
           <date date-type="accepted"><day>30</day><month>March</month><year>2021</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 </copyright-statement>
        <copyright-year>2021</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://esd.copernicus.org/articles/.html">This article is available from https://esd.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://esd.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://esd.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e187">In the Anthropocene, the social dynamics of human societies have become critical to understanding planetary-scale Earth system dynamics. The conceptual foundations of Earth system modelling have externalised social processes in ways that now hinder progress in understanding Earth resilience and informing governance of global environmental change.
New approaches to global modelling of the human World are needed to address these challenges. The current modelling landscape is highly diverse and heterogeneous, ranging from purely biophysical Earth system models, to hybrid macro-economic integrated assessments models, to a plethora of models of socio-cultural dynamics. World–Earth models capable of simulating complex and entangled human–Earth system processes of the Anthropocene are currently not available. They will need to draw on and selectively integrate elements from the diverse range of fields and approaches; thus, future World–Earth modellers require a structured approach to identify, classify, select, combine and critique model components from multiple modelling traditions.
Here, we develop taxonomies for ordering the multitude of societal and biophysical subsystems and their interactions. We suggest three taxa for modelled subsystems: (i) biophysical, where dynamics is usually represented by “natural laws” of physics, chemistry or ecology (i.e. the usual components of Earth system models); (ii) socio-cultural, dominated by processes of human behaviour, decision-making and collective social dynamics (e.g. politics, institutions, social networks
and even science itself); and (iii) socio-metabolic, dealing with the material interactions of social and biophysical subsystems (e.g. human bodies, natural resources and agriculture). We show how higher-order taxonomies can be derived for classifying and describing the interactions between two or more subsystems. This then allows us to highlight the kinds of social–ecological feedback loops where new modelling efforts need to be directed.
As an example, we apply the taxonomy to a stylised World–Earth system model that endogenises the socially transmitted choice of discount rates in a greenhouse gas emissions game to illustrate the effects of social–ecological feedback loops that are usually not considered in<?pagebreak page1116?> current modelling efforts.
The proposed taxonomy can contribute to guiding the design and operational development of more comprehensive World–Earth models for understanding Earth resilience and charting sustainability transitions within planetary boundaries and other future trajectories in the Anthropocene.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
<sec id="Ch1.S1.SS1">
  <label>1.1</label><title>Revisiting Earth system analysis for the Anthropocene</title>
      <p id="d1e206">In the age of the Anthropocene, human societies have emerged as a planetary-scale geological force shaping the future trajectory of the whole Earth system <xref ref-type="bibr" rid="bib1.bibx23 bib1.bibx120 bib1.bibx74 bib1.bibx136 bib1.bibx71 bib1.bibx122" id="paren.1"/>. Cumulative greenhouse gas emissions and extensive modifications of the biosphere have accelerated since the Neolithic and industrial revolutions, especially through the rapid globalisation of social–economic systems during the 20th century, threatening the stability of the interglacial state <xref ref-type="bibr" rid="bib1.bibx72" id="paren.2"/> that has enabled the development and well-being of human societies <xref ref-type="bibr" rid="bib1.bibx108 bib1.bibx121" id="paren.3"/>. Political and societal developments during the 21st century and their feedback interactions with the planetary climate and biophysical environment will be decisive for the future trajectory of the Earth system <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx122" id="paren.4"/>. Business as usual is taking the planet into a “hothouse Earth” state unprecedented for millions of years in geological history <xref ref-type="bibr" rid="bib1.bibx141 bib1.bibx44" id="paren.5"/>, while calls for rapid decarbonisation of the global economic system to meet the Paris climate agreement <xref ref-type="bibr" rid="bib1.bibx110" id="paren.6"/> will also have complex consequences involving an intensified entanglement of social, economic, and biophysical processes and their resulting feedback dynamics, up to the planetary scale <xref ref-type="bibr" rid="bib1.bibx82" id="paren.7"/>. Despite extensive debate about the Anthropocene <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx51 bib1.bibx13 bib1.bibx144" id="paren.8"/>, and growing recognition of the limitations of current Earth system models for analysis and policy advice in the context of these shifting dynamics  <xref ref-type="bibr" rid="bib1.bibx131 bib1.bibx132 bib1.bibx134 bib1.bibx28 bib1.bibx29 bib1.bibx18" id="paren.9"/>, little has been done to address the fundamental challenge of systematically reviewing the conceptual foundations of Earth system modelling to include dynamic social processes, rather than externalising them <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx89" id="paren.10"/>.</p>
      <p id="d1e240">To understand planetary-scale social–ecological dynamics, models of World–Earth systems are urgently needed <xref ref-type="bibr" rid="bib1.bibx112 bib1.bibx113 bib1.bibx111 bib1.bibx132 bib1.bibx134 bib1.bibx28 bib1.bibx29 bib1.bibx30 bib1.bibx18" id="paren.11"/>. Epistemologically, we conceptualise World–Earth systems as planetary-scale systems consisting of the interacting biophysical subsystems of the Earth, and the social, cultural, economic and technological subsystems of the World of human societies. It should be noted here that in the context of global change analysis and modelling, the term “Earth system” was intended to include human societies and their activities and artefacts <xref ref-type="bibr" rid="bib1.bibx89 bib1.bibx112 bib1.bibx113" id="paren.12"/>. However, in currently influential science and policy contexts, notably the Intergovernmental Panel on Climate Change (IPCC) <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx37" id="paren.13"/>, “Earth system models” deal only with the physical dynamics of the atmosphere, ocean, land surface and cryosphere, and a limited set of interactions with the biosphere. While some might see tautology in the term “World–Earth systems”, we use it to highlight that human societies, their cultures, knowledge and artefacts (the “World”) should now be included on equal terms in a new family of models to conduct systematic global analyses of the Anthropocene. A fully co-evolutionary approach is needed, in the sense of  representing social–ecological feedback dynamics across scales.</p>
      <p id="d1e252">Future World–Earth modelling efforts will largely be pieced together from existing conceptualisations and modelling tools and traditions of social and biophysical subsystems, which encode the state of the art in our understanding of the Anthropocene. Current efforts in World–Earth systems modelling are highly stylised (e.g. <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx45 bib1.bibx59 bib1.bibx53 bib1.bibx92 bib1.bibx125" id="altparen.14"/>) or tend to be proof-of-concept prototypes <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx30" id="paren.15"/>. None currently operate in a process-detailed, well-validated and data-driven mode. To serve these nascent efforts in enabling World–Earth systems analysis of the Anthropocene, this article addresses the core question of which are the relevant categories within which World–Earth models, as essential “scientific macroscopes” <xref ref-type="bibr" rid="bib1.bibx113" id="paren.16"/>, should operate. The problem for both scientific integration and real-world application is that the characteristic basis of the interactions of social and biophysical subsystems is often not explicit in current models.  Often, the interactions between these subsystems are not recognised at all. By framing a taxonomy around the current dominant distinctions – and disciplinary divides – we can begin to explore links and feedback mechanisms between taxa in more structured, systematic and transdisciplinary ways. With this taxonomy, we develop initial tools and terminologies that enable model builders and model users to be clear about their social, cultural, epistemological and perhaps also axiological standpoints.</p>
      <?pagebreak page1117?><p id="d1e264">We want to emphasise that this taxonomic approach does not presuppose that there is “one world” (an ontological position) when models of different worlds are combined, nor do we intend it to serve as a universal blueprint for models of essentially everything. Instead, we argue that a taxonomy can help to more efficiently focus modellers’ attention on the ontological and epistemic commitments within their models. This approach opens Earth system analysis to deeper dialogues with proponents of non-human actors as shapers of the world <xref ref-type="bibr" rid="bib1.bibx69 bib1.bibx86" id="paren.17"/> or even the possibility of no world at  all <xref ref-type="bibr" rid="bib1.bibx42" id="paren.18"/>.</p>
      <p id="d1e274">While the present article proposes a conceptual basis for World–Earth modelling, the proposed taxonomy is employed in the companion paper by <xref ref-type="bibr" rid="bib1.bibx30" id="text.19"/> to develop the operational World–Earth modelling framework copan:CORE. Here, this framework is cast into software and applied to construct and study an example of a novel World–Earth model that seeks to overcome the long-standing challenge of endogenising the choice of discount factors (describing how much societies value the present relative to the future) in climate mitigation studies.</p>
</sec>
<sec id="Ch1.S1.SS2">
  <label>1.2</label><title>Structuring the landscape of global environmental change models</title>
      <p id="d1e288">Diverse scientific modelling communities aim to capture different aspects of social–ecological dynamics embedded in the Earth system up to planetary scales. Some processes operating in the Earth system are commonly described as being governed by the “natural laws” and generalisable principles of physics, chemistry and (to some extent at least) ecology (e.g. atmosphere and ocean circulation as governed by the physical laws of fluid and thermodynamics), whereas others are thought to be dominated by human behaviour, decision-making and collective social dynamics (e.g. the regularities underlying individual and social learning). This tendency for separate treatment of these different kinds of processes in the natural and social sciences gives rise to problems when dealing with the many real-world subsystems that operate in both domains simultaneously. What is more, different scientific communities use different methods and adhere to different viewpoints as to the nature and character of such subsystems and their interactions. There is now a number of conceptualisations of social–ecological or coupled human–environment systems in environmental, sustainability and Earth system science (e.g. <xref ref-type="bibr" rid="bib1.bibx135 bib1.bibx112 bib1.bibx34 bib1.bibx61 bib1.bibx11" id="altparen.20"/>), but we see a pressing need to structure modelling efforts across communities, providing a joint framework while maintaining the conceptual flexibility required for successful cross-disciplinary collaboration.</p>
      <p id="d1e294">Here, we propose a taxonomic framework for structuring the multitude of subsystems that are represented in current mathematical and computer simulation models. The motivation for proposing such an ordering scheme is
<list list-type="order"><list-item>
      <p id="d1e299">to provide the means for collecting and structuring information on what components of social–ecological systems relevant to global change challenges are already present in models in different disciplines;</p></list-item><list-item>
      <p id="d1e303">to point out uncharted terrain in the Earth system modelling landscape;</p></list-item><list-item>
      <p id="d1e307">to provide the foundations for a systematic approach to constructing future co-evolutionary World–Earth models, where feedback mechanisms between components can be traced and studied.</p></list-item></list>
This conceptual work aims to contribute to a central quest of sustainability science <xref ref-type="bibr" rid="bib1.bibx85" id="paren.21"/> that “seeks to understand the fundamental character of interactions between nature and society.” <xref ref-type="bibr" rid="bib1.bibx62" id="paren.22"/>.</p>
</sec>
<sec id="Ch1.S1.SS3">
  <label>1.3</label><title>Definitions and explanations of key terms</title>
      <p id="d1e325">In this article, we use the term subsystem to refer to any dynamic component in models of World–Earth systems. In this broad category, we can include both the kinds of subsystems that are governed mainly by “natural laws” of physics, chemistry or ecology (e.g. seasonal precipitation, ocean nutrient upwelling) and those that are governed mainly by human behaviour, decision-making and collective social dynamics (e.g. international food trade, carbon taxes). Many scientific communities similarly make this distinction between biophysical (“natural”, ecological, environmental) subsystems and socio-cultural (social, human, “anthroposphere”) subsystems. We also highlight socio-metabolic subsystems at the overlap of societal and natural “spheres” of the Earth system (Fig. <xref ref-type="fig" rid="Ch1.F1"/>). We suggest that explicit attention to these subsystems and their interactions is needed in order to deepen the understanding of transformative change in the planetary social–ecological system, making a valuable contribution to the design and operational development of future, more comprehensive World–Earth models for charting sustainability transitions into a safe and just operating space for humanity <xref ref-type="bibr" rid="bib1.bibx108 bib1.bibx103 bib1.bibx25" id="paren.23"/>.</p>
      <p id="d1e333">A further note on the term biophysical: here, we use this word as a shorthand term to refer to Earth's interacting living and non-living components, encompassing geophysical (e.g. climatic, tectonic), biogeophysical, biogeochemical and ecological processes. These categories are significant in Earth system science because feedbacks involving these processes tend to have different dynamic characteristics. Accordingly, they have been dealt with very differently in Earth system analysis and modelling <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx48 bib1.bibx124" id="paren.24"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e341">Proposed taxonomy of subsystems in World–Earth systems models.
The blue and green overlapping discs represent the current discipline-based domains in which the subsystems and processes of nature, human societies and their interactions are modelled. Our scheme structures this continuum into three taxa (light grey layers) for model subsystems (dark grey discs): (i) a biophysical taxon (ENV), (ii) a socio-metabolic taxon (MET) and a socio-cultural taxon (CUL). Links within and between these modelled subsystems (shown as black arrows in the figure) can further be classified using a 3 <inline-formula><mml:math id="M1" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 3 taxonomy of interactions (Fig. <xref ref-type="fig" rid="Ch1.F2"/>, Sect. <xref ref-type="sec" rid="Ch1.S3"/>).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-f01.png"/>

        </fig>

      <p id="d1e362">The co-evolution of Earth's geosphere and biosphere is a central concept in Earth system science <xref ref-type="bibr" rid="bib1.bibx77 bib1.bibx16 bib1.bibx76 bib1.bibx117 bib1.bibx70 bib1.bibx137" id="paren.25"/>, but<?pagebreak page1118?> the global models that currently dominate the field represent just a snapshot of the system, focused on the biophysical dynamics that play out over decades to centuries. We use the term co-evolution to describe the complex dynamics that arise from the reciprocal interactions of subsystems, each of which changes the conditions for the future time evolution of the other (not excluding but also not limited to processes of Darwinian co-evolution involving natural selection). Earth system models (ESMs) include key physical feedbacks and increasingly permit the investigation of biophysical feedbacks, but as we have indicated, they lack socio-metabolic and socio-cultural subsystems, relying on narrative-based inputs for dealing with anthropogenic changes. Integrated assessment models (IAMs) used in the global change context <xref ref-type="bibr" rid="bib1.bibx31 bib1.bibx132" id="paren.26"/> include some interactions of social and biophysical subsystems in order, say, to assess potential economic consequences of climate change and alternative climate policy responses. However, they lack the kinds of interactions and feedback mechanisms (e.g. by impacts of climatic changes on socio-metabolic subsystems, or by the effects of socio-cultural formation of public opinion and coalitions in political negotiations on environmental policies) that societies throughout history have shown to be important; this is revealed, for example, by studies of social–ecological collapse and its connection to past climate changes <xref ref-type="bibr" rid="bib1.bibx138 bib1.bibx95 bib1.bibx27 bib1.bibx24 bib1.bibx6" id="paren.27"/>. To explore and illustrate the consequences of these typically neglected interactions and feedbacks, we have studied a conceptual model that gives rise to complex co-evolutionary dynamics and bifurcations between qualitatively different system dynamics: a model of socially transmitted discount rates in a greenhouse gas emissions game, discussed in Sect. <xref ref-type="sec" rid="Ch1.S4"/>.</p>
      <p id="d1e376">For completeness, we also provide brief definitions of our working terminology: a “link” or “interaction” is a causal influence of one subsystem on another that is operationally non-decomposable into smaller links; a “mechanism” is a micro-description of how exactly this causal influence is exerted; a “process” is a set of links that “belong together” from some suitable theoretical point of view; a “loop” is a closed path in the network of links; and an “impact” of a link is the change in the target system attributable to this link.</p>
      <p id="d1e379">We should note here that this taxonomy is dealing with causal narratives from different scientific disciplines that are encoded in models; as such, it does not require any a priori theories and hypotheses about causality. Causal narratives are our starting point because they are necessary for and are explicitly encoded in simulation modelling – and our classification lets us interrogate them more systematically and exposes them explicitly.</p>
</sec>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>A taxonomy of subsystems in World–Earth systems models</title>
      <p id="d1e391">In this section, we introduce the biophysical (ENV), socio-metabolic (MET) and socio-cultural (CUL) taxa for classifying subsystems in models of World–Earth systems (Fig. <xref ref-type="fig" rid="Ch1.F1"/>). For each taxon, we give examples of corresponding subsystems from different modelling fields. We also discuss how the suggested taxonomy relates to earlier conceptualisations of human societies embedded in and interacting with environmental systems (Sect. <xref ref-type="sec" rid="Ch1.S2.SS4"/>).</p>
      <p id="d1e398">We have followed three guidelines in constructing this taxonomy for models of World–Earth systems:
<list list-type="order"><list-item>
      <p id="d1e403"><italic>compactness</italic>, because we aim at a “top-level” framework that is useful and tangible, with as few classifications as possible, covering the scope of co-evolutionary modelling research parsimoniously and in a self-containing way;</p></list-item><list-item>
      <p id="d1e409"><italic>compatibility</italic> with existing disciplines and research fields within, between and beyond the persistent natural/social sciences divide, because we view the scientific endeavour of understanding links and feedbacks in co-evolutionary World–Earth systems as an integrative and transdisciplinary opportunity;</p></list-item><list-item>
      <?pagebreak page1119?><p id="d1e415"><italic>operative capacity</italic> for model classification and construction, because we want to advance efforts rapidly in World–Earth modelling. This guideline differs from the previous two in that it deals with practical aspects of modelling. We include it because it flags the need for critical reflection on the suitability of combined models for the tasks at hand. We want to be able to expand the scope of modelling to be more inclusive, allowing more differentiation and well-founded permutations of approaches.</p></list-item></list></p>
      <p id="d1e420">Models encode knowledge outside of the mind of the modeller, so these guiding principles are intended to ensure that bridging across currently very distinct modelling approaches still permits tracing back how the techniques relate to the theories, assumptions and framings of the contributory disciplines.</p>
      <p id="d1e423">The proposed taxonomy reflects the long-standing structure – and the underlying divides – of the scientific disciplines dealing with the respective subsystems. We argue that it also provides a blueprint for navigating the fragmented modelling landscape and bringing new opportunities for cross-disciplinary bridging. The anthropocentric and dialectic distinction between the realms of nature or “the environment” and of human societies has a long intellectual history. Deep philosophical and scientific puzzles are connected with the attempts to draw a sharp distinction between these domains and to satisfactorily integrate properties such as mental states, intentions and life itself.</p>
      <p id="d1e427">With the progressive improvements in biophysical Earth system modelling <xref ref-type="bibr" rid="bib1.bibx104 bib1.bibx123" id="paren.28"/> and the concomitantly growing reliance on model-based insights for global decision-making over a wider range of urgent sustainability issues <xref ref-type="bibr" rid="bib1.bibx90 bib1.bibx111 bib1.bibx17" id="paren.29"/>, as is the case, for example, for the Paris climate agreement <xref ref-type="bibr" rid="bib1.bibx129" id="paren.30"/> informed by the IPCC <xref ref-type="bibr" rid="bib1.bibx124 bib1.bibx8 bib1.bibx31" id="paren.31"/> and the policy processes derived from it, these conceptually challenging issues can now have direct practical implications.
As an illustration of such different conceptions of Earth system processes, in models of the contemporary Earth system, land vegetation can be treated as inanimate carbon, a transpiration “pump” affecting precipitation and soil moisture patterns (e.g. <xref ref-type="bibr" rid="bib1.bibx119" id="altparen.32"/>), or as the animate matter of biodiverse ecosystems that sustain human communities (e.g. <xref ref-type="bibr" rid="bib1.bibx102" id="altparen.33"/>). Similarly, different assumptions in models about non-material factors such as human rationality, cognition, motivations, institutions and social connections lead to very different likelihoods for alternative sustainability pathways for the world's economies and material resource use <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx87 bib1.bibx9 bib1.bibx99" id="paren.34"/>.</p>
      <p id="d1e452">For these reasons, we follow a pragmatic approach in proposing a taxonomic framework that draws upon examples and allows for overlap between the domains of nature and human societies, where materiality meets intention (noting that in complex social–ecological systems, purposeful intervention will be accompanied by unintended or unanticipated side effects). Following this approach, modelled subsystems in the biophysical taxon are situated in the material domain of nature, those in the socio-metabolic taxon lie in the overlap domain and those in the socio-cultural taxon reside in the immaterial domain of human cultures (Fig. <xref ref-type="fig" rid="Ch1.F1"/>).</p>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Biophysical taxon</title>
      <p id="d1e464">The biophysical taxon (ENV) contains the processes and subsystems that are typically included in current comprehensive Earth system models, but it views them from the perspective of the Anthropocene shift to human “co-control”. These subsystem models are governed by deterministic and stochastic mathematical equations, often developed from first principles about the physical relationships involved. There is a case for subdividing the biophysical taxon into an ecological sub-taxon (subsystems associated with life) and a geophysical sub-taxon (subsystems not associated with life), as they have distinct, albeit co-evolving, dynamics <xref ref-type="bibr" rid="bib1.bibx135 bib1.bibx70" id="paren.35"/>, and this subdivision would correspond to widely accepted geosphere–biosphere conceptualisations of the Earth system <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx89 bib1.bibx118" id="paren.36"/>. However, we apply our principle of compactness, because geosphere–biosphere links and processes have been comprehensively documented over the past few decades, as they underpin current Earth system and global integrated assessment modelling. Rather than retracing these links (after all, the existing models are not going to be completely reconfigured in light of the issues we explore in this paper), we have opted to take today's state of the art in biophysical global modelling as our main point of departure, following the principle of compatibility introduced above.</p>
      <p id="d1e473">Earth system models have developed from coupled atmosphere–ocean general circulation models, progressively coupling in components describing biogeochemical and biogeophysical dynamics. On the decadal to millennial timescales relevant for the analysis of anthropogenic climate change and its medium-term consequences, examples of these modelled subsystems where human-controlled dynamics are prominent concerns include atmospheric chemistry, ocean productivity, sea ice, land vegetation, and major elemental cycles such as those of nitrogen, phosphorus and sulfur <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx89" id="paren.37"/>. Furthermore, as it becomes clearer that palaeoclimate models can play a vital role in “deep future” studies of human-controlled processes in the Anthropocene, Earth system dynamics operating on longer timescales are relevant <xref ref-type="bibr" rid="bib1.bibx145 bib1.bibx122" id="paren.38"/>. Thus, for these purposes, the biophysical taxon would include subsystems involving the lithosphere (e.g. rock weathering, isostatic depression and<?pagebreak page1120?> rebound associated with the advance and retreat of ice sheets on land) and even external drivers such as large-body impacts <xref ref-type="bibr" rid="bib1.bibx14" id="paren.39"/>, if these provide “natural experiments” or analogues for future change.</p>
      <p id="d1e485">Research fields dealing with models of subsystems belonging to the biophysical taxon include, among others, geophysics, meteorology, oceanography, biology, ecology, biogeochemistry and geology. Few of these sciences have yet grasped the methodological and theoretical tools for dealing with the human dimensions of anthropogenic change.  From our planetary-scale perspective, the ENV taxon exhibits a substantial overlap with categories such as models of “the environment”, “nature” or “ecology”, with their specific disciplinary connotations, although many of these models have tended to be small-scale, context-specific and idiographic. An exception to this is global dynamic vegetation models such as LPJ <xref ref-type="bibr" rid="bib1.bibx119" id="paren.40"/>, which focus on representing the physical dynamics of ecological processes and structures in an Earth system context and not on ecological dynamics as such (i.e. interactions between living organisms). We note a current drive for further refinements of ecological dynamic network processes in large-scale modelling <xref ref-type="bibr" rid="bib1.bibx102 bib1.bibx52" id="paren.41"/> within the ENV taxon that may improve global-scale conceptualisations of ecosystems in ways compatible with both Earth system modelling and socio-ecological systems research and resilience thinking.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Socio-metabolic taxon</title>
      <p id="d1e502">The socio-metabolic taxon contains processes and subsystems that form the material basis and products of societies, making direct interconnections between human societies and the biophysical environment that sustains them. This taxon comprises models of demographics and social structure (e.g. population size, age and sex distribution and health parameters; and social categories with material or resource-use consequences, such as class, clan, caste and ethnicity). It also includes “the technosphere”: society's artefacts, factors of production and technologies (e.g. labour, land, capital, natural resources, raw material and energy; tools, machines and infrastructure; and cultivated landscapes, domesticated animals and plants respectively), and economic systems (manufacturing, distribution and consumption of goods and services) <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx50 bib1.bibx85 bib1.bibx57" id="paren.42"/>.</p>
      <p id="d1e508">The broad field of economics currently dominates descriptions of parts of the socio-metabolic taxon in quantitative models, but many other disciplines such as geography, industrial metabolism, social ecology, and science and technology studies also play a role. In modelling terms, this taxon typically involves representations of both the biophysical planet Earth and the socio-cultural World of human societies. This implies hybrid models of the type that are currently included in integrated assessment models of global change, and it entails strong simplifying assumptions. We suggest that our approach can bring much-needed clarity and transparency about the role of such models in understanding World–Earth systems (see similar arguments in <xref ref-type="bibr" rid="bib1.bibx132" id="altparen.43"/>). One should note that IAMs and economic models are typically expressed in terms of financial value and not material flows that directly interact with subsystems in ENV (with mostly empirical input–output theories of economics being an exception, <xref ref-type="bibr" rid="bib1.bibx73" id="altparen.44"/>).</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Socio-cultural taxon</title>
      <p id="d1e525">The socio-cultural taxon contains processes and subsystems that are described in models of the behaviour of human minds and their immaterial legacies, abstracted from their biophysical foundations and often described as lying in the realm of human agency <xref ref-type="bibr" rid="bib1.bibx99" id="paren.45"/>. Of the three taxa proposed, processes and subsystems in the socio-cultural taxon are the least formalised in mathematical and computer simulation models to date, despite substantial efforts in this direction in many fields of the social sciences (e.g. <xref ref-type="bibr" rid="bib1.bibx32" id="altparen.46"/>) and a likelihood that they may be only partly formalisable. Research fields dealing with models of processes and subsystems in the socio-cultural taxon include sociology, anthropology, behavioural economics, political science and social ecology. Our taxonomic approach can enable the diverse modelling activities now underway to engage more directly with the incipient World–Earth modelling effort.</p>
      <p id="d1e534">Examples of modelled subsystems in this taxon include individual and collective opinions, behaviours, preferences and expectations, and their social network dynamics; information and communication networks; institutions and organisations; financial markets and trade; political processes; and social norms and value systems <xref ref-type="bibr" rid="bib1.bibx85" id="paren.47"/>. Notably, the CUL taxon can also include processes of digital transformation and artificial intelligence that increasingly restructure and shape the socio-cultural sphere of human societies.
It also provides a locus for
debating the challenge of reflexiveness in science, especially in fields where
modelling plays a vital role in shaping knowledge and action <xref ref-type="bibr" rid="bib1.bibx143" id="paren.48"/>. For instance, future World–Earth modelling will have to grapple
with ways to recognise Earth system science as an endogenous generator of
scientific conceptions of “Earth”.
Relevant for modelling efforts, socio-cultural subsystems can vary on substantially different timescales. Near-instantaneous information exchanges are possible on online social networks and within and between increasingly advanced algorithms (e.g. algorithmic trading systems on financial markets), whereas elections and governance processes act on the order of years. Formal institutions (e.g. laws) change on the order of decades and informal institutions (e.g. religions) develop over time frames on the order of centuries to millennia <xref ref-type="bibr" rid="bib1.bibx140 bib1.bibx98" id="paren.49"/>.</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page1121?><sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Relations to other conceptualisations of social–ecological systems</title>
      <p id="d1e555">Our model-centred taxonomy is inspired by previous systemic conceptualisations of human societies embedded in the Earth system, building upon them in a way that may help to bridge across diverse disciplines and theoretic traditions.</p>
      <p id="d1e558">In one of the earliest Earth system conceptualisations, <xref ref-type="bibr" rid="bib1.bibx135" id="text.50"/> distinguishes the inanimate matter of the geosphere, the living biosphere and the noosphere of networked consciousness, the latter reverberating in recent conceptualisations of the technosphere and planetary human–Earth system interactions <xref ref-type="bibr" rid="bib1.bibx57 bib1.bibx71" id="paren.51"/>. Along these lines, <xref ref-type="bibr" rid="bib1.bibx112" id="text.52"><named-content content-type="post">Fig. 34</named-content></xref> introduced the ecosphere (directly corresponding to our ENV taxon, entailing geophysical and ecological interactions), the anthroposphere (broadly related to MET but with some socio-cultural features), and the global subject (closely related to CUL).</p>
      <p id="d1e572">Conceptualisations in resilience theory, ecological economics and sustainability science emphasise the interactions and interdependence of biosphere and society <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx39 bib1.bibx40" id="paren.53"/>, with many sustainability practitioners adding the economy to make “three pillars” or a “pie of sustainability” consisting of economy embedded in society embedded in biosphere <xref ref-type="bibr" rid="bib1.bibx41" id="paren.54"/>. These fields have typically focused on local to regional geographic scales or specific sectors and have not placed much emphasis on global modelling; however, in general terms, their view of society contains aspects of our MET taxon, although “the economy” is more restricted than MET. <xref ref-type="bibr" rid="bib1.bibx58" id="text.55"/> argues that the field of ecological economics would benefit from more attention to the creative processes of “art”, which we would frame as CUL aspects that are largely absent from current conceptualisations in that field and also more broadly (as also argued by <xref ref-type="bibr" rid="bib1.bibx60" id="altparen.56"/>, and <xref ref-type="bibr" rid="bib1.bibx142" id="altparen.57"/>).</p>
      <p id="d1e590"><xref ref-type="bibr" rid="bib1.bibx34" id="text.58"/> explicitly develop the concept of social metabolism, in terms of the set of flows between nature and culture, in order to describe deliberate global sustainability transitions. Governance-centred classification schemes in social–ecological systems research <xref ref-type="bibr" rid="bib1.bibx61 bib1.bibx11" id="paren.59"/>, in the tradition of Ostrom <xref ref-type="bibr" rid="bib1.bibx95" id="paren.60"/>, can also be brought into our taxonomy. Categories of the governance (sub)system link CUL and MET, and the (sub)system to be governed (ENV and MET) links the biophysical resources to be used with the social agents who will use them.</p>
      <p id="d1e602">The taxonomy approach means that things that were previously included in models as opaque and unquestioned systems can be unpacked and critically examined. This would be of particular benefit to model users who were not the model builders. For example, education may be explicitly linked to demography (as in various integrated assessment models), so it would typically be treated as a quantifiable and accumulable process in the MET taxon – i.e. investment in women's education results in a lower birth rate and, therefore, less future land use. In CUL, education would perhaps be treated in a more relational way –  dealing with factors such as the spread of ideas, the development of communities and changes in power structures.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Taxonomy of subsystem interactions in World–Earth systems models</title>
      <p id="d1e614">In this section, we describe a taxonomy of modelled interactions between subsystems that builds upon the taxonomy of subsystems. The three taxonomic classes for World–Earth subsystems give rise to nine taxa for directed interactions connecting these subsystems. Given a pair of taxonomic classes of subsystems <inline-formula><mml:math id="M2" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M3" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula>, the taxonomic class for directed interactions between <inline-formula><mml:math id="M4" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M5" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> is denoted as <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>→</mml:mo><mml:mi>B</mml:mi></mml:mrow></mml:math></inline-formula>. Here, a directed interaction is understood in the sense of a modelled subsystem in <inline-formula><mml:math id="M7" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> exerting a causal influence on another modelled subsystem in <inline-formula><mml:math id="M8" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula>. For example, greenhouse gas emissions produced by an industrial subsystem in MET that exert an influence on the Earth's radiative budget in ENV would belong to the interaction taxon MET <inline-formula><mml:math id="M9" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV. Three of the nine interaction taxa correspond to self-interactions within taxa, whereas six interaction taxa connect distinct subsystem taxa (Fig. <xref ref-type="fig" rid="Ch1.F2"/>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e683">Taxonomic matrix for classifying directed interactions between subsystems in World–Earth systems models. This <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> classification system builds upon the taxonomy of three classes for subsystems introduced in Sect. <xref ref-type="sec" rid="Ch1.S2"/>. The unshaded matrix elements (here containing examples of interactions) correspond to the interaction arrows drawn between the three subsystem taxa shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>. Shaded elements correspond to self-interactions. The examples for directed interaction mechanisms given in the matrix elements are indicative and based on our particular areas of research.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-f02.png"/>

      </fig>

      <p id="d1e708">In the following, we focus on describing examples of such modelled interactions between pairs of subsystems that are potentially relevant for future trajectories of World–Earth systems in the Anthropocene and give examples of published models containing them. The content presented in the subsections necessarily differs in scope and depth reflecting today's dominant modelling priorities, but we have aimed to ensure that the information is comparable. All subsections below provide (i) a general description of the interaction taxa with some examples and (ii) a summary of how these interactions are represented in current models.</p>
      <p id="d1e712">Furthermore, possible extensions of our taxonomic approach to classify feedback loops and more complex interaction networks between subsystems are discussed (Sect. <xref ref-type="sec" rid="Ch1.S3.SS10"/>). We acknowledge that finding a conceptualisation that is satisfactory for all purposes is unlikely, but our particular pragmatic taxonomy can be useful for constructing models of World–Earth systems. It has already proven fruitful in the development of the copan:CORE open World–Earth modelling framework <xref ref-type="bibr" rid="bib1.bibx30" id="paren.61"/> by guiding the choice of process classes and entities that can be described in the framework as well by defining the coupling interfaces of model components that can be integrated using copan:CORE.</p><?xmltex \hack{\newpage}?>
<?pagebreak page1122?><sec id="Ch1.S3.SS1">
  <label>3.1</label><?xmltex \opttitle{ENV $\rightarrow$ ENV: biophysical Earth system self-interactions}?><title>ENV <inline-formula><mml:math id="M11" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV: biophysical Earth system self-interactions</title>
      <p id="d1e736">This taxon encompasses interactions between biophysical subsystems of the type studied in current process-detailed Earth system models such as those in Phase 5 of the Coupled Model Intercomparison Project (CMIP5) model ensemble <xref ref-type="bibr" rid="bib1.bibx126" id="paren.62"/> used in the IPCC reports <xref ref-type="bibr" rid="bib1.bibx124" id="paren.63"/>. For example, this includes modelled geophysical fluxes of energy and momentum between the atmosphere and ocean, interactions between land vegetation, atmospheric dynamics and the hydrological cycle, or, more generally, exchanges of organic compounds between different compartments of biogeochemical cycles (excluding human activities here).</p>
      <p id="d1e745">To date, a detailed representation of these biophysical interactions is largely missing in current first attempts at modelling social–ecological dynamics at the planetary scale (e.g. <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx53" id="altparen.64"/>). However, emerging socio-hydrological <xref ref-type="bibr" rid="bib1.bibx26 bib1.bibx64" id="paren.65"/> and agent-based land-use dynamics models at regional scales <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx111 bib1.bibx106" id="paren.66"/> include some processes involving interactions between biophysical subsystems such as the atmosphere, hydrological cycles and land vegetation.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><?xmltex \opttitle{ENV $\rightarrow$ MET: climate impacts, provisioning and regulating ecosystem services, etc.}?><title>ENV <inline-formula><mml:math id="M12" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET: climate impacts, provisioning and regulating ecosystem services, etc.</title>
      <p id="d1e773">This taxon describes modelled interactions through which biophysical subsystems exert an influence on socio-metabolic subsystems. Relevant examples in the context of global change in the Anthropocene include the impacts of climate change on human societies <xref ref-type="bibr" rid="bib1.bibx8" id="paren.67"/>, such as damage to settlements, production sites, and infrastructure and supply chains <xref ref-type="bibr" rid="bib1.bibx97" id="paren.68"/>; impacts on agriculture or human health; and impacts on provisioning and regulating ecosystem services such as resource flows <xref ref-type="bibr" rid="bib1.bibx83" id="paren.69"/>.</p>
      <p id="d1e785">Some of these interactions such as climate change impacts are now being included in IAMs (a prominent example being the DICE model; <xref ref-type="bibr" rid="bib1.bibx93" id="altparen.70"/>) and stylised models (e.g. Sect. <xref ref-type="sec" rid="Ch1.S4"/> in this paper; <xref ref-type="bibr" rid="bib1.bibx63" id="altparen.71"/>), but challenges remain, for example, in estimating damage functions and the social cost of carbon <xref ref-type="bibr" rid="bib1.bibx94" id="paren.72"/>. Influence from weather and climate on agriculture are studied on a global scale using model chains involving terrestrial vegetation models such as LPJ <xref ref-type="bibr" rid="bib1.bibx119" id="paren.73"/> and agricultural economics models such as MAgPIE <xref ref-type="bibr" rid="bib1.bibx91" id="paren.74"/>. As another example, models of the distribution of vector-born diseases such as malaria are employed to assess the impacts of climate change on human health <xref ref-type="bibr" rid="bib1.bibx19" id="paren.75"/>.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><?xmltex \opttitle{ENV $\rightarrow$ CUL: observation, monitoring, cultural ecosystem services, etc.}?><title>ENV <inline-formula><mml:math id="M13" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL: observation, monitoring, cultural ecosystem services, etc.</title>
      <p id="d1e825">This taxon contains modelled interactions through which the state of the biophysical environment directly influences socio-cultural subsystems. These links can be mediated through the observation, monitoring and assessment of environmental change from local to global scales (e.g. chemical pollution, deforestation or rising greenhouse gas concentrations in the atmosphere) by social actors that, in turn, are processed by public opinion formation and policymaking in socio-cultural subsystems <xref ref-type="bibr" rid="bib1.bibx85" id="paren.76"/>. The links described by the ENV <inline-formula><mml:math id="M14" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL taxon also relate to cultural identity connected to the environment, sense of place <xref ref-type="bibr" rid="bib1.bibx81" id="paren.77"/> and, more generally, what has been described as cultural ecosystem services <xref ref-type="bibr" rid="bib1.bibx83" id="paren.78"/>. For example, <xref ref-type="bibr" rid="bib1.bibx9" id="text.79"/> modelled the effect of changes in extreme events resulting from climate change on the risk perception of individuals. Changes in risk perception may result in changes in emission behaviour given the perceived behaviour of others (social norms) and structural conditions in society, thereby feeding back on future climate change.</p>
      <?pagebreak page1123?><p id="d1e847"><?xmltex \hack{\newpage}?>The ENV <inline-formula><mml:math id="M15" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL taxon also play a role in regional-scale models of poverty traps, where decline in natural capital reduces traditional ecological knowledge as a form of cultural capital <xref ref-type="bibr" rid="bib1.bibx68" id="paren.80"/>, or in models of human perceptions of local scenic beauty in policy contexts <xref ref-type="bibr" rid="bib1.bibx10" id="paren.81"/>. At the moment, most models deal with these interactions only at a sub-global level; however, there is increasing recognition of the need for the more dynamic understanding that formal modelling can provide of such complex psychologically and culturally mediated aspects of human behaviour in the Anthropocene <xref ref-type="bibr" rid="bib1.bibx114" id="paren.82"/>.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><?xmltex \opttitle{MET $\rightarrow$ MET: economic and socio-metabolic self-interactions}?><title>MET <inline-formula><mml:math id="M16" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET: economic and socio-metabolic self-interactions</title>
      <p id="d1e883">This taxon describes modelled interactions between MET subsystems that connect the material manifestations and artefacts of human societies. Examples include the energy system driving factories, supply chains connecting resource extractors to complex networked production sites, or machines constructing infrastructure such as power grids, airports and roads.</p>
      <p id="d1e886">Certain processes involving such interactions (e.g. links between the energy system and other sectors, such as industrial production) are represented in IAMs in an abstracted, macroeconomic fashion. Agent-based models resolving the dynamics of supply chains also exist, and they allow for the impacts of climate shocks on the global economy to be described in much greater detail (e.g. <xref ref-type="bibr" rid="bib1.bibx97" id="altparen.83"/>). Another class of examples are population models that may include factors such as the influence of income on fertility <xref ref-type="bibr" rid="bib1.bibx79" id="paren.84"/>. However, to our best knowledge, process-detailed models of the socio-industrial metabolism <xref ref-type="bibr" rid="bib1.bibx36 bib1.bibx33" id="paren.85"/> or the technosphere <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx50" id="paren.86"/> comparable in complexity to biophysical Earth system models have not been published so far.</p>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><?xmltex \opttitle{MET $\rightarrow$ ENV: greenhouse gas emissions, land-use change and biodiversity loss, impacts on other planetary boundary processes, etc.}?><title>MET <inline-formula><mml:math id="M17" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV: greenhouse gas emissions, land-use change and biodiversity loss, impacts on other planetary boundary processes, etc.</title>
      <p id="d1e918">This taxon encompasses modelled influences exerted by socio-metabolic subsystems on the biophysical environment including various forms of the “colonisation of nature” <xref ref-type="bibr" rid="bib1.bibx35" id="paren.87"/>. Prominent examples in the context of global change and sustainability transformation include human impacts on the environment addressed by the planetary boundaries framework <xref ref-type="bibr" rid="bib1.bibx108 bib1.bibx109 bib1.bibx121" id="paren.88"/> such as anthropogenic emissions of greenhouse gases <xref ref-type="bibr" rid="bib1.bibx124" id="paren.89"/>, nitrogen and phosphorous, other forms of chemical pollution and novel entities (e.g. nanoparticles, genetically engineered organisms), land-use change and induced biodiversity loss, and exploitation and use of natural resources <xref ref-type="bibr" rid="bib1.bibx100" id="paren.90"/>. This taxon also includes various forms of the conversion of energy and entropy fluxes in the biophysical Earth system by human technologies such as harvesting of renewable energy by wind turbines and photovoltaic cells <xref ref-type="bibr" rid="bib1.bibx65" id="paren.91"/> or different approaches to geoengineering <xref ref-type="bibr" rid="bib1.bibx133" id="paren.92"/>.</p>
      <p id="d1e940">The interactions described by the MET <inline-formula><mml:math id="M18" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV taxon are central in IAM and ESM studies of the global environmental impacts of human activities in the Anthropocene such as anthropogenic climate change as driven by greenhouse gas emissions and land-use change <xref ref-type="bibr" rid="bib1.bibx8 bib1.bibx31" id="paren.93"/>. The latter two key processes are also frequently included in emerging studies of planetary social–ecological dynamics using stylised models <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx1 bib1.bibx53 bib1.bibx55 bib1.bibx67 bib1.bibx92" id="paren.94"/>.</p>
</sec>
<sec id="Ch1.S3.SS6">
  <label>3.6</label><?xmltex \opttitle{MET $\rightarrow$ CUL: needs, constraints, etc.}?><title>MET <inline-formula><mml:math id="M19" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL: needs, constraints, etc.</title>
      <p id="d1e972">This taxon describes modelled influences and constraints imposed upon socio-cultural dynamics by the material basis of human societies (socio-metabolic subsystems). These include, for example, the effects, needs and constraints induced by the biophysical “hardware” that runs socio-cultural processes: infrastructure, machines, computers, human bodies and brains, and the associated availability of energy and other resources. It also includes the effects of technological evolution, revenues generated from economic activity, supply of valued goods (e.g. on opinion formation and behavioural change in the socio-cultural domain), or the consequences of change in demographic distribution of pressure groups on political systems and institutions.</p>
      <p id="d1e975">As a recent example, the <xref ref-type="bibr" rid="bib1.bibx9" id="text.95"/> model mentioned above (Sect. <xref ref-type="sec" rid="Ch1.S3.SS3"/>) has one parameter to reflect structural constraints in society that affects the degree to which emission behaviour can be changed. MET <inline-formula><mml:math id="M20" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL links also appear in models of resource use in social–ecological systems, where social learning of harvesting effort depends on the harvest rate <xref ref-type="bibr" rid="bib1.bibx139 bib1.bibx4 bib1.bibx46" id="paren.96"/> and fish catches influence perceptions about the state of the fishery <xref ref-type="bibr" rid="bib1.bibx80 bib1.bibx66" id="paren.97"/>, or in models of economic impacts on individual voting behaviour <xref ref-type="bibr" rid="bib1.bibx75" id="paren.98"/>.</p>
</sec>
<sec id="Ch1.S3.SS7">
  <label>3.7</label><?xmltex \opttitle{CUL $\rightarrow$ CUL: socio-cultural self-interactions}?><title>CUL <inline-formula><mml:math id="M21" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL: socio-cultural self-interactions</title>
      <?pagebreak page1124?><p id="d1e1016">This taxon contains modelled self-interactions between subsystems in the socio-cultural domain that have been described as parts of the noosphere <xref ref-type="bibr" rid="bib1.bibx135" id="paren.99"/>, the global subject <xref ref-type="bibr" rid="bib1.bibx112" id="paren.100"/> or the mental component of the Earth system <xref ref-type="bibr" rid="bib1.bibx78" id="paren.101"/>. Examples include the interaction of processes of opinion dynamics and preference formation on social networks, governance systems and underlying value systems <xref ref-type="bibr" rid="bib1.bibx47" id="paren.102"/> as well as interactions between different institutional layers such as governance systems, formal and informal institutions <xref ref-type="bibr" rid="bib1.bibx140 bib1.bibx98" id="paren.103"/>.</p>
      <p id="d1e1034">Some of these processes related to human behaviour and decision-making <xref ref-type="bibr" rid="bib1.bibx87" id="paren.104"/> have already been studied in models of social–ecological systems on local and regional scales <xref ref-type="bibr" rid="bib1.bibx115 bib1.bibx116" id="paren.105"/> and have been modelled in various fields ranging from social simulation to the physics of social dynamics <xref ref-type="bibr" rid="bib1.bibx20" id="paren.106"/>. However, thus far, they are largely not included in IAMs of global change or stylised models of planetary social–ecological systems <xref ref-type="bibr" rid="bib1.bibx134 bib1.bibx28 bib1.bibx29" id="paren.107"/>.</p>
</sec>
<sec id="Ch1.S3.SS8">
  <label>3.8</label><?xmltex \opttitle{CUL $\rightarrow$ ENV: environmental governance, nature conservation areas, social taboos, sacred places etc.}?><title>CUL <inline-formula><mml:math id="M22" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV: environmental governance, nature conservation areas, social taboos, sacred places etc.</title>
      <p id="d1e1065">This taxon encompasses modelled influences that socio-cultural subsystems exert on the biophysical environment. An example of such a class of interactions is environmental governance realised through formal institutions <xref ref-type="bibr" rid="bib1.bibx96 bib1.bibx40" id="paren.108"/>, for instance, where the designation of a piece of land as a nature protection area excludes certain forms of land use which have a direct impact on environmental processes there. Similarly, nature protection areas for biodiversity conservation have been represented in marine reserve models <xref ref-type="bibr" rid="bib1.bibx43" id="paren.109"/>. Another related example of CUL <inline-formula><mml:math id="M23" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV links are nature-related values and informal institutions such as respecting sacred places in the landscape and following social taboos regarding resource use <xref ref-type="bibr" rid="bib1.bibx22" id="paren.110"/>. Different forms of environmental governance have been modelled via so-called decision or sustainability paradigms <xref ref-type="bibr" rid="bib1.bibx112 bib1.bibx5 bib1.bibx56" id="paren.111"/>.</p>
      <p id="d1e1087">Direct CUL <inline-formula><mml:math id="M24" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV links arguably cannot be found in the real world, in that socio-cultural influences on environmental processes must be mediated by their physical manifestations in the socio-metabolic domain (e.g. in the case of nature protection areas through the constrained actions of resource users, government enforcement efforts and infrastructure such as fences). However, such direct CUL <inline-formula><mml:math id="M25" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV links may be implemented in models, even on the global scale, such as in trade-off assessments of multiple land uses (e.g. <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx101" id="altparen.112"/>).</p>
</sec>
<sec id="Ch1.S3.SS9">
  <label>3.9</label><?xmltex \opttitle{CUL $\rightarrow$ MET: socio-economic policies and governance choices, value-driven consumption, etc.}?><title>CUL <inline-formula><mml:math id="M26" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET: socio-economic policies and governance choices, value-driven consumption, etc.</title>
      <p id="d1e1123">Finally, this taxon contains modelled links pointing from socio-cultural to socio-metabolic subsystems. Examples include socio-economic policies and governance choices such as taxes, regulations or caps that influence the economy (e.g. carbon caps or taxes in the climate change mitigation context) or demographics (e.g. family planning and immigration policies) as well as the physical manifestations of financial market dynamics such as real estate bubbles. CUL <inline-formula><mml:math id="M27" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET interactions also encompass the influence of cultural values, norms and lifestyles on economic demand and consumption as well as consequent changes in industrial production, building, transportation and other sectors.</p>
      <p id="d1e1133">Policy measures such as taxes, regulations or caps are much studied by IAMs of anthropogenic climate change <xref ref-type="bibr" rid="bib1.bibx31" id="paren.113"/>, whereas the influences of value and norm change on economic activities, such as general resource use <xref ref-type="bibr" rid="bib1.bibx139 bib1.bibx4 bib1.bibx46" id="paren.114"/> and fishing <xref ref-type="bibr" rid="bib1.bibx80 bib1.bibx66" id="paren.115"/>, have been studied in the social–ecological modelling literature – but at a mostly local to regional level.</p>
</sec>
<sec id="Ch1.S3.SS10">
  <label>3.10</label><title>Higher-order taxonomies of feedback loops and more complex interaction networks</title>
      <p id="d1e1153">Beyond the taxonomy of interactions introduced above, higher-order taxonomies could also be derived. For example, a taxonomy of feedback loops can be derived from the <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> taxonomy of links, leading to six taxa for feedback loops of length two in models of World–Earth systems: given a pair of interaction taxa <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>→</mml:mo><mml:mi>B</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:math></inline-formula>, the resulting taxon for loops between <inline-formula><mml:math id="M31" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M32" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> may be denoted as <inline-formula><mml:math id="M33" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> <?xmltex \igopts{height=8.535827pt}?><inline-graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-g01.png"/> <inline-formula><mml:math id="M34" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula>. Many such feedback loops relevant for sustainability are not or only rigidly treated in current ESMs and IAMs. For example, the ENV <?xmltex \igopts{height=8.535827pt}?><inline-graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-g01.png"/> MET feedback loop is typically not sufficiently represented in IPCC-style analyses, because the impacts of climate change on human societies are not explicitly modelled or ill-constrained in IAMs (Sect. <xref ref-type="sec" rid="Ch1.S3.SS5"/>). Furthermore, feedback loops of the type CUL <?xmltex \igopts{height=8.535827pt}?><inline-graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-g01.png"/> <inline-formula><mml:math id="M35" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>, where <inline-formula><mml:math id="M36" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> may be subsystems from ENV, MET or CUL are mostly missing altogether, in large part because CUL is not represented (or is only fragmentarily included) in current ESMs and IAMs.</p>
      <p id="d1e1253">Longer and more complex paths and subgraphs of causal interactions between subsystems could be classified by further higher-order taxonomies (e.g. inspired by the study of motifs, small subgraphs, in complex network theory; <xref ref-type="bibr" rid="bib1.bibx84" id="altparen.116"/>). This approach quickly leads to a combinatorial explosion – for example, for three-loops of the type <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>→</mml:mo><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>C</mml:mi><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:math></inline-formula> involving three modelled subsystems <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math></inline-formula> and their interactions, enumeration and counting of all possible combinations shows that there are already 11 distinct taxa for feedback loops of this kind. However, there are systematic methods available for classifying and clustering causal loop diagrams that could be leveraged to bring order into more complex models of World–Earth systems <xref ref-type="bibr" rid="bib1.bibx130 bib1.bibx107" id="paren.117"/>. Overall, such higher-order taxonomies could help in the design of models or model suites that can deal with different aspects of (non-linear) interactions between World–Earth subsystems and serve as tools for understanding the emergent co-evolutionary macrodynamics.</p>
</sec>
</sec>
<?pagebreak page1125?><sec id="Ch1.S4">
  <label>4</label><title>An exemplary model showing complex co-evolutionary dynamics in a World–Earth system</title>
      <p id="d1e1307">At present, to our best knowledge, process-detailed World–Earth models that are comprehensive in the sense of the proposed taxonomies are not available. Therefore, in this section, we give an illustrative example of a stylised World–Earth system model that covers all classes of real-world processes that appear relevant in major global feedbacks.  Even such a very simple World–Earth system model can contain a social–ecological feedback loop involving the subsystem interactions introduced above (Sect. <xref ref-type="sec" rid="Ch1.S3"/>) and leading to a biophysical Earth system dynamics that depends crucially on a social–cultural evolution and vice versa. We also demonstrate how the taxonomies described above can be applied to classify model components and reveal the interaction structures that are implicit in the model equations. The companion paper of this article applies the taxonomies to develop a more complex illustrative World–Earth model using the copan:CORE framework <xref ref-type="bibr" rid="bib1.bibx30" id="paren.118"/>.</p>
      <p id="d1e1315">The example model studied here, copan:DISCOUNT, describes a world where climate change drives a change in countries' value systems,
represented here just by the long-term discount factors their governments use in policymaking,
which can be interpreted as their relative interest in future welfare as opposed to current welfare.
These discount factors drive countries' emissions and, in turn, drive climate change, represented by a global atmospheric carbon stock.
While the detailed description of the model's assumptions below will make it clear that this causal loop involves eight of the nine interaction taxa shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>, the model is so designed that the description of the resulting dynamics from all of these interactions can be reduced to just two ordinary differential equations: one for the fraction of “patient” countries and one for atmospheric carbon stock.  The novelty of this model is that it endogenises the socially transmitted choice of discount rates in a greenhouse gas emissions game to illustrate the effects of social–ecological feedback loops that are currently typically not considered in current climate economics and IAM modelling efforts.</p>
      <p id="d1e1320">The aim of this particular model design is to show clearly that while the taxonomy developed in this paper aims at being helpful in designing and analysing World–Earth models, this does not mean the different taxa need always be easily identifiable from the final model equations.</p>
      <p id="d1e1323">Before relating its ingredients to the introduced taxa,
let us describe the model without referring to that classification.
In our model,
we assume that each country's metabolic activities are guided by a trade-off between
the undesired future impacts of climate change caused by global carbon emissions
and the present costs of avoiding these emissions domestically.
Similar to the literature on international environmental agreements and integrated assessment modelling,
this tradeoff is modelled as a non-cooperative game between countries applying cost-benefit optimisation.
The tradeoff and, hence, the evolution of the carbon stock is strongly influenced by the discount factor <inline-formula><mml:math id="M39" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>
that measures the relative importance a country assigns to future welfare as compared to present welfare.
The higher the <inline-formula><mml:math id="M40" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>, the more a country cares about the future and
the more they will reduce their emissions in order to avoid future climate impacts.
While the economic literature treats <inline-formula><mml:math id="M41" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> as an exogenous parameter that has to be chosen by society (e.g. <xref ref-type="bibr" rid="bib1.bibx3" id="altparen.119"/>),
our model treats <inline-formula><mml:math id="M42" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> as a social trait that changes in individual countries over time
because countries observe each other's welfare and value of <inline-formula><mml:math id="M43" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>
and may learn what a useful <inline-formula><mml:math id="M44" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> is by imitating successful countries and adopting their value of <inline-formula><mml:math id="M45" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>.
Because of the existence of climatic tipping points,
this social dynamics does not only influence the state of the climate system but is in turn strongly influenced by it.
Depending on whether the system is far from or close to tipping points,
the trade-off between emissions reduction costs and additional climate damages can turn out quite differently,
and different values of <inline-formula><mml:math id="M46" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> will be successful.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e1389">Planetary social–ecological processes and interactions represented in the copan:DISCOUNT model displayed in matrix form following Fig. <xref ref-type="fig" rid="Ch1.F2"/>. The co-evolutionary cycle of dynamic interdependencies implemented in the model is indicated by the grey arrow.</p></caption>
        <?xmltex \igopts{height=241.848425pt}?><graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-f03.png"/>

      </fig>

      <p id="d1e1400">Let us now present and decompose the model's basic causal loop in terms of the taxonomy introduced above, as shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>,
starting in the central box.
The countries' metabolisms (MET) combust carbon (MET <inline-formula><mml:math id="M47" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET),
leading to emissions (MET <inline-formula><mml:math id="M48" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV) that increase the global atmospheric carbon stock <inline-formula><mml:math id="M49" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> (ENV),
part of which is then taken up by other carbon reservoirs (ENV <inline-formula><mml:math id="M50" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV).
<inline-formula><mml:math id="M51" display="inline"><mml:mi>C<?pagebreak page1126?></mml:mi></mml:math></inline-formula> increases global mean temperature, leading to climate change (ENV <inline-formula><mml:math id="M52" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV)
and, thus, to future climate impacts
(i) on the countries' metabolisms (ENV <inline-formula><mml:math id="M53" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET)
and (ii) on aspects of the environment people care about, such as biodiversity (ENV <inline-formula><mml:math id="M54" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV <inline-formula><mml:math id="M55" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL).
Countries evaluate these expected damages (MET <inline-formula><mml:math id="M56" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL; ENV <inline-formula><mml:math id="M57" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL)
and the costs of avoiding emissions (MET <inline-formula><mml:math id="M58" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL);
use their respective discount factors (CUL),
which they learn by imitation (CUL <inline-formula><mml:math id="M59" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL),
to assess possible domestic emissions constraints; and
then reach a strategic equilibrium with other countries (CUL <inline-formula><mml:math id="M60" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL)
and implement the chosen emissions constraints (CUL <inline-formula><mml:math id="M61" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET),
thereby closing the long loop.</p>
      <p id="d1e1512">In the statistical limit of this model for a large number of countries, derived in detail in the Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>,
this complex feedback dynamics is nicely reduced to just two equations:

              <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M62" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E1"><mml:mtd><mml:mtext>1</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>c</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mover accent="true"><mml:mi>F</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>[</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          where <inline-formula><mml:math id="M63" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> is excess atmospheric carbon stock, <inline-formula><mml:math id="M64" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> is the fraction of “patient” countries (those that apply a large value of <inline-formula><mml:math id="M65" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>),
<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a damage factor,
<inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a certain linear transformation of <inline-formula><mml:math id="M68" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>,
<inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the utility difference between a country using discount factor <inline-formula><mml:math id="M70" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and a country using <inline-formula><mml:math id="M71" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>,
and <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a resulting imitation probability. These parameters are
all derived in detail in the Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>.
Some of the various terms in these formulas can be classified clearly as belonging to one taxon, for example
business-as-usual emissions <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> belong to MET <inline-formula><mml:math id="M74" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV,
carbon uptake <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:math></inline-formula> belongs to ENV <inline-formula><mml:math id="M76" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV and
the imitation probability <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> belongs to CUL <inline-formula><mml:math id="M78" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL,
but others cannot, for example certain terms
occurring in the formula for <inline-formula><mml:math id="M79" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> combine climate damages <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (ENV <inline-formula><mml:math id="M81" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET <inline-formula><mml:math id="M82" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL) with countries' values systems, represented by <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (CUL).
The dynamics are
governed by about a dozen parameters controlling the relative speeds and intensities of subprocesses,
costs and benefits of emissions reductions, and details of the learning-by-imitation process,
as described in Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e1868">Typical dynamics of the copan:DISCOUNT model of the co-evolution of
the global atmospheric carbon stock <inline-formula><mml:math id="M84" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>
and the time preferences of countries,
represented by the fraction <inline-formula><mml:math id="M85" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> of patient countries.
Of five simulated stochastic trajectories (<bold>a</bold> and <bold>c</bold>, green lines)
starting at the same initial state (green dot),
some will converge fast to the more desirable stable steady state at <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
where climate damages <bold>(b)</bold> are still relatively low,
while other trajectories will approach the less desirable focus point (spiralling steady state) at <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">2.8</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.35</mml:mn></mml:mrow></mml:math></inline-formula>,
where climate damages are relatively high.
Depending on whether countries adjust their time preferences slowly <bold>(a)</bold> or fast <bold>(c)</bold>,
the focus point is
either a stable attractor catching most trajectories that come near it <bold>(a)</bold>
or an unstable repeller which many trajectories have to compass to approach the desirable state
after a long transient detour of high damages <bold>(c)</bold>.
Blue lines show the average development represented by two ordinary differential equations (see Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/> for details),
red lines are the corresponding nullclines (thin: <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>F</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>; thick: <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>),
and their other intersection at <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula> is a saddle point.
The parameters used are as follows: <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.45</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> <bold>(a)</bold> or <inline-formula><mml:math id="M98" display="inline"><mml:mn mathvariant="normal">1.3</mml:mn></mml:math></inline-formula> <bold>(c)</bold>, <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.1</mml:mn></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://esd.copernicus.org/articles/12/1115/2021/esd-12-1115-2021-f04.png"/>

      </fig>

      <?pagebreak page1127?><p id="d1e2196">Let us analyse a typical dynamics of the model, shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/>,
and relate it again to our taxonomy of subsystem interactions.
Consider the middle green trajectories in Fig. 4c
starting at a low atmospheric carbon stock of <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (fictitious units)
and a medium fraction of patient countries of <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> (green dot).
At this point, both patient and impatient countries evaluate the state of the world very similarly; therefore, not much imitation of discount factors occurs (weak CUL <inline-formula><mml:math id="M110" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL dynamics) and
<inline-formula><mml:math id="M111" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> may fluctuate somewhat but is not expected to change much.
At the same time, as the climate damage curve (Fig. 4b) is still relatively flat,
global emissions are higher than the natural uptake rate (strong MET <inline-formula><mml:math id="M112" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV influence),
and <inline-formula><mml:math id="M113" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> is likely to increase to about 1.7 without <inline-formula><mml:math id="M114" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> changing much.
During this initial pollution phase, climate damages increase (the ENV <inline-formula><mml:math id="M115" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET/CUL links becomes stronger)
and the slope of the damage curve increases as more climatic tipping points are neared or crossed.
This decreases the patient countries' evaluations faster than the impatient countries';
hence, patience becomes less attractive and countries fatalistically decrease their discount factor,
so that <inline-formula><mml:math id="M116" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> declines to almost or even exactly zero (the CUL <inline-formula><mml:math id="M117" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL dynamics initially become stronger and then weaker again)
while <inline-formula><mml:math id="M118" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> grows to about 3.0.
In that region, most tipping points are crossed and the damage curve flattens again,
causing the opposite effect (i.e. making patience more attractive).
If the idea of patience has not “died-out” at that point (i.e. <inline-formula><mml:math id="M119" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> is still <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>),
discount factors now swing to the other extreme with <inline-formula><mml:math id="M121" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> approaching unity (CUL <inline-formula><mml:math id="M122" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL dynamics becoming temporarily very strong),
shown by one green trajectory,
while emissions are first almost in equilibrium with natural carbon uptake at about <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3.2</mml:mn></mml:mrow></mml:math></inline-formula> (weak MET <inline-formula><mml:math id="M124" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV effect)
and then decline ever faster once the vast majority of countries become patient (stronger MET <inline-formula><mml:math id="M125" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV).
This trajectory finally converges to the stable steady state at a low carbon stock of about <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>.
Note that there is also some small probability that this point is reached much faster without the long detour
if the stochastic social dynamics at the starting point give patience a random advantage,
as on two of the plotted trajectories.</p>
      <p id="d1e2373">As is typical in models with various interactions, changes in their relative interaction rates can cause highly non-linear and even qualitative changes in model behaviour.
A comparison of Fig. <xref ref-type="fig" rid="Ch1.F4"/>a and c (also see the caption of Fig. 4) shows that this is particularly true for World–Earth models when the rates of socio-cultural processes of the CUL <inline-formula><mml:math id="M128" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL type are changed (as can be claimed is indeed happening in reality since the middle of the 20th century). It should be emphasised again that these socio-cultural processes are specifically those that are least or not at all represented in current models of global change, pointing to the necessity and expected progress in understanding when including them in more comprehensive World–Earth models.</p>
      <p id="d1e2385">Overall, the copan:DISCOUNT model provides a first test of the taxonomy's guiding principles. It demonstrates the taxonomy's operative capacity to trace links between established dynamical systems methodology and macro-behaviour; it is compatible with diverse research fields, here linking, among others, carbon cycles and social learning; and it has appropriate compactness, as tracing the loops and flows between taxa in this World–Earth model does not require us to rethink the whole structure of the taxonomy.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e2397">In this article, we have presented a taxonomy of processes and co-evolutionary interactions in models of World–Earth systems (i.e. planetary-scale social–ecological systems). For reasons of compactness and compatibility with existing research fields and methodologies, we have proposed three taxa for modelled subsystems and have also described a classification of modelled interactions between subsystems into nine taxa. We have illustrated the clarity that this taxonomic framework confers, using a stylised model of social–ecological co-evolutionary dynamics on a planetary scale that includes explicitly socio-cultural processes and feedbacks.</p>
      <p id="d1e2400">We argue that a relatively simple taxonomy is important for stimulating the discourse on conceptualisations of World–Earth systems. It can help with operational model development as is illustrated by the work reported in the companion paper <xref ref-type="bibr" rid="bib1.bibx30" id="paren.120"/>. The proposed taxonomy can also help in interdisciplinary communication, model critique and potentially even participatory modelling processes by providing an organisational scheme and a shared vocabulary to refer to the different components that need to be brought together. However, we acknowledge that alternative, more detailed taxonomies can be beneficial in more specialised settings (e.g. ecological processes are now subsumed in the biophysical taxon), but it may be useful to distinguish them from the geophysical for a clearer understanding of interactions with the socio-metabolic taxon. In other contexts, it may be useful to establish a socio-epistemic taxon separate from the socio-cultural taxon for describing subsystems, processes and interactions involving processes such as symbolic representations and transformations of knowledge through science and technology <xref ref-type="bibr" rid="bib1.bibx105" id="paren.121"/>. Along these lines, our framework may be helpful as a blueprint for constructing such alternative, possibly more detailed taxonomies.</p>
      <p id="d1e2409">Throughout the paper, we have illustrated the taxonomic framework using examples of subsystems, processes and interactions that are already represented in mathematical and computer simulation models in various disciplines. We have not attempted to provide a comprehensive classification of all such modelling components that would be relevant for capturing future trajectories of World–Earth systems in the Anthropocene. We have also not addressed dynamics beyond the reach of current modelling capabilities, such as long-term evolutionary processes acting within the biophysical taxon or broad patterns and singularities in the dynamics of technology, science, art and history <xref ref-type="bibr" rid="bib1.bibx128" id="paren.122"/>. However, we have shown the merits of epistemological pluralism, to enable productive dialogue and interaction between the diversity of World modelling approaches and the biophysical Earth representations that exist and that have agency in a Latourian sense (e.g. through the IPCC processes).</p>
      <p id="d1e2415">Applying the proposed taxonomy reveals relevant directions in the future development of models of global change to appropriately represent the dynamics of up to planetary-scale social–ecological systems in the Anthropocene. Regarding the sticky problem of representing causality in such a complex system, every possible contributory model is a Pandora's box out of which theoretical controversies and cross-disciplinary battles emerge. The taxonomy outlined here at least partly illuminates what is in this box, making it easier<?pagebreak page1128?> to have more open discussions among modellers about their theories and hypotheses about causality.</p>
      <p id="d1e2419">While current Earth system models focus exclusively on representing biophysical subsystems and their interactions and integrated assessment models capitalise on those in the socio-metabolic taxon, socio-cultural subsystems and processes such as the dynamics of opinions and social networks, behaviours, values and institutions as well as their feedbacks to biophysical and socio-metabolic subsystems remain largely uncovered in planetary-scale models of global change. Integrating these decisive dynamics in World–Earth Models is a challenging but highly promising research endeavour <xref ref-type="bibr" rid="bib1.bibx112 bib1.bibx113 bib1.bibx123" id="paren.123"/> that is comparable to the development of biophysical Earth system science and models in the past decades following the foundational blueprints of the Bretherton reports (<xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx89" id="altparen.124"/>). We use the copan:DISCOUNT model to demonstrate the value of the taxonomy for tracing how dynamics and feedbacks loop through different taxa, enabling better model design and communication about path-breaking approaches to World–Earth modelling.
Following this track will help to develop models that go beyond a climate-driven view of global change and to bridge the “divide” that keeps being spotlighted as the problematic hyphen in prevalent social–ecological and human-nature system concepts, among others. It will also contribute to a deeper understanding of the functioning of complex World–Earth systems machinery in the Anthropocene. By supporting the development and discussion of new family of models and not pushing for a rigid and universalising model of everything, applying the taxonomy promises to yield important insights into well-designed policy interventions to foster global sustainability transformation, build World–Earth resilience and avoid social–ecological collapse.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<?pagebreak page1129?><app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>The copan:DISCOUNT model</title>
      <p id="d1e2440">The illustrative model copan:DISCOUNT simulates the co-evolution of <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
the excess global atmospheric carbon stock above an equilibrium value that would be attained for zero greenhouse gas emissions,
and the fraction <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>∈</mml:mo><mml:mo>[</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> of the world's countries that care strongly about their future welfare.
While <inline-formula><mml:math id="M131" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> represents the macroscopic state of nature,
<inline-formula><mml:math id="M132" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> represents the macroscopic state of the global human society.</p>
      <p id="d1e2491">As the derivation of the model below will show,
the time evolution of <inline-formula><mml:math id="M133" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M134" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> is eventually given by Eqs. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) and (<xref ref-type="disp-formula" rid="Ch1.E2"/>).
Their governing parameters are
business-as-usual emissions <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
an abatement cost factor <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
a carbon uptake rate <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
a learning rate <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
a damage coefficient <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
a mean tipping point location <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and spread <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> ,
two candidate discount rates <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
an economic growth factor <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
the total number of countries <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
a curiosity parameter <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
and
a myopic rationality parameter <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mi>q</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
The equations are derived by combining
a standard emissions game model from the literature on international environmental agreements <xref ref-type="bibr" rid="bib1.bibx7" id="paren.125"/>
with a social imitation dynamics that governs the evolution of the countries' time-discounting factors
as follows.</p>
<sec id="App1.Ch1.S1.SS1">
  <label>A1</label><title>Countries' welfare</title>
      <p id="d1e2688">At each point in continuous time, <inline-formula><mml:math id="M147" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>,
a number of <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> similar countries, <inline-formula><mml:math id="M149" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>,
choose their individual abatement levels (carbon equivalents per time), <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
Global abatement and carbon emissions per time (an interaction of type MET <inline-formula><mml:math id="M151" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV) are then
            <disp-formula id="App1.Ch1.S1.E3" content-type="numbered"><label>A1</label><mml:math id="M152" display="block"><mml:mrow><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> are global business-as-usual emissions.</p>
      <p id="d1e2836">Country <inline-formula><mml:math id="M154" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> chooses <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> rationally but myopically,
only taking its own welfare in the present and in “the future” (after a fixed time interval of, say, 50 years)  into account.
Its present welfare, <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, is given by some business-as-usual welfare, normalised to unity,
minus the costs of emissions reductions (MET <inline-formula><mml:math id="M157" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL),
which are a quadratic function of <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as usual in stylised models of international environmental agreements <xref ref-type="bibr" rid="bib1.bibx7" id="paren.126"/>,
            <disp-formula id="App1.Ch1.S1.E4" content-type="numbered"><label>A2</label><mml:math id="M159" display="block"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>c</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> is a cost parameter
that is normalised with <inline-formula><mml:math id="M161" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> to make the Nash equilibrium outcome (see below) independent of <inline-formula><mml:math id="M162" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula>.</p>
      <p id="d1e2993">Country <inline-formula><mml:math id="M163" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>'s future welfare (belonging to MET), <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, is
a higher business-as-usual welfare given by a growth parameter <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
minus the value of additional damages from climate change caused by the present emissions,
which are a linear function of <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:
            <disp-formula id="App1.Ch1.S1.E5" content-type="numbered"><label>A3</label><mml:math id="M167" display="block"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo>-</mml:mo><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> is a damage factor that depends on the current carbon stock (see below).
Note that while these additional damages <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are caused by the present emissions,
total damages will still be a non-linear function of stock <inline-formula><mml:math id="M170" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>
as the factor <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> changes with <inline-formula><mml:math id="M172" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>,
representing the presence of tipping points (see below).</p>
</sec>
<sec id="App1.Ch1.S1.SS2">
  <label>A2</label><title>Discounting emissions</title>
      <p id="d1e3181">As <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> increases in <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> while <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> decreases,
choosing an optimal value for <inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> involves a trade-off between present and future welfare,
which we assume is done in the usual way by using some current discount factor <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (an element of taxon CUL)
that measures the relative weight of future welfare in country <inline-formula><mml:math id="M178" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>'s optimisation target (“utility”) at time <inline-formula><mml:math id="M179" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>,
<inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:
            <disp-formula id="App1.Ch1.S1.E6" content-type="numbered"><label>A4</label><mml:math id="M181" display="block"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msubsup><mml:mi>W</mml:mi><mml:mi>i</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msubsup><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          For simplicity, we assume that only two different discount factors are possible,
<inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>,
and call a country with <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:math></inline-formula> “patient”,
so that the state of global society at time <inline-formula><mml:math id="M184" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> can be summarised by the fraction <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of patient countries:
            <disp-formula id="App1.Ch1.S1.E7" content-type="numbered"><label>A5</label><mml:math id="M186" display="block"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>|</mml:mo><mml:mo mathvariant="italic">{</mml:mo><mml:mi>i</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo mathvariant="italic">}</mml:mo><mml:mo>|</mml:mo><mml:mo>/</mml:mo><mml:mi>N</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <?pagebreak page1130?><p id="d1e3482">Given carbon stock <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (ENV) and discount factors <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
the countries thus face a simultaneous multi-agent multi-objective optimisation problem, with
each <inline-formula><mml:math id="M189" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> trying to optimise their utility
            <disp-formula id="App1.Ch1.S1.E8" content-type="numbered"><label>A6</label><mml:math id="M190" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mo mathsize="1.1em">(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo mathsize="1.1em">)</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>c</mml:mi><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo mathsize="1.5em">(</mml:mo><mml:mi>G</mml:mi><mml:mo>-</mml:mo><mml:mi>s</mml:mi><mml:mo mathsize="1.1em">(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo mathsize="1.1em">)</mml:mo><mml:mo mathsize="1.5em">)</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          by choosing <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
As in the literature on international environmental agreements (e.g. <xref ref-type="bibr" rid="bib1.bibx7" id="altparen.127"/>),
we assume this is solved by making the choices independently and non-cooperatively,
i.e. using <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> for all <inline-formula><mml:math id="M193" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> simultaneously,
leading to a system of <inline-formula><mml:math id="M194" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> equations whose solutions <inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> form the Nash equilibrium choices (CUL <inline-formula><mml:math id="M196" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL),

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M197" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S1.E9"><mml:mtd><mml:mtext>A7</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>c</mml:mi><mml:mi>N</mml:mi></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S1.E10"><mml:mtd><mml:mtext>A8</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.0}{9.0}\selectfont$\displaystyle}?><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>c</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            and the aggregate abatement (CUL <inline-formula><mml:math id="M198" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET) and emissions
            <disp-formula id="App1.Ch1.S1.E11" content-type="numbered"><label>A9</label><mml:math id="M199" display="block"><mml:mrow><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>c</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where
            <disp-formula id="App1.Ch1.S1.E12" content-type="numbered"><label>A10</label><mml:math id="M200" display="block"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">β</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="App1.Ch1.S1.SS3">
  <label>A3</label><title>Evolution of discount factors</title>
      <p id="d1e4198">While economic models treat the discount factor of a country as an exogenous parameter,
we assume that the value of <inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a social trait that may be changed over time
due to the observation of other countries' discount factors and their resulting utility (CUL <inline-formula><mml:math id="M202" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL).
As in many models of the spread of social traits (e.g. <xref ref-type="bibr" rid="bib1.bibx127 bib1.bibx139" id="altparen.128"/>),
we assume that each country <inline-formula><mml:math id="M203" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> may adopt another country <inline-formula><mml:math id="M204" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula>'s value of <inline-formula><mml:math id="M205" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula>
(social learning by imitation)
and that the probability <inline-formula><mml:math id="M206" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> for doing so depends on the difference between <inline-formula><mml:math id="M207" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M208" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula>'s current utility,
<inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
in a non-linear, sigmoid-shaped fashion,
with
<inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo><mml:mo>→</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo><mml:mo>→</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M213" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:math></inline-formula>.
The utility difference between a country using <inline-formula><mml:math id="M214" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and a country using <inline-formula><mml:math id="M215" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> is
            <disp-formula id="App1.Ch1.S1.E13" content-type="numbered"><label>A11</label><mml:math id="M216" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>]</mml:mo><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mo>-</mml:mo><mml:mfenced open="[" close="]"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
          This difference is zero if the discounting summary statistics <inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> equals
            <disp-formula id="App1.Ch1.S1.E14" content-type="numbered"><label>A12</label><mml:math id="M218" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>F</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>:=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msup><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>N</mml:mi><mml:mo>[</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>G</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          As <inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>&gt;</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:math></inline-formula>, we have <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> if <inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>F</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
meaning that, depending on the stock and the fraction of patient countries,
either patience or impatience might be more attractive; thus,
one can expect interesting learning dynamics.</p>
      <p id="d1e4789">We assume that at each point in time, each country <inline-formula><mml:math id="M222" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> independently has a probability rate <inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>
to perform a “learning step”.
If <inline-formula><mml:math id="M224" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> does perform a learning step at time <inline-formula><mml:math id="M225" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>,
it compares its current utility <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> with that of a randomly drawn country <inline-formula><mml:math id="M227" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula>
and sets its discount factor <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to the value of <inline-formula><mml:math id="M229" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
with a probability given by the generalised logistic function:
            <disp-formula id="App1.Ch1.S1.E15" content-type="numbered"><label>A13</label><mml:math id="M230" display="block"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>exp⁡</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:mi>q</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> are parameters so that <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msup><mml:mi>P</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e5058">The “curiosity” parameter <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> can be interpreted as a measure of a country's curiosity-driven exploration of a different discount factor without expecting a welfare increase. The larger the <inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the more frequently switches will occur; however, these switches will occur in both directions between the two candidate discount rates, mainly generating more variance and fluctuations that can be seen as a form of “noise”.
The “myopic rationality” parameter <inline-formula><mml:math id="M237" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula> can be interpreted as a measure of a country's rationality, because the probability of switching to the other country's discount rate is higher if the other country has higher welfare (and zero if that is not the case) – but it is a myopic rationality because the agent only takes its present welfare into account. The larger the <inline-formula><mml:math id="M238" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>, the faster discount factors will converge to the one currently generating the largest welfare.</p>
      <p id="d1e5097">To get a deterministic evolution that can be represented by an ordinary differential equation,
we only track the expected fraction <inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of patient countries, which evolves as
            <disp-formula id="App1.Ch1.S1.E16" content-type="numbered"><label>A14</label><mml:math id="M240" display="block"><mml:mrow><mml:mover accent="true"><mml:mi>F</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>[</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          whereas the actual number of patient countries would follow a stochastic dynamics
involving binomial distributions
that converges to the above in the statistical limit <inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:math></inline-formula>.
Note that <inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>F</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> if <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>∈</mml:mo><mml:mo mathvariant="italic">{</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo mathvariant="italic">}</mml:mo></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>F</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> otherwise.</p>
</sec>
<sec id="App1.Ch1.S1.SS4">
  <label>A4</label><title>Carbon stock damage factor</title>
      <p id="d1e5308">For ease of presentation, we drop the denotation of time dependence from here on.
We assume that the atmospheric carbon stock evolves according to a simplistic dynamics involving only emissions and carbon uptake by other carbon stocks:
            <disp-formula id="App1.Ch1.S1.E17" content-type="numbered"><label>A15</label><mml:math id="M245" display="block"><mml:mrow><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with a constant carbon uptake rate <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> (ENV <inline-formula><mml:math id="M247" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV).
Note that <inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> if <inline-formula><mml:math id="M249" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> equals
            <disp-formula id="App1.Ch1.S1.E18" content-type="numbered"><label>A16</label><mml:math id="M250" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          In order that <inline-formula><mml:math id="M251" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> for all times,
we require that <inline-formula><mml:math id="M252" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> whenever <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
which is ensured by assuming that the parameters fulfil
<inline-formula><mml:math id="M254" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">⩾</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>c</mml:mi><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">μ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
where <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e5580">We further assume that <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
the value (MET <inline-formula><mml:math id="M257" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL; ENV <inline-formula><mml:math id="M258" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL) of the additional damages from climate change (ENV <inline-formula><mml:math id="M259" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> MET; ENV <inline-formula><mml:math id="M260" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> CUL)
due to a marginal increase in emissions at an existing carbon stock <inline-formula><mml:math id="M261" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> (ENV <inline-formula><mml:math id="M262" display="inline"><mml:mo>→</mml:mo></mml:math></inline-formula> ENV),
is a positive function of <inline-formula><mml:math id="M263" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> that has a unique maximum at some critical stock <inline-formula><mml:math id="M264" display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula>
at which small changes in stock lead to large changes in damages due to the presence of tipping points.
To approximate a damage function that is a sum of a number of sigmoid-shaped functions
representing individual tipping points whose locations and amplitudes are roughly normally distributed,
we take <inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to be Gaussian:
            <disp-formula id="App1.Ch1.S1.E19" content-type="numbered"><label>A17</label><mml:math id="M266" display="block"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with parameters <inline-formula><mml:math id="M267" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
This completes our derivation of the two ordinary differential equations for <inline-formula><mml:math id="M270" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M271" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>.</p>
</sec>
<?pagebreak page1131?><sec id="App1.Ch1.S1.SS5">
  <label>A5</label><title>Steady states' stability</title>
      <p id="d1e5778">We can distinguish three types of steady states where <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mi>F</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>:</p>
      <p id="d1e5803"><list list-type="order">
            <list-item>

      <p id="d1e5808">All countries are impatient, <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> (which implies <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>:=</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>),
and <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.
The latter is equivalent to <inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:math></inline-formula>
which generically has one or three solutions in <inline-formula><mml:math id="M277" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> with <inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
If there are three, the middle one is always unstable.
The others are stable if <inline-formula><mml:math id="M279" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.</p>
            </list-item>
            <list-item>

      <p id="d1e5996">All countries are patient, <inline-formula><mml:math id="M280" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (which implies <inline-formula><mml:math id="M281" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>)
and <inline-formula><mml:math id="M282" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.
The latter is equivalent to <inline-formula><mml:math id="M283" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mi>r</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:math></inline-formula>
which again generically has one or three solutions in <inline-formula><mml:math id="M284" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> with <inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
Again, if there are three, the middle one is always unstable.
Again, the others are stable if <inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.
The possibility of two stable states with <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, one with a small <inline-formula><mml:math id="M288" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> and one with a large <inline-formula><mml:math id="M289" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>,
indicates that even if all countries eventually become patient,
this may happen too slowly to prevent a level of climate change (large <inline-formula><mml:math id="M290" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>) that makes ambitious mitigation even for patient countries too costly in view of the small amount of climate damages that could then still be avoided.</p>
            </list-item>
            <list-item>

      <p id="d1e6200"><inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>F</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>F</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
This has at most four different solutions in <inline-formula><mml:math id="M293" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula> with <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>,
each of which correspond at most to one solution in <inline-formula><mml:math id="M295" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>.
We know of no simple conditions for assessing their stability; however, from our numerical experiments, we conjecture that
(i) at most one of them is stable, namely the one with the largest <inline-formula><mml:math id="M296" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>;
(ii) its stability depends only on the learning rate <inline-formula><mml:math id="M297" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>, being stable up to a critical value <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, then unstable; and
(iii) for <inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>&lt;</mml:mo><mml:msup><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>,
it is a stable focus, and the leftmost steady state with <inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> is unstable.
Hence, at most four stable steady states can exist –
at most two with <inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, and either at most two with <inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> or at most one with <inline-formula><mml:math id="M303" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> plus the stable focus with <inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>F</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>.</p>
            </list-item>
          </list></p><?xmltex \hack{\clearpage}?>
</sec>
</app>
  </app-group><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e6399">A Python script for integrating and analysing the copan:DISCOUNT model is available at <uri>http://www.github.com/pik-copan/pycopandiscount</uri> (last access: 20 April 2021; <ext-link xlink:href="https://doi.org/10.5281/zenodo.4704936" ext-link-type="DOI">10.5281/zenodo.4704936</ext-link>, <xref ref-type="bibr" rid="bib1.bibx54" id="altparen.129"/>).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e6414">JFD designed and coordinated the research. JFD led the writing of the paper with strong contributions from WL, SC and JH. JH developed the copan:DISCOUNT model, performed model simulations and analysed results. All other authors contributed to writing the paper and developing and discussing the presented taxonomic framework.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e6420">The authors declare that they have no conflict of interest.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e6426">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e6432">This article is part of the special issue “Social dynamics and planetary boundaries in Earth system modelling”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e6438">This work has been carried out within the framework of the PIK project on “Co-evolutionary Pathways in the Earth system” (COPAN). We are thankful to the participants of the LOOPS 2014 workshop on “Closing the loop – Towards co-evolutionary modelling of global society-environment interactions”, held at Kloster Chorin, Germany, and the LOOPS 2015 workshop on “From limits to growth to planetary boundaries: defining the safe and just space for humanity” held in New Forest, Southampton, UK, for inspiring discussions that sparked this paper. Ilona M. Otto, Marc Wiedermann and Finn Müller-Hansen are acknowledged for helpful comments on ideas presented in this paper. We are grateful for the excellent quality of creative stimulus prompted by the comments of Carsten Herrmann-Pillath,  and Birgit Müller.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e6443">This research has been supported by the Leibniz-Gemeinschaft (grant no. SAW-2017-PIK-4), the Stordalen Foundation (Planetary Boundary Research Network, PB.net), the Earth League (grant no. EarthDoc programme), the BMBF (grant no. project GLUES), the Swedish Research Council Formas (grant no. 2014-589), the Mistra (core grant to the Stockholm Resilience Centre), the Heinrich Böll Foundation (PhD scholarship), and the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013/ERC grant agreement no. 283950 SES-LINK) and the European Union's Horizon 2020 Research and Innovation programme (ERC grant agreement no. 682472 – MUSES, and ERC grant agreement no. 743080 ERA).<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>The article processing charges for this open-access publication were covered by the Potsdam Institute for Climate Impact Research (PIK).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e6452">This paper was edited by James Dyke and reviewed by Carsten Herrmann-Pillath and Birgit Müller.</p>
  </notes><ref-list>
    <title>References</title>

      <ref id="bib1.bibx1"><?xmltex \def\ref@label{{Anderies et~al.(2013)Anderies, Carpenter, Steffen, and
Rockstr{\"{o}}m}}?><label>Anderies et al.(2013)Anderies, Carpenter, Steffen, and
Rockström</label><?label Anderies2013?><mixed-citation>Anderies, J. M., Carpenter, S., Steffen, W., and Rockström, J.: The
topology of non-linear global carbon dynamics: from tipping points to
planetary boundaries, Environ. Res. Lett., 8, 044048, <ext-link xlink:href="https://doi.org/10.1088/1748-9326/8/4/044048" ext-link-type="DOI">10.1088/1748-9326/8/4/044048</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx2"><?xmltex \def\ref@label{{Arneth et~al.(2014)Arneth, Brown, and Rounsevell}}?><label>Arneth et al.(2014)Arneth, Brown, and Rounsevell</label><?label Arneth2014?><mixed-citation>
Arneth, A., Brown, C., and Rounsevell, M.: Global models of human
decision-making for land-based mitigation and adaptation assessment,
Nat. Clim. Change, 4, 550–557, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx3"><?xmltex \def\ref@label{{Arrow et~al.(2013)Arrow, Cropper, Gollier, Groom, Heal, Newell,
Nordhaus, Pindyck, Pizer, Portney, Sterner, Tol, and Weitzman}}?><label>Arrow et al.(2013)Arrow, Cropper, Gollier, Groom, Heal, Newell,
Nordhaus, Pindyck, Pizer, Portney, Sterner, Tol, and Weitzman</label><?label Arrow2013?><mixed-citation>Arrow, K. J., Cropper, M. L., Gollier, C., Groom, B., Heal, G. M., Newell,
R. G., Nordhaus, W. D., Pindyck, R. S., Pizer, W. A., Portney, P. R.,
Sterner, T., Tol, R. S. J., and Weitzman, M. L.: How Should Benefits and
Costs Be Discounted in an Intergenerational Context?, The Views of an Expert Panel (December 19, 2013). Resources for the Future Discussion Paper No. 12–53, <ext-link xlink:href="https://doi.org/10.2139/ssrn.2199511" ext-link-type="DOI">10.2139/ssrn.2199511</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx4"><?xmltex \def\ref@label{{Barfuss et~al.(2017)Barfuss, Donges, Wiedermann, and
Lucht}}?><label>Barfuss et al.(2017)Barfuss, Donges, Wiedermann, and
Lucht</label><?label barfuss2017sustainable?><mixed-citation>Barfuss, W., Donges, J. F., Wiedermann, M., and Lucht, W.: Sustainable use of renewable resources in a stylized social–ecological network model under heterogeneous resource distribution, Earth Syst. Dynam., 8, 255–264, <ext-link xlink:href="https://doi.org/10.5194/esd-8-255-2017" ext-link-type="DOI">10.5194/esd-8-255-2017</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx5"><?xmltex \def\ref@label{{Barfuss et~al.(2018)Barfuss, Donges, Lade, and
Kurths}}?><label>Barfuss et al.(2018)Barfuss, Donges, Lade, and
Kurths</label><?label barfuss2018optimization?><mixed-citation>
Barfuss, W., Donges, J. F., Lade, S. J., and Kurths, J.: When optimization for governing human-environment tipping elements is neither sustainable nor safe, Nat. Commun., 9, 1–10, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx6"><?xmltex \def\ref@label{{Barfuss et~al.(2020)Barfuss, Donges, Vasconcelos, Kurths, and
Levin}}?><label>Barfuss et al.(2020)Barfuss, Donges, Vasconcelos, Kurths, and
Levin</label><?label barfuss2020caring?><mixed-citation>
Barfuss, W., Donges, J. F., Vasconcelos, V. V., Kurths, J., and Levin, S. A.:
Caring for the future can turn tragedy into comedy for long-term collective
action under risk of collapse, P. Natl. Acad. Sci. USA, 117, 12915–12922, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx7"><?xmltex \def\ref@label{{Barrett(1994)}}?><label>Barrett(1994)</label><?label Barrett1994?><mixed-citation>
Barrett, S.: Self-enforcing international environmental agreements, Oxford
Economic Papers, Oxford, UK, 1994.</mixed-citation></ref>
      <ref id="bib1.bibx8"><?xmltex \def\ref@label{{Barros et~al.(2014)Barros, Field, Dokken, Mastrandrea, Mach, Bilir,
Chatterjee, Ebi, Estrada, Genova, Girma, Kissel, Levy, MacCracken,
Mastrandrea, and White}}?><label>Barros et al.(2014)Barros, Field, Dokken, Mastrandrea, Mach, Bilir,
Chatterjee, Ebi, Estrada, Genova, Girma, Kissel, Levy, MacCracken,
Mastrandrea, and White</label><?label IPCC2014WG2?><mixed-citation>
Barros, V., Field, C., Dokken, D., Mastrandrea, M., Mach, K., Bilir, T.,
Chatterjee, M., Ebi, K., Estrada, Y., Genova, R., Girma, B., Kissel, E.,
Levy, A., MacCracken, S., Mastrandrea, P., and White, L. (Eds.): Climate
Change 2014: Impacts, Adaptation, and Vulnerability, in: Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, USA, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx9"><?xmltex \def\ref@label{{Beckage et~al.(2018)Beckage, Gross, Lacasse, Carr, Metcalf, Winter,
Howe, Fefferman, Franck, Zia, Kinzig, and Hoffman}}?><label>Beckage et al.(2018)Beckage, Gross, Lacasse, Carr, Metcalf, Winter,
Howe, Fefferman, Franck, Zia, Kinzig, and Hoffman</label><?label Beckage2018?><mixed-citation>
Beckage, B., Gross, L., Lacasse, K., Carr, E., Metcalf, S., Winter, J., Howe,
P., Fefferman, N., Franck, T., Zia, A., Kinzig, A., and Hoffman, F.: Linking
models of human behaviour and climate alters projected climate change, Nat. Clim. Change, 8, 79–84, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx10"><?xmltex \def\ref@label{{Bienabe and Hearne(2006)}}?><label>Bienabe and Hearne(2006)</label><?label bienabe2006public?><mixed-citation>
Bienabe, E. and Hearne, R. R.: Public preferences for biodiversity conservation and scenic beauty within a framework of environmental services payments, Forest Policy Econ., 9, 335–348, 2006.</mixed-citation></ref>
      <ref id="bib1.bibx11"><?xmltex \def\ref@label{{Biggs et~al.(2012)Biggs, Schl{\"{u}}ter, Biggs, Bohensky, BurnSilver,
Cundill, Dakos, Daw, Evans, Kotschy et~al.}}?><label>Biggs et al.(2012)Biggs, Schlüter, Biggs, Bohensky, BurnSilver,
Cundill, Dakos, Daw, Evans, Kotschy et al.</label><?label Biggs2012?><mixed-citation>
Biggs, R., Schlüter, M., Biggs, D., Bohensky, E. L.<?pagebreak page1133?>, BurnSilver, S., Cundill, G., Dakos, V., Daw, T. M., Evans, L. S., Kotschy, K., Leitch, A. M., Meek, C., Quinlan, A., Raudsepp-Hearne, C., Robards, M. D., Schoon, M. L., Schultz, L., and West, P. C.: Toward
principles for enhancing the resilience of ecosystem services,
Annu. Rev. Env. Resour., 37, 421–448, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx12"><?xmltex \def\ref@label{{Boysen et~al.(2017)Boysen, Lucht, and Gerten}}?><label>Boysen et al.(2017)Boysen, Lucht, and Gerten</label><?label boysen2017trade?><mixed-citation>
Boysen, L. R., Lucht, W., and Gerten, D.: Trade-offs for food production,
nature conservation and climate limit the terrestrial carbon dioxide removal
potential, Global Change Biol., 23, 4303–4317, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx13"><?xmltex \def\ref@label{{Brondizio et~al.(2016)Brondizio, O'brien, Bai, Biermann, Steffen,
Berkhout, Cudennec, Lemos, Wolfe, Palma-Oliveira et~al.}}?><label>Brondizio et al.(2016)Brondizio, O'brien, Bai, Biermann, Steffen,
Berkhout, Cudennec, Lemos, Wolfe, Palma-Oliveira et al.</label><?label brondizio2016re?><mixed-citation>
Brondizio, E. S., O'Brien, K., Bai, X., Biermann, F., Steffen, W., Berkhout, F., Cudennec, C., Lemos, M. C., Wolfe, A., Palma-Oliveira, J., and Chen, C.-T. A.:
Re-conceptualizing the Anthropocene: A call for collaboration,
Glob. Environ. Change, 39, 318–327, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx14"><?xmltex \def\ref@label{{Brugger et~al.(2017)Brugger, Feulner, and Petri}}?><label>Brugger et al.(2017)Brugger, Feulner, and Petri</label><?label brugger2017baby?><mixed-citation>
Brugger, J., Feulner, G., and Petri, S.: Baby, it's cold outside: Climate model simulations of the effects of the asteroid impact at the end of the
Cretaceous, Geophys. Res. Lett., 44, 419–427, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx15"><?xmltex \def\ref@label{{Brundtland(1987)}}?><label>Brundtland(1987)</label><?label Brundtland1987?><mixed-citation>
Brundtland, G. H.: Report of the World Commission on Environment and
Development: Our common future, United Nations,  New York,   374 pp., 1987.</mixed-citation></ref>
      <ref id="bib1.bibx16"><?xmltex \def\ref@label{{Budyko et~al.(1987)Budyko, Ronov, and Yanshin}}?><label>Budyko et al.(1987)Budyko, Ronov, and Yanshin</label><?label budyko1987history?><mixed-citation>
Budyko, M. I., Ronov, A. B., and Yanshin, A. L.: History of the Earth's
atmosphere, Springer, Berlin, Germany, 1987.</mixed-citation></ref>
      <ref id="bib1.bibx17"><?xmltex \def\ref@label{{Calder et~al.(2018)Calder, Craig, Culley, de~Cani, Donnelly, Douglas, Edmonds, Gascoigne, Gilbert, Hargrove et~al.}}?><label>Calder et al.(2018)Calder, Craig, Culley, de Cani, Donnelly, Douglas, Edmonds, Gascoigne, Gilbert, Hargrove et al.</label><?label calder2018computational?><mixed-citation>Calder, M., Craig, C., Culley, D., de Cani, R., Donnelly, C. A., Douglas, R., Edmonds, B., Gascoigne, J., Gilbert, N., Hargrove, C., Hinds, D., Lane, D. C., Mitchell, D., Pavey, G., Robertson, D., Rosewell, B., Sherwin, S., Walport, M., and Wilson, A.: Computational
modelling for decision-making: where, why, what, who and how,
Roy. Soc. Open Sci., 5, 172096, <ext-link xlink:href="https://doi.org/10.1098/rsos.172096" ext-link-type="DOI">10.1098/rsos.172096</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx18"><?xmltex \def\ref@label{{Calvin and Bond-Lamberty(2018)}}?><label>Calvin and Bond-Lamberty(2018)</label><?label calvin2018integrated?><mixed-citation>Calvin, K. and Bond-Lamberty, B.: Integrated human-earth system
modeling-state of the science and future directions, Environ. Res. Lett., 13, 063006, <ext-link xlink:href="https://doi.org/10.1088/1748-9326/aac642" ext-link-type="DOI">10.1088/1748-9326/aac642</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx19"><?xmltex \def\ref@label{{Caminade et~al.(2014)Caminade, Kovats, Rocklov, Tompkins, Morse,
Col{\'{o}}n-Gonz{\'{a}}lez, Stenlund, Martens, and Lloyd}}?><label>Caminade et al.(2014)Caminade, Kovats, Rocklov, Tompkins, Morse,
Colón-González, Stenlund, Martens, and Lloyd</label><?label caminade2014impact?><mixed-citation>
Caminade, C., Kovats, S., Rocklov, J., Tompkins, A. M., Morse, A. P.,
Colón-González, F. J., Stenlund, H., Martens, P., and Lloyd, S. J.:
Impact of climate change on global malaria distribution, P. Natl. Acad. Sci. USA, 111, 3286–3291, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx20"><?xmltex \def\ref@label{{Castellano et~al.(2009)Castellano, Fortunato, and
Loreto}}?><label>Castellano et al.(2009)Castellano, Fortunato, and
Loreto</label><?label castellano2009statistical?><mixed-citation>Castellano, C., Fortunato, S., and Loreto, V.: Statistical physics of social
dynamics, Rev. Mod. Phys., 81, 591–646, <ext-link xlink:href="https://doi.org/10.1103/RevModPhys.81.591" ext-link-type="DOI">10.1103/RevModPhys.81.591</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx21"><?xmltex \def\ref@label{{Charney et~al.(1977)Charney, Quirk, Chow, and
Kornfield}}?><label>Charney et al.(1977)Charney, Quirk, Chow, and
Kornfield</label><?label charney1977comparative?><mixed-citation>
Charney, J., Quirk, W. J., Chow, S.-H., and Kornfield, J.: A comparative study of the effects of albedo change on drought in semi-arid regions, J. Atmos. Sci., 34, 1366–1385, 1977.</mixed-citation></ref>
      <ref id="bib1.bibx22"><?xmltex \def\ref@label{{Colding and Folke(2001)}}?><label>Colding and Folke(2001)</label><?label colding2001social?><mixed-citation>
Colding, J. and Folke, C.: Social taboos: “invisible” systems of local
resource management and biological conservation, Ecol. Appl., 11,
584–600, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx23"><?xmltex \def\ref@label{{Crutzen(2002)}}?><label>Crutzen(2002)</label><?label Crutzen2002geology?><mixed-citation>Crutzen, P. J.: Geology of mankind, Nature, 415, p. 23, <ext-link xlink:href="https://doi.org/10.1038/415023a" ext-link-type="DOI">10.1038/415023a</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx24"><?xmltex \def\ref@label{{Cumming and Peterson(2017)}}?><label>Cumming and Peterson(2017)</label><?label cumming2017unifying?><mixed-citation>
Cumming, G. S. and Peterson, G. D.: Unifying research on social-ecological
resilience and collapse, Trends Ecol. Evol., 32, 695–713, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx25"><?xmltex \def\ref@label{{Dearing et~al.(2014)Dearing, Wang, Zhang, Dyke, Haberl, Hossain,
Langdon, Lenton, Raworth, Brown et~al.}}?><label>Dearing et al.(2014)Dearing, Wang, Zhang, Dyke, Haberl, Hossain,
Langdon, Lenton, Raworth, Brown et al.</label><?label dearing2014safe?><mixed-citation>
Dearing, J. A., Wang, R., Zhang, K., Dyke, J. G., Haberl, H., Hossain, Md. S., Langdon, P. G., Lenton, T. M., Raworth, K., Brown, S., Carstensen, J., Cole, M. J., Cornell, S. E., Dawson, T. P., Doncaster, C. P., Eigenbrod, F., Flörke, M., Jeffers, E., Mackay, A. W., Nykvist, B., and Poppy, G. M.: Safe and just
operating spaces for regional social-ecological systems, Glob. Environ. Change, 28, 227–238, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx26"><?xmltex \def\ref@label{{Di~Baldassarre et~al.(2017)Di~Baldassarre, Martinez, Kalantari, and
Viglione}}?><label>Di Baldassarre et al.(2017)Di Baldassarre, Martinez, Kalantari, and
Viglione</label><?label Baldassarre2017?><mixed-citation>Di Baldassarre, G., Martinez, F., Kalantari, Z., and Viglione, A.: Drought and flood in the Anthropocene: feedback mechanisms in reservoir operation, Earth Syst. Dynam., 8, 225–233, <ext-link xlink:href="https://doi.org/10.5194/esd-8-225-2017" ext-link-type="DOI">10.5194/esd-8-225-2017</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx27"><?xmltex \def\ref@label{{Donges et~al.(2015)Donges, Donner, Marwan, Breitenbach, Rehfeld, and Kurths}}?><label>Donges et al.(2015)Donges, Donner, Marwan, Breitenbach, Rehfeld, and Kurths</label><?label Donges2015?><mixed-citation>Donges, J. F., Donner, R. V., Marwan, N., Breitenbach, S. F. M., Rehfeld, K., and Kurths, J.: Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns, Clim. Past, 11, 709–741, <ext-link xlink:href="https://doi.org/10.5194/cp-11-709-2015" ext-link-type="DOI">10.5194/cp-11-709-2015</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx28"><?xmltex \def\ref@label{{Donges et~al.(2017{\natexlab{a}})Donges, Lucht, M{\"{u}}ller-Hansen,
and Steffen}}?><label>Donges et al.(2017a)Donges, Lucht, Müller-Hansen,
and Steffen</label><?label Donges2017a?><mixed-citation>
Donges, J. F., Lucht, W., Müller-Hansen, F., and Steffen, W.: The
technosphere in Earth System analysis: A coevolutionary perspective,
The Anthropocene Review, 4, 23–33, 2017a.</mixed-citation></ref>
      <ref id="bib1.bibx29"><?xmltex \def\ref@label{{Donges et~al.(2017{\natexlab{b}})Donges, Winkelmann, Lucht, Cornell, Dyke, Rockstr{\"{o}}m, Heitzig, and Schellnhuber}}?><label>Donges et al.(2017b)Donges, Winkelmann, Lucht, Cornell, Dyke, Rockström, Heitzig, and Schellnhuber</label><?label Donges2017b?><mixed-citation>
Donges, J. F., Winkelmann, R., Lucht, W., Cornell, S. E., Dyke, J. G.,
Rockström, J., Heitzig, J., and Schellnhuber, H. J.: Closing the loop:
Reconnecting human dynamics to Earth System science, The Anthropocene
Review, 4, 151–157, 2017b.</mixed-citation></ref>
      <ref id="bib1.bibx30"><?xmltex \def\ref@label{{Donges et~al.(2020)Donges, Heitzig, Barfuss, Wiedermann, Kassel,
Kittel, Kolb, Kolster, M\"{u}ller-Hansen, Otto, Zimmerer, and
Lucht}}?><label>Donges et al.(2020)Donges, Heitzig, Barfuss, Wiedermann, Kassel,
Kittel, Kolb, Kolster, Müller-Hansen, Otto, Zimmerer, and
Lucht</label><?label Donges2018?><mixed-citation>Donges, J. F., Heitzig, J., Barfuss, W., Wiedermann, M., Kassel, J. A., Kittel, T., Kolb, J. J., Kolster, T., Müller-Hansen, F., Otto, I. M., Zimmerer, K. B., and Lucht, W.: Earth system modeling with endogenous and dynamic human societies: the copan:CORE open World–Earth modeling framework, Earth Syst. Dynam., 11, 395–413, <ext-link xlink:href="https://doi.org/10.5194/esd-11-395-2020" ext-link-type="DOI">10.5194/esd-11-395-2020</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx31"><?xmltex \def\ref@label{{Edenhofer et~al.(2014)Edenhofer, Pichs-Madruga, Sokona, Farahani,
Kadner, Seyboth, Adler, Baum, Brunner, Eickemeier, Kriemann, Savolainen,
Schl{\"{o}}mer, von Stechow, Zwickel, and Minx}}?><label>Edenhofer et al.(2014)Edenhofer, Pichs-Madruga, Sokona, Farahani,
Kadner, Seyboth, Adler, Baum, Brunner, Eickemeier, Kriemann, Savolainen,
Schlömer, von Stechow, Zwickel, and Minx</label><?label IPCC2014WG3?><mixed-citation>
Edenhofer, O., Pichs-Madruga, R., Sokona, Y., Farahani, E., Kadner, S.,
Seyboth, K., Adler, A., Baum, I., Brunner, S., Eickemeier, P., Kriemann, B.,
Savolainen, J., Schlömer, S., von Stechow, C., Zwickel, T., and Minx,
J. (Eds.): Climate Change 2014: Mitigation of Climate Change, in: Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, Cambridge University Press, Cambridge, United
Kingdom and New York, USA, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx32"><?xmltex \def\ref@label{{Farmer and Foley(2009)}}?><label>Farmer and Foley(2009)</label><?label farmer2009economy?><mixed-citation>
Farmer, J. D. and Foley, D.: The economy needs agent-based modelling, Nature,
460, 685–686, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx33"><?xmltex \def\ref@label{{Fischer-Kowalski(2003)}}?><label>Fischer-Kowalski(2003)</label><?label Fischer2003history?><mixed-citation>
Fischer-Kowalski, M.: On the history of industrial metabolism, in:
Perspectives on Industrial Ecology, edited by: Bourg, D.,  Erkman, S., and  Chirac, J., Routledge, London, 35–45, 2003.</mixed-citation></ref>
      <ref id="bib1.bibx34"><?xmltex \def\ref@label{{Fischer-Kowalski and Erb(2006)}}?><label>Fischer-Kowalski and Erb(2006)</label><?label FischerKowalski2006?><mixed-citation>
Fischer-Kowalski, M. and Erb, K.-H.: Epistemologische und konzeptuelle
Grundlagen der sozialen Ökologie, Mitt. Osterr. Geogr. G., 148, 33–56, 2006.</mixed-citation></ref>
      <ref id="bib1.bibx35"><?xmltex \def\ref@label{{Fischer-Kowalski and Haberl(1993)}}?><label>Fischer-Kowalski and Haberl(1993)</label><?label Fischer1993metabolism?><mixed-citation>
Fischer-Kowalski, M. and Haberl, H.: Metabolism and colonization, Modes of
production and the physical exchange between societies and nature,
Innovation-Abingdon, 6, 415–442, 1993.</mixed-citation></ref>
      <ref id="bib1.bibx36"><?xmltex \def\ref@label{{Fischer-Kowalski and H{\"{u}}ttler(1998)}}?><label>Fischer-Kowalski and Hüttler(1998)</label><?label Fischer1998?><mixed-citation>
Fischer-Kowalski, M. and Hüttler, W.: Society's metabolism,
J. Ind. Ecol., 2, 107–136, 1998.</mixed-citation></ref>
      <ref id="bib1.bibx37"><?xmltex \def\ref@label{{Flato et~al.(2013)Flato, Marotzke, Abiodun, Braconnot, Chou, Collins, Cox, Driouech, Emori, Eyring, Forest, Gleckler, Guilyardi, Jakob, Kattsov, Reason, and Rummukainen}}?><label>Flato et al.(2013)Flato, Marotzke, Abiodun, Braconnot, Chou, Collins, Cox, Driouech, Emori, Eyring, Forest, Gleckler, Guilyardi, Jakob, Kattsov, Reason, and Rummukainen</label><?label IPCCClimateModelsFlato2013?><mixed-citation>Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S., Collins, W.,
Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P.,
Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and Rummukainen, M.:
Evaluation of Climate Models, in: Climate Change 2013 – The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, USA, 741–866, <ext-link xlink:href="https://doi.org/10.1017/CBO9781107415324.020" ext-link-type="DOI">10.1017/CBO9781107415324.020</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx38"><?xmltex \def\ref@label{{Flato(2011)}}?><label>Flato(2011)</label><?label flato2011earth?><mixed-citation>
Flato, G. M.: Earth system models: an overview, WIRES. Clim. Change, 2, 783–800, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx39"><?xmltex \def\ref@label{{Folke(2006)}}?><label>Folke(2006)</label><?label Folke2006resilience?><mixed-citation>
Folke, C.: Resilience: The emergence of a perspective for social-ecological
systems analyses, Glob. Environ. Change, 16, 253–267, 2006.</mixed-citation></ref>
      <ref id="bib1.bibx40"><?xmltex \def\ref@label{{Folke et~al.(2011)Folke, Jansson, Rockstr{\"{o}}m, Olsson, Carpenter,
Chapin~III, Cr{\'{e}}pin, Daily, Danell, Ebbesson
et~al.}}?><label>Folke et al.(2011)Folke, Jansson, Rockström, Olsson, Carpenter,
Chapin III, Crépin, Daily, Danell, Ebbesson
et al.</label><?label Folke2011reconnecting?><mixed-citation>
Folke, C., Jansson, Å., Rockström, <?pagebreak page1134?>J., Olsson, P., Carpenter, S. R., Chapin, F. S., Crépin, A.-S., Daily, G., Danell, K., Ebbesson, J., Elmqvist, T., Galaz, V., Moberg, F., Nilsson, M., Österblom, H., Ostrom, E., Persson, Å., Peterson, G., Polasky, S., Steffen, W., Walker, B., and Westley, F.: Reconnecting to the biosphere, AMBIO, 40, 719–738, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx41"><?xmltex \def\ref@label{{Folke et~al.(2016)Folke, Biggs, Norstr{\"{o}}m, Reyers, and
Rockstr{\"{o}}m}}?><label>Folke et al.(2016)Folke, Biggs, Norström, Reyers, and
Rockström</label><?label folke2016social?><mixed-citation>Folke, C., Biggs, R., Norström, A. V., Reyers, B., and Rockström, J.:
Social-ecological resilience and biosphere-based sustainability science,
Ecol. Soc., 21, 41, <ext-link xlink:href="https://doi.org/10.5751/ES-08748-210341" ext-link-type="DOI">10.5751/ES-08748-210341</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx42"><?xmltex \def\ref@label{{Gabriel(2013)}}?><label>Gabriel(2013)</label><?label gabriel2013welt?><mixed-citation>
Gabriel, M.: Warum es die Welt nicht gibt, Ullstein, Berlin, 270 pp., 2013.</mixed-citation></ref>
      <ref id="bib1.bibx43"><?xmltex \def\ref@label{{Gaines et~al.(2010)Gaines, White, Carr, and
Palumbi}}?><label>Gaines et al.(2010)Gaines, White, Carr, and
Palumbi</label><?label gaines2010designing?><mixed-citation>
Gaines, S. D., White, C., Carr, M. H., and Palumbi, S. R.: Designing marine
reserve networks for both conservation and fisheries management, P. Natl. Acad. Sci. USA, 107, 18286–18293, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx44"><?xmltex \def\ref@label{{Ganopolski et~al.(2016)Ganopolski, Winkelmann, and
Schellnhuber}}?><label>Ganopolski et al.(2016)Ganopolski, Winkelmann, and
Schellnhuber</label><?label Ganopolski2016?><mixed-citation>Ganopolski, A., Winkelmann, R., and Schellnhuber, H. J.: Critical
insolation-CO<inline-formula><mml:math id="M305" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> relation for diagnosing past and future glacial inception, Nature, 529, 200–203, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx45"><?xmltex \def\ref@label{{Garrett(2015)}}?><label>Garrett(2015)</label><?label Garrett2015?><mixed-citation>Garrett, T. J.: Long-run evolution of the global economy – Part 2: Hindcasts of innovation and growth, Earth Syst. Dynam., 6, 673–688, <ext-link xlink:href="https://doi.org/10.5194/esd-6-673-2015" ext-link-type="DOI">10.5194/esd-6-673-2015</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx46"><?xmltex \def\ref@label{{Geier et~al.(2019)Geier, Barfuss, Wiedermann, Kurths, and
Donges}}?><label>Geier et al.(2019)Geier, Barfuss, Wiedermann, Kurths, and
Donges</label><?label geier2019physics?><mixed-citation>
Geier, F., Barfuss, W., Wiedermann, M., Kurths, J., and Donges, J. F.: The
physics of governance networks: critical transitions in contagion dynamics on
multilayer adaptive networks with application to the sustainable use of
renewable resources, Eur. Phys. J.-Spec. Top., 228, 2357–2369, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx47"><?xmltex \def\ref@label{{Gerten et~al.(2018)Gerten, Sch\"{o}nfeld, and Schauberger}}?><label>Gerten et al.(2018)Gerten, Schönfeld, and Schauberger</label><?label Gerten2018?><mixed-citation>Gerten, D., Schönfeld, M., and Schauberger, B.: On deeper human dimensions in Earth system analysis and modelling, Earth Syst. Dynam., 9, 849–863, <ext-link xlink:href="https://doi.org/10.5194/esd-9-849-2018" ext-link-type="DOI">10.5194/esd-9-849-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx48"><?xmltex \def\ref@label{{Gregory et~al.(2009)Gregory, Jones, Cadule, and
Friedlingstein}}?><label>Gregory et al.(2009)Gregory, Jones, Cadule, and
Friedlingstein</label><?label gregory2009quantifying?><mixed-citation>
Gregory, J. M., Jones, C., Cadule, P., and Friedlingstein, P.: Quantifying
carbon cycle feedbacks, J. Climate, 22, 5232–5250, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx49"><?xmltex \def\ref@label{{Haff(2012)}}?><label>Haff(2012)</label><?label Haff2012technology?><mixed-citation>Haff, P. K.: Technology and human purpose: the problem of solids transport on the Earth's surface, Earth Syst. Dynam., 3, 149–156, <ext-link xlink:href="https://doi.org/10.5194/esd-3-149-2012" ext-link-type="DOI">10.5194/esd-3-149-2012</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx50"><?xmltex \def\ref@label{{Haff(2014)}}?><label>Haff(2014)</label><?label Haff2014humans?><mixed-citation>
Haff, P. K.: Humans and technology in the Anthropocene: Six rules, The
Anthropocene Review, 1, 126–136, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx51"><?xmltex \def\ref@label{{Hamilton(2015)}}?><label>Hamilton(2015)</label><?label hamilton2015getting?><mixed-citation>
Hamilton, C.: Getting the Anthropocene so wrong, The Anthropocene Review, 2,
102–107, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx52"><?xmltex \def\ref@label{{Harfoot et~al.(2014)Harfoot, Newbold, Tittensor, Emmott, Hutton,
Lyutsarev, Smith, Scharlemann, and Purves}}?><label>Harfoot et al.(2014)Harfoot, Newbold, Tittensor, Emmott, Hutton,
Lyutsarev, Smith, Scharlemann, and Purves</label><?label harfoot2014emergent?><mixed-citation>Harfoot, M. B., Newbold, T., Tittensor, D. P., Emmott, S., Hutton, J.,
Lyutsarev, V., Smith, M. J., Scharlemann, J. P., and Purves, D. W.: Emergent
global patterns of ecosystem structure and function from a mechanistic
general ecosystem model, PLoS Biol., 12, e1001841, <ext-link xlink:href="https://doi.org/10.1371/journal.pbio.1001841" ext-link-type="DOI">10.1371/journal.pbio.1001841</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx53"><?xmltex \def\ref@label{{Heck et~al.(2016)Heck, Donges, and Lucht}}?><label>Heck et al.(2016)Heck, Donges, and Lucht</label><?label Heck2016?><mixed-citation>Heck, V., Donges, J. F., and Lucht, W.: Collateral transgression of planetary boundaries due to climate engineering by terrestrial carbon dioxide removal, Earth Syst. Dynam., 7, 783–796, <ext-link xlink:href="https://doi.org/10.5194/esd-7-783-2016" ext-link-type="DOI">10.5194/esd-7-783-2016</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx54"><?xmltex \def\ref@label{Heitzig and Donges(2021)}?><label>Heitzig and Donges(2021)</label><?label Zenodo?><mixed-citation>Heitzig, J. and Donges, J.: pycopandiscount v1.0,  Zenodo [code],  <ext-link xlink:href="https://doi.org/10.5281/zenodo.4704936" ext-link-type="DOI">10.5281/zenodo.4704936</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx55"><?xmltex \def\ref@label{{Heitzig et~al.(2016)Heitzig, Kittel, Donges, and
Molkentin}}?><label>Heitzig et al.(2016)Heitzig, Kittel, Donges, and
Molkentin</label><?label Heitzig2016?><mixed-citation>Heitzig, J., Kittel, T., Donges, J. F., and Molkenthin, N.: Topology of sustainable management of dynamical systems with desirable states: from defining planetary boundaries to safe operating spaces in the Earth system, Earth Syst. Dynam., 7, 21–50, <ext-link xlink:href="https://doi.org/10.5194/esd-7-21-2016" ext-link-type="DOI">10.5194/esd-7-21-2016</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx56"><?xmltex \def\ref@label{{Heitzig et~al.(2018)Heitzig, Barfuss, and
Donges}}?><label>Heitzig et al.(2018)Heitzig, Barfuss, and
Donges</label><?label heitzig2018thought?><mixed-citation>Heitzig, J., Barfuss, W., and Donges, J. F.: A thought experiment on
sustainable management of the earth system, Sustainability-Basel, 10, 1947, <ext-link xlink:href="https://doi.org/10.3390/su10061947" ext-link-type="DOI">10.3390/su10061947</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx57"><?xmltex \def\ref@label{{Herrmann-Pillath(2018)}}?><label>Herrmann-Pillath(2018)</label><?label herrmann2018case?><mixed-citation>
Herrmann-Pillath, C.: The case for a new discipline: technosphere science,
Ecol. Econ., 149, 212–225, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx58"><?xmltex \def\ref@label{{Herrmann-Pillath(2020)}}?><label>Herrmann-Pillath(2020)</label><?label herrmann2020art?><mixed-citation>Herrmann-Pillath, C.: The art of co-creation: An intervention in the philosophy of ecological economics, Ecol. Econ., 169, 106526, <ext-link xlink:href="https://doi.org/10.1016/j.ecolecon.2019.106526" ext-link-type="DOI">10.1016/j.ecolecon.2019.106526</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx59"><?xmltex \def\ref@label{{Jarvis et~al.(2015)Jarvis, Jarvis, and Hewitt}}?><label>Jarvis et al.(2015)Jarvis, Jarvis, and Hewitt</label><?label Jarvis2015?><mixed-citation>Jarvis, A. J., Jarvis, S. J., and Hewitt, C. N.: Resource acquisition, distribution and end-use efficiencies and the growth of industrial society, Earth Syst. Dynam., 6, 689–702, <ext-link xlink:href="https://doi.org/10.5194/esd-6-689-2015" ext-link-type="DOI">10.5194/esd-6-689-2015</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx60"><?xmltex \def\ref@label{{Jax et~al.(2013)Jax, Barton, Chan, De~Groot, Doyle, Eser, G{\"{o}}rg,
G{\'{o}}mez-Baggethun, Griewald, Haber et~al.}}?><label>Jax et al.(2013)Jax, Barton, Chan, De Groot, Doyle, Eser, Görg,
Gómez-Baggethun, Griewald, Haber et al.</label><?label jax2013ecosystem?><mixed-citation>
Jax, K., Barton, D. N., Chan, K. M. A., de Groot, R., Doyle, U., Eser, U., Görg, C., Gómez-Baggethun, E., Griewald, Y., Haber, W., Haines-Young, R., Heink, U., Jahn, T., Joosten, H., Kerschbaumer, L., Korn, H., Luck, G. W., Matzdorf, B., Muraca, B., Neßhöver, C., Norton, B., Ott, K., Potschin, M., Rauschmayer, F., von Haaren, C., and Wichmann, S.:
Ecosystem services and ethics, Ecol. Econ., 93, 260–268, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx61"><?xmltex \def\ref@label{{Jentoft et~al.(2007)Jentoft, van Son, and Bj{\o}rkan}}?><label>Jentoft et al.(2007)Jentoft, van Son, and Bjørkan</label><?label Jentoft2007?><mixed-citation>
Jentoft, S., van Son, T. C., and Bjørkan, M.: Marine protected areas: a
governance system analysis, Hum. Ecol., 35, 611–622, 2007.</mixed-citation></ref>
      <ref id="bib1.bibx62"><?xmltex \def\ref@label{{Kates et~al.(2001)Kates, Clark, Corell, Hall, Jaeger, Lowe, McCarthy, Schellnhuber, Bolin, Dickson, Faucheux, Gallopin, Gr{\"{u}}bler, Huntley, J{\"{a}}ger, Jodha, Kasperson, Mabogunje, Matson, Mooney, III, and Uno Svedin}}?><label>Kates et al.(2001)Kates, Clark, Corell, Hall, Jaeger, Lowe, McCarthy, Schellnhuber, Bolin, Dickson, Faucheux, Gallopin, Grübler, Huntley, Jäger, Jodha, Kasperson, Mabogunje, Matson, Mooney, III, and Uno Svedin</label><?label Kates2001sustainability?><mixed-citation>Kates, R. W., Clark, W. C., Corell, R., Hall, J. M., Jaeger, C. C., Lowe, I.,
McCarthy, J. J., Schellnhuber, H. J., Bolin, B., Dickson, N. M., Faucheux,
S., Gallopin, G. C., Grübler, A., Huntley, B., Jäger, J., Jodha,
N. S., Kasperson, R. E., Mabogunje, A., Matson, P., Mooney, H., Moore III, B., O'Riordan, T., and Svedin, U.: Sustainability Science, Science, 292, 641–642, <ext-link xlink:href="https://doi.org/10.1126/science.1059386" ext-link-type="DOI">10.1126/science.1059386</ext-link>, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx63"><?xmltex \def\ref@label{{Kellie-Smith and Cox(2011)}}?><label>Kellie-Smith and Cox(2011)</label><?label Kellie2011?><mixed-citation>
Kellie-Smith, O. and Cox, P. M.: Emergent dynamics of the climate-economy
system in the Anthropocene, Philos. T. Roy. Soc. A, 369, 868–886, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx64"><?xmltex \def\ref@label{{Keys and Wang-Erlandsson(2017)}}?><label>Keys and Wang-Erlandsson(2017)</label><?label Keys2017?><mixed-citation>Keys, P. W. and Wang-Erlandsson, L.: On the social dynamics of moisture recycling, Earth Syst. Dynam., 9, 829–847, <ext-link xlink:href="https://doi.org/10.5194/esd-9-829-2018" ext-link-type="DOI">10.5194/esd-9-829-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx65"><?xmltex \def\ref@label{{Kleidon(2016)}}?><label>Kleidon(2016)</label><?label Kleidon2016thermodynamic?><mixed-citation>
Kleidon, A.: Thermodynamic foundations of the Earth system, Cambridge
University Press, Cambridge, UK, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx66"><?xmltex \def\ref@label{{Lade et~al.(2015)Lade, Niiranen, Hentati-Sundberg, Blenckner,
Boonstra, Orach, Quaas, {\"{O}}sterblom, and Schl{\"{u}}ter}}?><label>Lade et al.(2015)Lade, Niiranen, Hentati-Sundberg, Blenckner,
Boonstra, Orach, Quaas, Österblom, and Schlüter</label><?label lade2015empirical?><mixed-citation>
Lade, S. J., Niiranen, S., Hentati-Sundberg, J., Blenckner, T., Boonstra,
W. J., Orach, K., Quaas, M. F., Österblom, H., and Schlüter, M.: An
empirical model of the Baltic Sea reveals the importance of social dynamics
for ecological regime shifts, P. Natl. Acad. Sci. USA, 112, 11120–11125, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx67"><?xmltex \def\ref@label{{Lade et~al.(2017{\natexlab{a}})Lade, Donges, Fetzer, Anderies, Beer, Cornell, Gasser, Norberg, Richardson, Rockstr\"{o}m, and Steffen}}?><label>Lade et al.(2017a)Lade, Donges, Fetzer, Anderies, Beer, Cornell, Gasser, Norberg, Richardson, Rockström, and Steffen</label><?label Lade2017?><mixed-citation>Lade, S. J., Donges, J. F., Fetzer, I., Anderies, J. M., Beer, C., Cornell, S. E., Gasser, T., Norberg, J., Richardson, K., Rockström, J., and Steffen, W.: Analytically tractable climate–carbon cycle feedbacks under 21st century anthropogenic forcing, Earth Syst. Dynam., 9, 507–523, <ext-link xlink:href="https://doi.org/10.5194/esd-9-507-2018" ext-link-type="DOI">10.5194/esd-9-507-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx68"><?xmltex \def\ref@label{{Lade et~al.(2017)Lade, Haider, Engstr{\"{o}}m, and
Schl{\"{u}}ter}}?><label>Lade et al.(2017)Lade, Haider, Engström, and
Schlüter</label><?label lade2017resilience?><mixed-citation>Lade, S. J., Haider, L. J., Engström, G., and Schlüter, M.: Resilience offers escape from trapped thinking on poverty alleviation, Science Advances, 3, e1603043, <ext-link xlink:href="https://doi.org/10.1126/sciadv.1603043" ext-link-type="DOI">10.1126/sciadv.1603043</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx69"><?xmltex \def\ref@label{{Latour(2017)}}?><label>Latour(2017)</label><?label latour2017facing?><mixed-citation>
Latour, B.: Facing Gaia: Eight lectures on the new climatic regime, John  Polity Press, Cambridge, UK,  327 pp., 2017.</mixed-citation></ref>
      <ref id="bib1.bibx70"><?xmltex \def\ref@label{{Lenton et~al.(2004)Lenton, Schellnhuber, and
Szathmary}}?><label>Lenton et al.(2004)Lenton, Schellnhuber, and
Szathmary</label><?label lenton2004climbing?><mixed-citation>Lenton, T., Schellnhuber, H., and Szathmary, E.: Climbing the co-evolution
ladder, Nature, 431,  913, <ext-link xlink:href="https://doi.org/10.1038/431913a" ext-link-type="DOI">10.1038/431913a</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx71"><?xmltex \def\ref@label{{Lenton and Latour(2018)}}?><label>Lenton and Latour(2018)</label><?label lenton2018gaia?><mixed-citation>
Lenton, T. M. and Latour, B.: Gaia 2.0, Science, 361, 1066–1068, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx72"><?xmltex \def\ref@label{{Lenton et~al.(2016)Lenton, Pichler, and Weisz}}?><label>Lenton et al.(2016)Lenton, Pichler, and Weisz</label><?label Lenton2016?><mixed-citation>Lenton, T. M., Pichler, P.-P., and Weisz, H.: Revolutions in energy input and material cycling in Earth history and human history, Earth Syst. Dynam., 7, 353–370, <ext-link xlink:href="https://doi.org/10.5194/esd-7-353-2016" ext-link-type="DOI">10.5194/esd-7-353-2016</ext-link>, 2016.</mixed-citation></ref>
      <?pagebreak page1135?><ref id="bib1.bibx73"><?xmltex \def\ref@label{{Leontief(1936)}}?><label>Leontief(1936)</label><?label leontief1936quantitative?><mixed-citation>
Leontief, W. W.: Quantitative input and output relations in the economic
systems of the United States, Rev. Econ. Statistics, 18,
105–125, 1936.</mixed-citation></ref>
      <ref id="bib1.bibx74"><?xmltex \def\ref@label{{Lewis and Maslin(2015)}}?><label>Lewis and Maslin(2015)</label><?label lewis2015defining?><mixed-citation>
Lewis, S. L. and Maslin, M. A.: Defining the anthropocene, Nature, 519,
171–180, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx75"><?xmltex \def\ref@label{{Lewis-Beck and Ratto(2013)}}?><label>Lewis-Beck and Ratto(2013)</label><?label lewis2013economic?><mixed-citation>
Lewis-Beck, M. S. and Ratto, M. C.: Economic voting in Latin America: A general model, Elect. Stud., 32, 489–493, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx76"><?xmltex \def\ref@label{{Lovelock(1989)}}?><label>Lovelock(1989)</label><?label Lovelock1989geophysiology?><mixed-citation>
Lovelock, J. E.: Geophysiology, the science of Gaia, Rev. Geophys.,
27, 215–222, 1989.</mixed-citation></ref>
      <ref id="bib1.bibx77"><?xmltex \def\ref@label{{Lovelock and Margulis(1974)}}?><label>Lovelock and Margulis(1974)</label><?label Lovelock1974?><mixed-citation>
Lovelock, J. E. and Margulis, L.: Atmospheric homeostasis by and for the
biosphere: the Gaia hypothesis, Tellus, 26, 2–10, 1974.</mixed-citation></ref>
      <ref id="bib1.bibx78"><?xmltex \def\ref@label{{Lucht and Pachauri(2004)}}?><label>Lucht and Pachauri(2004)</label><?label Lucht2004?><mixed-citation>
Lucht, W. and Pachauri, R.: The mental component of the Earth system, in:
Earth system analysis for sustainability, edited by: Schellnhuber, H.-J.,
Crutzen, P., Clark, W., Claussen, M., and Held, H., Dahlem Workshop Reports,
Cambridge University Press, Cambridge, UK, 341–365, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx79"><?xmltex \def\ref@label{{Lutz and Skirbekk(2008)}}?><label>Lutz and Skirbekk(2008)</label><?label lutz2008low?><mixed-citation>
Lutz, W. and Skirbekk, V.: Low fertility in Europe in a global demographic
context, in: Demographic Change and Intergenerational Justice,
Springer, Berlin, Heidelberg, 3–19, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx80"><?xmltex \def\ref@label{{Martin and Schl{\"{u}}ter(2015)}}?><label>Martin and Schlüter(2015)</label><?label martin2015combining?><mixed-citation>Martin, R. and Schlüter, M.: Combining system dynamics and agent-based
modeling to analyze social-ecological interactions – an example from modeling restoration of a shallow lake, Front. Environ. Sci., 3, 66, <ext-link xlink:href="https://doi.org/10.3389/fenvs.2015.00066" ext-link-type="DOI">10.3389/fenvs.2015.00066</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx81"><?xmltex \def\ref@label{{Masterson et~al.(2017)Masterson, Stedman, Enqvist, Teng{\"{o}}, Giusti, Wahl, and Svedin}}?><label>Masterson et al.(2017)Masterson, Stedman, Enqvist, Tengö, Giusti, Wahl, and Svedin</label><?label Masterson2017?><mixed-citation>Masterson, V., Stedman, R., Enqvist, J., Tengö, M., Giusti, M., Wahl, D.,
and Svedin, U.: The contribution of sense of place to social-ecological
systems research: a review and research agenda, Ecol. Soc., 22,  49, <ext-link xlink:href="https://doi.org/10.5751/ES-08872-220149" ext-link-type="DOI">10.5751/ES-08872-220149</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx82"><?xmltex \def\ref@label{{Mengel et~al.(2018)Mengel, Nauels, Rogelj, and
Schleussner}}?><label>Mengel et al.(2018)Mengel, Nauels, Rogelj, and
Schleussner</label><?label Mengel2018?><mixed-citation>Mengel, M., Nauels, A., Rogelj, J., and Schleussner, C.-F.: Committed sea-level rise under the Paris Agreement and the legacy of delayed mitigation action, Nat. Commun., 9, 601, <ext-link xlink:href="https://doi.org/10.1038/s41467-018-02985-8" ext-link-type="DOI">10.1038/s41467-018-02985-8</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx83"><?xmltex \def\ref@label{{{Millennium Ecosystem Assessment}(2005)}}?><label>Millennium Ecosystem Assessment(2005)</label><?label assessment2005ecosystems?><mixed-citation>
Millennium Ecosystem Assessment: Ecosystems and human well-being, Island
Press, Washington, D.C., USA, 2005.</mixed-citation></ref>
      <ref id="bib1.bibx84"><?xmltex \def\ref@label{{Milo et~al.(2002)Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii, and Alon}}?><label>Milo et al.(2002)Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii, and Alon</label><?label milo2002network?><mixed-citation>
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon,
U.: Network motifs: simple building blocks of complex networks, Science, 298,
824–827, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx85"><?xmltex \def\ref@label{{Mooney et~al.(2013)Mooney, Duraiappah, and Larigauderie}}?><label>Mooney et al.(2013)Mooney, Duraiappah, and Larigauderie</label><?label Mooney2013?><mixed-citation>
Mooney, H. A., Duraiappah, A., and Larigauderie, A.: Evolution of natural and
social science interactions in global change research programs, P. Natl. Acad. Sci. USA, 110, 3665–3672, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx86"><?xmltex \def\ref@label{{Morton(2013)}}?><label>Morton(2013)</label><?label morton2013hyperobjects?><mixed-citation>
Morton, T.: Hyperobjects: Philosophy and Ecology after the End of the World, University of Minnesota Press, Minneapolis, 240 pp., 2013.</mixed-citation></ref>
      <ref id="bib1.bibx87"><?xmltex \def\ref@label{{M{\"{u}}ller-Hansen et~al.(2017)M{\"{u}}ller-Hansen, Schl{\"{u}}ter,
M{\"{a}}s, Donges, Kolb, Thonicke, and Heitzig}}?><label>Müller-Hansen et al.(2017)Müller-Hansen, Schlüter,
Mäs, Donges, Kolb, Thonicke, and Heitzig</label><?label muller2017towards?><mixed-citation>Müller-Hansen, F., Schlüter, M., Mäs, M., Donges, J. F., Kolb, J. J., Thonicke, K., and Heitzig, J.: Towards representing human behavior and decision making in Earth system models – an overview of techniques and approaches, Earth Syst. Dynam., 8, 977–1007, <ext-link xlink:href="https://doi.org/10.5194/esd-8-977-2017" ext-link-type="DOI">10.5194/esd-8-977-2017</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx88"><?xmltex \def\ref@label{{National Research Council(1986)}}?><label>National Research Council(1986)</label><?label Bretherton1986?><mixed-citation>National Research Council: Earth System Science: Overview: A Program for
Global Change, Washington, DC, The National Academies Press,
<ext-link xlink:href="https://doi.org/10.17226/19210" ext-link-type="DOI">10.17226/19210</ext-link>, 1986.</mixed-citation></ref>
      <ref id="bib1.bibx89"><?xmltex \def\ref@label{{National Research Council(1988)}}?><label>National Research Council(1988)</label><?label Bretherton1988?><mixed-citation>National Research Council: Earth System Science: A closer view, Washington, DC, The National
Academies Press, available at: <uri>https://doi.org/10.17226/19088</uri>, 1988.</mixed-citation></ref>
      <ref id="bib1.bibx90"><?xmltex \def\ref@label{{{National Research Council}(2007)}}?><label>National Research Council(2007)</label><?label national2007models?><mixed-citation>National Research Council: Models in Environmental Regulatory Decision
Making, The National Academies Press, Washington, D.C., USA, 286 pp., <ext-link xlink:href="https://doi.org/10.17226/11972" ext-link-type="DOI">10.17226/11972</ext-link>, 2007.</mixed-citation></ref>
      <ref id="bib1.bibx91"><?xmltex \def\ref@label{{Nelson et~al.(2014)Nelson, Valin, Sands, Havl{\'{\i}}k, Ahammad,
Deryng, Elliott, Fujimori, Hasegawa, Heyhoe et~al.}}?><label>Nelson et al.(2014)Nelson, Valin, Sands, Havlík, Ahammad,
Deryng, Elliott, Fujimori, Hasegawa, Heyhoe et al.</label><?label nelson2014climate?><mixed-citation>
Nelson, G. C., Valin, H., Sands, R. D., Havlík, P., Ahammad, H., Deryng, D., Elliott, J., Fujimori, S., Hasegawa, T., Heyhoe, E., Kyle, P., Lampe, M. V., Lotze-Campen, H., d’Croz, D. M., van  Meijl, H., van der  Mensbrugghe, D., Müller, C., Popp, A., Robertson, R., Robinson, S., Schmid, E., Schmitz, C., Tabeau, A., and Willenbockel, D.: Climate
change effects on agriculture: Economic responses to biophysical shocks,
P. Natl. Acad. Sci. USA, 111, 3274–3279, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx92"><?xmltex \def\ref@label{{Nitzbon et~al.(2017)Nitzbon, Heitzig, and Parlitz}}?><label>Nitzbon et al.(2017)Nitzbon, Heitzig, and Parlitz</label><?label Nitzbon2017?><mixed-citation>Nitzbon, J., Heitzig, J., and Parlitz, U.: Sustainability, collapse and
oscillations in a simple World-Earth model, Environ. Res. Lett., 12, 074020,  <ext-link xlink:href="https://doi.org/10.1088/1748-9326/aa7581" ext-link-type="DOI">10.1088/1748-9326/aa7581</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx93"><?xmltex \def\ref@label{{Nordhaus(1992)}}?><label>Nordhaus(1992)</label><?label nordhaus1992optimal?><mixed-citation>
Nordhaus, W. D.: An optimal transition path for controlling greenhouse gases,
Science, 258, 1315–1319, 1992.</mixed-citation></ref>
      <ref id="bib1.bibx94"><?xmltex \def\ref@label{{Nordhaus(2017)}}?><label>Nordhaus(2017)</label><?label nordhaus2017revisiting?><mixed-citation>Nordhaus, W. D.: Revisiting the social cost of carbon, P. Natl. Acad. Sci. USA,  114,  1518–1523, <ext-link xlink:href="https://doi.org/10.1073/pnas.1609244114" ext-link-type="DOI">10.1073/pnas.1609244114</ext-link>,  2017.</mixed-citation></ref>
      <ref id="bib1.bibx95"><?xmltex \def\ref@label{{Ostrom(2009)}}?><label>Ostrom(2009)</label><?label ostrom2009general?><mixed-citation>
Ostrom, E.: A general framework for analyzing sustainability of
social-ecological systems, Science, 325, 419–422, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx96"><?xmltex \def\ref@label{{Ostrom et~al.(2007)Ostrom, Janssen, and Anderies}}?><label>Ostrom et al.(2007)Ostrom, Janssen, and Anderies</label><?label Ostrom2007going?><mixed-citation>
Ostrom, E., Janssen, M. A., and Anderies, J. M.: Going beyond panaceas,
P. Natl. Acad. Sci. USA, 104, 15176–15178, 2007.</mixed-citation></ref>
      <ref id="bib1.bibx97"><?xmltex \def\ref@label{{Otto et~al.(2017)Otto, Willner, Wenz, Frieler, and
Levermann}}?><label>Otto et al.(2017)Otto, Willner, Wenz, Frieler, and
Levermann</label><?label Otto2017modeling?><mixed-citation>
Otto, C., Willner, S. N., Wenz, L., Frieler, K., and Levermann, A.: Modeling
loss-propagation in the global supply network: The dynamic agent-based model
acclimate, J. Econ. Dyn. Control, 83, 232–269, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx98"><?xmltex \def\ref@label{{Otto et~al.(2020{\natexlab{a}})Otto, Donges, Cremades, Bhowmik,
Hewitt, Lucht, Rockstr{\"{o}}m, Allerberger, McCaffrey, Doe
et~al.}}?><label>Otto et al.(2020a)Otto, Donges, Cremades, Bhowmik,
Hewitt, Lucht, Rockström, Allerberger, McCaffrey, Doe
et al.</label><?label otto2020social?><mixed-citation>
Otto, I. M., Donges, J. F., Cremades, R., Bhowmik, A., Hewitt, R. J., Lucht, W., Rockström, J., Allerberger, F., McCaffrey, M., Doe, S. S. P., Lenferna, A., Morán, N., van  Vuuren, D. P., and Schellnhuber, H. J.:
Social tipping dynamics for stabilizing Earth's climate by 2050,
P. Natl. Acad. Sci. USA, 117, 2354–2365, 2020a.</mixed-citation></ref>
      <ref id="bib1.bibx99"><?xmltex \def\ref@label{{Otto et~al.(2020{\natexlab{b}})Otto, Wiedermann, Cremades, Donges,
Auer, and Lucht}}?><label>Otto et al.(2020b)Otto, Wiedermann, Cremades, Donges,
Auer, and Lucht</label><?label otto2020human?><mixed-citation>Otto, I. M., Wiedermann, M., Cremades, R., Donges, J. F., Auer, C., and Lucht, W.: Human agency in the anthropocene, Ecol. Econ., 167, 106463, <ext-link xlink:href="https://doi.org/10.1016/j.ecolecon.2019.106463" ext-link-type="DOI">10.1016/j.ecolecon.2019.106463</ext-link>, 2020b.</mixed-citation></ref>
      <ref id="bib1.bibx100"><?xmltex \def\ref@label{{Perman et al.(2003)}}?><label>Perman et al.(2003)</label><?label Perman2003natural?><mixed-citation>
Perman, R., Ma, Y., McGilvray, J., and Common, M.:: Natural resource and environmental economics, Pearson Education, Harlow, England, 726 pp.
2003.</mixed-citation></ref>
      <ref id="bib1.bibx101"><?xmltex \def\ref@label{{Phalan(2018)}}?><label>Phalan(2018)</label><?label phalan2018have?><mixed-citation>Phalan, B. T.: What have we learned from the land sparing-sharing model?,
Sustainability-Basel, 10, 1760, <ext-link xlink:href="https://doi.org/10.3390/su10061760" ext-link-type="DOI">10.3390/su10061760</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx102"><?xmltex \def\ref@label{{Purves et~al.(2013)Purves, Scharlemann, Harfoot, Newbold, Tittensor, Hutton, and Emmott}}?><label>Purves et al.(2013)Purves, Scharlemann, Harfoot, Newbold, Tittensor, Hutton, and Emmott</label><?label purves2013ecosystems?><mixed-citation>Purves, D., Scharlemann, J. P., Harfoot, M., Newbold, T., Tittensor, D. P.,
Hutton, J., and Emmott, S.: Ecosystems: time to model all life on Earth,
Nature, 493, 295–297, <ext-link xlink:href="https://doi.org/10.1038/493295a" ext-link-type="DOI">10.1038/493295a</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx103"><?xmltex \def\ref@label{{Raworth(2012)}}?><label>Raworth(2012)</label><?label Raworth2012?><mixed-citation>Raworth, K.: A safe and just space for humanity: can we live within the
doughnut, Oxfam Policy and Practice: Climate Change and Resilience, Oxfam International, available at: <uri>https://oxfamilibrary.openrepository.com/handle/10546/210490?show=full</uri> (last access: 24 September 2021), 8, 1–26, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx104"><?xmltex \def\ref@label{{Reichler and Kim(2008)}}?><label>Reichler and Kim(2008)</label><?label reichler2008well?><mixed-citation>
Reichler, T. and Kim, J.: How well do coupled models simulate today's climate?, B. Am. Meteorol. Soc., 89, 303–311, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx105"><?xmltex \def\ref@label{{Renn(2018)}}?><label>Renn(2018)</label><?label renn2018evolution?><mixed-citation>
Renn, J.: The Evolution of Knowledge: Rethinking Science in the Anthropocene,
HoST-Journal of History of Science and Technology, 12, 1–22, 2018.</mixed-citation></ref>
      <?pagebreak page1136?><ref id="bib1.bibx106"><?xmltex \def\ref@label{{Robinson et~al.(2017)Robinson, Di~Vittorio, Alexander, Arneth,
Barton, Brown, Kettner, Lemmen, O'Neill, Janssen, Pugh, Rabin, Rounsevell,
Syvitski, Ullah, and Verburg}}?><label>Robinson et al.(2017)Robinson, Di Vittorio, Alexander, Arneth,
Barton, Brown, Kettner, Lemmen, O'Neill, Janssen, Pugh, Rabin, Rounsevell,
Syvitski, Ullah, and Verburg</label><?label Robinson2017?><mixed-citation>Robinson, D. T., Di Vittorio, A., Alexander, P., Arneth, A., Barton, C. M., Brown, D. G., Kettner, A., Lemmen, C., O'Neill, B. C., Janssen, M., Pugh, T. A. M., Rabin, S. S., Rounsevell, M., Syvitski, J. P., Ullah, I., and Verburg, P. H.: Modelling feedbacks between human and natural processes in the land system, Earth Syst. Dynam., 9, 895–914, <ext-link xlink:href="https://doi.org/10.5194/esd-9-895-2018" ext-link-type="DOI">10.5194/esd-9-895-2018</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx107"><?xmltex \def\ref@label{{Rocha et~al.(2015)Rocha, Peterson, and Biggs}}?><label>Rocha et al.(2015)Rocha, Peterson, and Biggs</label><?label rocha2015regime?><mixed-citation>Rocha, J. C., Peterson, G. D., and Biggs, R.: Regime shifts in the
Anthropocene: drivers, risks, and resilience, PLoS One, 10, e0134639, <ext-link xlink:href="https://doi.org/10.1371/journal.pone.0134639" ext-link-type="DOI">10.1371/journal.pone.0134639</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx108"><?xmltex \def\ref@label{{Rockstr{\"{o}}m et~al.(2009{\natexlab{a}})Rockstr{\"{o}}m, Steffen,
Noone, Persson, Chapin, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et~al.}}?><label>Rockström et al.(2009a)Rockström, Steffen,
Noone, Persson, Chapin, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et al.</label><?label Rockstrom2009safe?><mixed-citation>
Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F. S., Lambin, E. F., Lenton, T. M., Scheffer, M., Folke, C., Schellnhuber, H. J., Nykvist, B., de Wit, C. A., Hughes, T., van der Leeuw, S., Rodhe, H., Sörlin, S., Snyder, P. K., Costanza, R., Svedin, U., Falkenmark, M., Karlberg, L., Corell, R. W., Fabry, V. J., Hansen, J., Walker, B., Liverman, D., Richardson, K., Crutzen, P., and Foley, J. A.: A safe operating space for humanity, Nature, 461, 472–475,
2009a.</mixed-citation></ref>
      <ref id="bib1.bibx109"><?xmltex \def\ref@label{{Rockstr{\"{o}}m et~al.(2009{\natexlab{b}})Rockstr{\"{o}}m, Steffen,
Noone, Persson, Chapin~III, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et~al.}}?><label>Rockström et al.(2009b)Rockström, Steffen,
Noone, Persson, Chapin III, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et al.</label><?label Rockstrom2009planetary?><mixed-citation>Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F. S. I., Lambin, E., Lenton, T., Scheffer, M., Folke, C., Schellnhuber, H. J., Nykvist, B., de Wit, C., Hughes, T., van der Leeuw, S., Rodhe, H., Sörlin, S., Snyder, P., Costanza, R., Svedin, U., Falkenmark, M., Karlberg, L., Corell, R., Fabry, V., Hansen, J., Walker, B., Liverman, D., Richardson, K., Crutzen, P., and Foley, J.: Planetary Boundaries: Exploring the Safe Operating Space for
Humanity, Ecol. Soc., 14, 32, <ext-link xlink:href="https://doi.org/10.5751/ES-03180-140232" ext-link-type="DOI">10.5751/ES-03180-140232</ext-link>, 2009b.</mixed-citation></ref>
      <ref id="bib1.bibx110"><?xmltex \def\ref@label{{Rockstr{\"{o}}m et~al.(2017)Rockstr{\"{o}}m, Gaffney, Rogelj,
Meinshausen, Nakicenovic, and Schellnhuber}}?><label>Rockström et al.(2017)Rockström, Gaffney, Rogelj,
Meinshausen, Nakicenovic, and Schellnhuber</label><?label Rockstrom2017?><mixed-citation>
Rockström, J., Gaffney, O., Rogelj, J., Meinshausen, M., Nakicenovic, N.,
and Schellnhuber, H. J.: A roadmap for rapid decarbonization, Science, 355,
1269–1271, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx111"><?xmltex \def\ref@label{{Rounsevell et~al.(2014)Rounsevell, Arneth, Alexander, Brown,
de~Noblet-Ducoudr{\'{e}}, Ellis, Finnigan, Galvin, Grigg, Harman
et~al.}}?><label>Rounsevell et al.(2014)Rounsevell, Arneth, Alexander, Brown,
de Noblet-Ducoudré, Ellis, Finnigan, Galvin, Grigg, Harman
et al.</label><?label Rounsevell2014?><mixed-citation>Rounsevell, M. D. A., Arneth, A., Alexander, P., Brown, D. G., de Noblet-Ducoudré, N., Ellis, E., Finnigan, J., Galvin, K., Grigg, N., Harman, I., Lennox, J., Magliocca, N., Parker, D., O'Neill, B. C., Verburg, P. H., and Young, O.: Towards decision-based global land use models for improved understanding of the Earth system, Earth Syst. Dynam., 5, 117–137, <ext-link xlink:href="https://doi.org/10.5194/esd-5-117-2014" ext-link-type="DOI">10.5194/esd-5-117-2014</ext-link>, 2014.</mixed-citation></ref>
      <ref id="bib1.bibx112"><?xmltex \def\ref@label{{Schellnhuber(1998)}}?><label>Schellnhuber(1998)</label><?label Schellnhuber1998?><mixed-citation>
Schellnhuber, H.-J.: Discourse: Earth system analysis – The scope of the
challenge, in: Earth system analysis: Integrating science for
sustainability, edited by: Schellnhuber, H.-J. and Wenzel, V.,
Springer, Berlin, Germany, 3–195, 1998.</mixed-citation></ref>
      <ref id="bib1.bibx113"><?xmltex \def\ref@label{{Schellnhuber(1999)}}?><label>Schellnhuber(1999)</label><?label Schellnhuber1999?><mixed-citation>
Schellnhuber, H. J.: Earth system analysis and the second Copernican
revolution, Nature, 402, 19–23, 1999.</mixed-citation></ref>
      <ref id="bib1.bibx114"><?xmltex \def\ref@label{{Schill et~al.(2019)Schill, Anderies, Lindahl, Folke, Polasky,
C{\'{a}}rdenas, Cr{\'{e}}pin, Janssen, Norberg, and
Schl{\"{u}}ter}}?><label>Schill et al.(2019)Schill, Anderies, Lindahl, Folke, Polasky,
Cárdenas, Crépin, Janssen, Norberg, and
Schlüter</label><?label schill2019more?><mixed-citation>
Schill, C., Anderies, J. M., Lindahl, T., Folke, C., Polasky, S., Cárdenas, J. C., Crépin, A.-S., Janssen, M. A., Norberg, J., and Schlüter, M.: A more dynamic understanding of human behaviour for the Anthropocene, Nature Sustainability, 2, 1075–1082, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx115"><?xmltex \def\ref@label{{Schlüter et~al.(2012)Schlueter, McAllister, Arlinghaus, Bunnefeld,
Eisenack, Hoelker, MILNER-GULLAND, M{\"{u}}ller, Nicholson, Quaas
et~al.}}?><label>Schlüter et al.(2012)Schlueter, McAllister, Arlinghaus, Bunnefeld,
Eisenack, Hoelker, MILNER-GULLAND, Müller, Nicholson, Quaas
et al.</label><?label Schlueter2012?><mixed-citation>
Schlüter, M., McAllister, R. R. J., Arlinghaus, R., Bunnefeld, N., Eisenack, K., Hölker, F., Milner-Gulland, E. J., Müller, B., Nicholson, E., Quaas, M., und Stöven, M. T.: New horizons for managing the environment: A review of coupled
social-ecological systems modeling, Nat. Resour. Model., 25, 219–272,
2012.</mixed-citation></ref>
      <ref id="bib1.bibx116"><?xmltex \def\ref@label{{Schl{\"{u}}ter et~al.(2017)Schl{\"{u}}ter, Baeza, Dressler, Frank,
Groeneveld, Jager, Janssen, McAllister, M{\"{u}}ller, Orach
et~al.}}?><label>Schlüter et al.(2017)Schlüter, Baeza, Dressler, Frank,
Groeneveld, Jager, Janssen, McAllister, Müller, Orach
et al.</label><?label schluter2017framework?><mixed-citation>
Schlüter, M., Baeza, A., Dressler, G., Frank, K., Groeneveld, J., Jager, W., Janssen, M. A., McAllister, R. R. J., Müller, B., Orach, K., Schwarz, N., and Wijermans, N.: A
framework for mapping and comparing behavioural theories in models of
social-ecological systems, Ecol. Econ., 131, 21–35, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx117"><?xmltex \def\ref@label{{Schneider et~al.(2004)Schneider, Miller, Crist, and
Boston}}?><label>Schneider et al.(2004)Schneider, Miller, Crist, and
Boston</label><?label schneider2004scientists?><mixed-citation>
Schneider, S. H., Miller, J. R., Crist, E., and Boston, P. J. (Eds.): Scientists Debate Gaia: The Next Century, MIT Press, Cambridge, Massachusetts, USA, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx118"><?xmltex \def\ref@label{{Seitzinger et~al.(2015)Seitzinger, Gaffney, Brasseur, Broadgate,
Ciais, Claussen, Erisman, Kiefer, Lancelot, Monks
et~al.}}?><label>Seitzinger et al.(2015)Seitzinger, Gaffney, Brasseur, Broadgate,
Ciais, Claussen, Erisman, Kiefer, Lancelot, Monks
et al.</label><?label seitzinger2015international?><mixed-citation>
Seitzinger, S. P., Gaffney, O., Brasseur, G., Broadgate, W., Ciais, P., Claussen, M., Erisman, J. W., Kiefer, T., Lancelot, C., Monks, P. S., Smyth, K., Syvitski, J., and Uematsu, M.:
International Geosphere-Biosphere Programme and Earth system science: three
decades of co-evolution, Anthropocene, 12, 3–16, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx119"><?xmltex \def\ref@label{{Sitch et~al.(2003)Sitch, Smith, Prentice, Arneth, Bondeau, Cramer,
Kaplan, Levis, Lucht, Sykes et~al.}}?><label>Sitch et al.(2003)Sitch, Smith, Prentice, Arneth, Bondeau, Cramer,
Kaplan, Levis, Lucht, Sykes et al.</label><?label sitch2003evaluation?><mixed-citation>
Sitch, S., Smith, B., Prentice, I. C., Arneth, A., Bondeau, A., Cramer, W., Kaplan, J. O., Levis, S., Lucht, W., Sykes, M. T., Thonicke, K., and Venevsky, S.: Evaluation of
ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ
dynamic global vegetation model, Glob. Change Biol., 9, 161–185, 2003.</mixed-citation></ref>
      <ref id="bib1.bibx120"><?xmltex \def\ref@label{{Steffen et~al.(2007)Steffen, Crutzen, and
McNeill}}?><label>Steffen et al.(2007)Steffen, Crutzen, and
McNeill</label><?label Steffen2007anthropocene?><mixed-citation>
Steffen, W., Crutzen, P. J., and McNeill, J. R.: The Anthropocene: are humans
now overwhelming the great forces of nature, AMBIO, 36, 614–621, 2007.</mixed-citation></ref>
      <ref id="bib1.bibx121"><?xmltex \def\ref@label{{Steffen et~al.(2015)Steffen, Richardson, Rockstr{\"{o}}m, Cornell,
Fetzer, Bennett, Biggs, Carpenter, de~Vries, de~Wit
et~al.}}?><label>Steffen et al.(2015)Steffen, Richardson, Rockström, Cornell,
Fetzer, Bennett, Biggs, Carpenter, de Vries, de Wit
et al.</label><?label Steffen2015planetary?><mixed-citation>Steffen, W., Richardson, K., Rockström, J., Cornell, S. E., Fetzer, I., Bennett, E. M., Biggs, R., Carpenter, S. R., de Vries, W., de Wit, C. A., Folke, C., Gerten, D., Heinke, J., Mace, G. M., Persson, L. M., Ramanathan, V., Reyers, B., and Sörlin, S.: Planetary boundaries: Guiding human development on a changing planet, Science, 347, 1259855, <ext-link xlink:href="https://doi.org/10.1126/science.1259855" ext-link-type="DOI">10.1126/science.1259855</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx122"><?xmltex \def\ref@label{{Steffen et~al.(2018)Steffen, Rockstr\"{o}m, Richardson, Folke,
Barnosky, Cornell, Crucifix, Donges, Fetzer, Lade, Lenton, Liverman,
Scheffer, Summerhayes, Winkelmann, and
Schellnhuber}}?><label>Steffen et al.(2018)Steffen, Rockström, Richardson, Folke,
Barnosky, Cornell, Crucifix, Donges, Fetzer, Lade, Lenton, Liverman,
Scheffer, Summerhayes, Winkelmann, and
Schellnhuber</label><?label Steffen2017trajectories?><mixed-citation>
Steffen, W., Rockström, J., Richardson, K., Folke, C., Barnosky, A. D.,
Cornell, S. E., Crucifix, M., Donges, J. F., Fetzer, I., Lade, S. J., Lenton,
T. M., Liverman, D., Scheffer, M., Summerhayes, C., Winkelmann, R., and
Schellnhuber, H. J.: Trajectories of the Earth system in the Anthropocene,
P. Natl. Acad. Sci. USA, 115, 8252–8259, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx123"><?xmltex \def\ref@label{{Steffen et~al.(2020)Steffen, Richardson, Rockstr{\"{o}}m, Schellnhuber, Dube, Dutreuil, Lenton, and Lubchenco}}?><label>Steffen et al.(2020)Steffen, Richardson, Rockström, Schellnhuber, Dube, Dutreuil, Lenton, and Lubchenco</label><?label steffen2020emergence?><mixed-citation>
Steffen, W., Richardson, K., Rockström, J., Schellnhuber, H. J., Dube,
O. P., Dutreuil, S., Lenton, T. M., and Lubchenco, J.: The emergence and
evolution of Earth System Science, Nature Reviews Earth &amp; Environment, 1,
54–63, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx124"><?xmltex \def\ref@label{{Stocker et~al.(2013)Stocker, Qin, Plattner, Tignor, Allen, Boschung, Nauels, Xia, Bex, and Midgley}}?><label>Stocker et al.(2013)Stocker, Qin, Plattner, Tignor, Allen, Boschung, Nauels, Xia, Bex, and Midgley</label><?label IPCC2013WG1?><mixed-citation>Stocker, T., Qin, D., Plattner, G.-K., Tignor, M., Allen, S., Boschung, J.,
Nauels, A., Xia, Y., Bex, V., and Midgley, P. (Eds.): Climate Change 2013: The Physical Science Basis, in: Contribution of Working Group I to the Fifth
Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, United Kingdom and New York, USA,
<ext-link xlink:href="https://doi.org/10.1017/CBO9781107415324" ext-link-type="DOI">10.1017/CBO9781107415324</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx125"><?xmltex \def\ref@label{{Strnad et~al.(2019)Strnad, Barfuss, Donges, and
Heitzig}}?><label>Strnad et al.(2019)Strnad, Barfuss, Donges, and
Heitzig</label><?label strnad2019deep?><mixed-citation>Strnad, F. M., Barfuss, W., Donges, J. F., and Heitzig, J.: Deep reinforcement learning in World-Earth system models to discover sustainable management strategies, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29, 123122, <ext-link xlink:href="https://doi.org/10.1063/1.5124673" ext-link-type="DOI">10.1063/1.5124673</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx126"><?xmltex \def\ref@label{{Taylor et~al.(2012)Taylor, Stouffer, and Meehl}}?><label>Taylor et al.(2012)Taylor, Stouffer, and Meehl</label><?label Taylor2012?><mixed-citation>
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of CMIP5 and the experiment design, B. Am. Meteorol. Soc., 93, 485–498, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx127"><?xmltex \def\ref@label{{Traulsen et~al.(2010)Traulsen, Semmann, Sommerfeld, Krambeck, and
Milinski}}?><label>Traulsen et al.(2010)Traulsen, Semmann, Sommerfeld, Krambeck, and
Milinski</label><?label Traulsen2010?><mixed-citation>
Traulsen, A., Semmann, D., Sommerfeld, R. D., Krambeck, H.-J., and Milinski,
M.: Human strategy updating in evolutionary games,, P. Natl. Acad. Sci. USA, 107, 2962–2966, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx128"><?xmltex \def\ref@label{{Turchin(2008)}}?><label>Turchin(2008)</label><?label turchin2008arise?><mixed-citation>Turchin, P.: Arise “cliodynamics”, Nature, 454,   34–35, <ext-link xlink:href="https://doi.org/10.1038/454034a" ext-link-type="DOI">10.1038/454034a</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx129"><?xmltex \def\ref@label{{UNFCCC(2015)}}?><label>UNFCCC(2015)</label><?label paris2015?><mixed-citation>
UNFCCC:
Paris Agreement (Dec. 13, 2015),  UNFCCC, COP Report No. 21, Addenum, at 21, U.N. Doc. FCCC/CP/2015/10/Add, 1 (29 January 2016), 2015.</mixed-citation></ref>
      <ref id="bib1.bibx130"><?xmltex \def\ref@label{{Van~Dijk and Breedveld(1991)}}?><label>Van Dijk and Breedveld(1991)</label><?label van1991simulation?><mixed-citation>
Van Dijk, J. and Breedveld, P. C.: Simulation of system models containing
zero-order causal paths – I. Classification of zero-order causal paths,
J. Frankl. Inst., 328, 959–979, 1991.</mixed-citation></ref>
      <?pagebreak page1137?><ref id="bib1.bibx131"><?xmltex \def\ref@label{{van Vuuren et~al.(2012)van Vuuren, Bayer, Chuwah, Ganzeveld,
Hazeleger, van~den Hurk, Van~Noije, O'Neill, and Strengers}}?><label>van Vuuren et al.(2012)van Vuuren, Bayer, Chuwah, Ganzeveld,
Hazeleger, van den Hurk, Van Noije, O'Neill, and Strengers</label><?label vanVuuren2012?><mixed-citation>van Vuuren, D. P., Bayer, L. B., Chuwah, C., Ganzeveld, L., Hazeleger, W.,
van den Hurk, B., Van Noije, T., O'Neill, B., and Strengers, B. J.: A
comprehensive view on climate change: coupling of earth system and integrated
assessment models, Environ. Res. Lett., 7, 024012, <ext-link xlink:href="https://doi.org/10.1088/1748-9326/7/2/024012" ext-link-type="DOI">10.1088/1748-9326/7/2/024012</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx132"><?xmltex \def\ref@label{{van Vuuren et~al.(2016)van Vuuren, Lucas, H\"{a}yh\"{a}, Cornell, and
Stafford-Smith}}?><label>van Vuuren et al.(2016)van Vuuren, Lucas, Häyhä, Cornell, and
Stafford-Smith</label><?label vanVuuren2016?><mixed-citation>van Vuuren, D. P., Lucas, P. L., Häyhä, T., Cornell, S. E., and Stafford-Smith, M.: Horses for courses: analytical tools to explore planetary boundaries, Earth Syst. Dynam., 7, 267–279, <ext-link xlink:href="https://doi.org/10.5194/esd-7-267-2016" ext-link-type="DOI">10.5194/esd-7-267-2016</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx133"><?xmltex \def\ref@label{{Vaughan and Lenton(2011)}}?><label>Vaughan and Lenton(2011)</label><?label vaughan2011review?><mixed-citation>
Vaughan, N. E. and Lenton, T. M.: A review of climate geoengineering proposals, Climatic Change, 109, 745–790, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx134"><?xmltex \def\ref@label{{Verburg et~al.(2016)Verburg, Dearing, Dyke, van~der Leeuw,
Seitzinger, Steffen, and Syvitski}}?><label>Verburg et al.(2016)Verburg, Dearing, Dyke, van der Leeuw,
Seitzinger, Steffen, and Syvitski</label><?label Verburg2016?><mixed-citation>
Verburg, P. H., Dearing, J. A., Dyke, J. G., van der Leeuw, S., Seitzinger, S., Steffen, W., and Syvitski, J.: Methods and approaches to modelling the
Anthropocene, Glob. Environ. Change, 39, 328–340, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx135"><?xmltex \def\ref@label{{Vernadsky(1986)}}?><label>Vernadsky(1986)</label><?label Vernadsky1929?><mixed-citation>
Vernadsky, V. I.: The biosphere (An abridged version based on the French
edition of 1929), Synergetic Press, London, UK, 1986.</mixed-citation></ref>
      <ref id="bib1.bibx136"><?xmltex \def\ref@label{{Waters et~al.(2016)Waters, Zalasiewicz, Summerhayes, Barnosky,
Poirier, Ga{\l}uszka, Cearreta, Edgeworth, Ellis, Ellis
et~al.}}?><label>Waters et al.(2016)Waters, Zalasiewicz, Summerhayes, Barnosky,
Poirier, Gałuszka, Cearreta, Edgeworth, Ellis, Ellis
et al.</label><?label waters2016anthropocene?><mixed-citation>Waters, C. N., Zalasiewicz, J., Summerhayes, C., Barnosky, A. D., Poirier, C., Gałuszka, A., Cearreta, A., Edgeworth, M., Ellis, E. C., Ellis, M., Jeandel, C., Leinfelder, R., McNeill, J. R., Richter, D. deB., Steffen, W., Syvitski, J., Vidas, D., Wagreich, M., Williams, M., Zhisheng, A., Grinevald, J., Odada, E., Oreskes, N., Wolfe, A. P.: The Anthropocene is functionally and stratigraphically distinct from
the Holocene, Science, 351, aad2622, <ext-link xlink:href="https://doi.org/10.1126/science.aad2622" ext-link-type="DOI">10.1126/science.aad2622</ext-link>, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx137"><?xmltex \def\ref@label{{Watson(2008)}}?><label>Watson(2008)</label><?label watson2008implications?><mixed-citation>
Watson, A. J.: Implications of an anthropic model of evolution for emergence of complex life and intelligence, Astrobiology, 8, 175–185, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx138"><?xmltex \def\ref@label{{Weiss and Bradley(2001)}}?><label>Weiss and Bradley(2001)</label><?label weiss2001drives?><mixed-citation>
Weiss, H. and Bradley, R. S.: What drives societal collapse?, Science, 291,
609–610, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx139"><?xmltex \def\ref@label{{Wiedermann et~al.(2015)Wiedermann, Donges, Heitzig, Lucht, and
Kurths}}?><label>Wiedermann et al.(2015)Wiedermann, Donges, Heitzig, Lucht, and
Kurths</label><?label Wiedermann2015?><mixed-citation>Wiedermann, M., Donges, J. F., Heitzig, J., Lucht, W., and Kurths, J.:
Macroscopic description of complex adaptive networks co-evolving with dynamic
node states, Phys. Rev. E, 91, 052801, <ext-link xlink:href="https://doi.org/10.1103/PhysRevE.91.052801" ext-link-type="DOI">10.1103/PhysRevE.91.052801</ext-link>, 2015.
</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bibx140"><?xmltex \def\ref@label{{Williamson(1998)}}?><label>Williamson(1998)</label><?label Williamson1998?><mixed-citation>Williamson, O. E.: Transaction cost economics: how it works; where it is
headed, De Economist, 146, 23–58, <ext-link xlink:href="https://doi.org/10.1023/A:1003263908567" ext-link-type="DOI">10.1023/A:1003263908567</ext-link>, 1998.</mixed-citation></ref>
      <ref id="bib1.bibx141"><?xmltex \def\ref@label{{Winkelmann et~al.(2015)Winkelmann, Levermann, Ridgwell, and
Caldeira}}?><label>Winkelmann et al.(2015)Winkelmann, Levermann, Ridgwell, and
Caldeira</label><?label Winkelmann2015?><mixed-citation>Winkelmann, R., Levermann, A., Ridgwell, A., and Caldeira, K.: Combustion of
available fossil fuel resources sufficient to eliminate the Antarctic Ice
Sheet, Science Advances, 1, e1500589, <ext-link xlink:href="https://doi.org/10.1126/sciadv.1500589" ext-link-type="DOI">10.1126/sciadv.1500589</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx142"><?xmltex \def\ref@label{{Woroniecki et~al.(2020)Woroniecki, Wendo, Brink, Islar, Krause,
Vargas, and Mahmoud}}?><label>Woroniecki et al.(2020)Woroniecki, Wendo, Brink, Islar, Krause,
Vargas, and Mahmoud</label><?label woroniecki2020nature?><mixed-citation>Woroniecki, S., Wendo, H., Brink, E., Islar, M., Krause, T., Vargas, A.-M., and Mahmoud, Y.: Nature unsettled: How knowledge and power shape
“nature-based” approaches to societal challenges, Glob. Environ.
Change, 65, 102132, <ext-link xlink:href="https://doi.org/10.1016/j.gloenvcha.2020.102132" ext-link-type="DOI">10.1016/j.gloenvcha.2020.102132</ext-link>, 2020.</mixed-citation></ref>
      <ref id="bib1.bibx143"><?xmltex \def\ref@label{{Yearworth and Cornell(2016)}}?><label>Yearworth and Cornell(2016)</label><?label Yearworth2016?><mixed-citation>
Yearworth, M. and Cornell, S. E.: Contested modelling: a critical examination
of expert modelling in sustainability, Syst. Res. Behav. Sci., 33, 45–63, 2016.</mixed-citation></ref>
      <ref id="bib1.bibx144"><?xmltex \def\ref@label{{Zalasiewicz et~al.(2017)Zalasiewicz, Waters, Wolfe, Barnosky,
Cearreta, Edgeworth, Ellis, Fairchild, Gradstein, Grinevald
et~al.}}?><label>Zalasiewicz et al.(2017)Zalasiewicz, Waters, Wolfe, Barnosky,
Cearreta, Edgeworth, Ellis, Fairchild, Gradstein, Grinevald
et al.</label><?label zalasiewicz2017making?><mixed-citation>
Zalasiewicz, J., Waters, C. N., Wolfe, A. P., Barnosky, A. D., Cearreta, A., Edgeworth, M., Ellis, E. C., Fairchild, I. J., Gradstein, F. M., Grinevald, J., Haff, P., Head, M. J., Ivar do Sul, J. A., Jeandel, C., Leinfelder, R., McNeill, J. R., Oreskes, N., Poirier, C., Revkin, A., Richter, D. deB, Steffen, W., Summerhayes, C., Syvitski, J. P. M., Vidas, D., Wagreich, M., Wing, S., and Williams, M.: Making the case for a formal Anthropocene Epoch: an analysis of
ongoing critiques, Newsl. Stratigr., 50, 205–226, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx145"><?xmltex \def\ref@label{{Zeebe and Zachos(2013)}}?><label>Zeebe and Zachos(2013)</label><?label zeebe2013long?><mixed-citation>Zeebe, R. E. and Zachos, J. C.: Long-term legacy of massive carbon input to the Earth system: Anthropocene versus Eocene, Philos. T. Roy. Soc. A, 371,
20120006, <ext-link xlink:href="https://doi.org/10.1098/rsta.2012.0006" ext-link-type="DOI">10.1098/rsta.2012.0006</ext-link>, 2013.</mixed-citation></ref>

  </ref-list></back>
    <!--<article-title-html>Taxonomies for structuring models for World–Earth systems analysis of the Anthropocene: subsystems, their interactions and social–ecological feedback loops</article-title-html>
<abstract-html/>
<ref-html id="bib1.bib1"><label>Anderies et al.(2013)Anderies, Carpenter, Steffen, and
Rockström</label><mixed-citation>
Anderies, J. M., Carpenter, S., Steffen, W., and Rockström, J.: The
topology of non-linear global carbon dynamics: from tipping points to
planetary boundaries, Environ. Res. Lett., 8, 044048, <a href="https://doi.org/10.1088/1748-9326/8/4/044048" target="_blank">https://doi.org/10.1088/1748-9326/8/4/044048</a>, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>Arneth et al.(2014)Arneth, Brown, and Rounsevell</label><mixed-citation>
Arneth, A., Brown, C., and Rounsevell, M.: Global models of human
decision-making for land-based mitigation and adaptation assessment,
Nat. Clim. Change, 4, 550–557, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>Arrow et al.(2013)Arrow, Cropper, Gollier, Groom, Heal, Newell,
Nordhaus, Pindyck, Pizer, Portney, Sterner, Tol, and Weitzman</label><mixed-citation>
Arrow, K. J., Cropper, M. L., Gollier, C., Groom, B., Heal, G. M., Newell,
R. G., Nordhaus, W. D., Pindyck, R. S., Pizer, W. A., Portney, P. R.,
Sterner, T., Tol, R. S. J., and Weitzman, M. L.: How Should Benefits and
Costs Be Discounted in an Intergenerational Context?, The Views of an Expert Panel (December 19, 2013). Resources for the Future Discussion Paper No. 12–53, <a href="https://doi.org/10.2139/ssrn.2199511" target="_blank">https://doi.org/10.2139/ssrn.2199511</a>, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>Barfuss et al.(2017)Barfuss, Donges, Wiedermann, and
Lucht</label><mixed-citation>
Barfuss, W., Donges, J. F., Wiedermann, M., and Lucht, W.: Sustainable use of renewable resources in a stylized social–ecological network model under heterogeneous resource distribution, Earth Syst. Dynam., 8, 255–264, <a href="https://doi.org/10.5194/esd-8-255-2017" target="_blank">https://doi.org/10.5194/esd-8-255-2017</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>Barfuss et al.(2018)Barfuss, Donges, Lade, and
Kurths</label><mixed-citation>
Barfuss, W., Donges, J. F., Lade, S. J., and Kurths, J.: When optimization for governing human-environment tipping elements is neither sustainable nor safe, Nat. Commun., 9, 1–10, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>Barfuss et al.(2020)Barfuss, Donges, Vasconcelos, Kurths, and
Levin</label><mixed-citation>
Barfuss, W., Donges, J. F., Vasconcelos, V. V., Kurths, J., and Levin, S. A.:
Caring for the future can turn tragedy into comedy for long-term collective
action under risk of collapse, P. Natl. Acad. Sci. USA, 117, 12915–12922, 2020.
</mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>Barrett(1994)</label><mixed-citation>
Barrett, S.: Self-enforcing international environmental agreements, Oxford
Economic Papers, Oxford, UK, 1994.
</mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>Barros et al.(2014)Barros, Field, Dokken, Mastrandrea, Mach, Bilir,
Chatterjee, Ebi, Estrada, Genova, Girma, Kissel, Levy, MacCracken,
Mastrandrea, and White</label><mixed-citation>
Barros, V., Field, C., Dokken, D., Mastrandrea, M., Mach, K., Bilir, T.,
Chatterjee, M., Ebi, K., Estrada, Y., Genova, R., Girma, B., Kissel, E.,
Levy, A., MacCracken, S., Mastrandrea, P., and White, L. (Eds.): Climate
Change 2014: Impacts, Adaptation, and Vulnerability, in: Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, USA, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>Beckage et al.(2018)Beckage, Gross, Lacasse, Carr, Metcalf, Winter,
Howe, Fefferman, Franck, Zia, Kinzig, and Hoffman</label><mixed-citation>
Beckage, B., Gross, L., Lacasse, K., Carr, E., Metcalf, S., Winter, J., Howe,
P., Fefferman, N., Franck, T., Zia, A., Kinzig, A., and Hoffman, F.: Linking
models of human behaviour and climate alters projected climate change, Nat. Clim. Change, 8, 79–84, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>Bienabe and Hearne(2006)</label><mixed-citation>
Bienabe, E. and Hearne, R. R.: Public preferences for biodiversity conservation and scenic beauty within a framework of environmental services payments, Forest Policy Econ., 9, 335–348, 2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>Biggs et al.(2012)Biggs, Schlüter, Biggs, Bohensky, BurnSilver,
Cundill, Dakos, Daw, Evans, Kotschy et al.</label><mixed-citation>
Biggs, R., Schlüter, M., Biggs, D., Bohensky, E. L., BurnSilver, S., Cundill, G., Dakos, V., Daw, T. M., Evans, L. S., Kotschy, K., Leitch, A. M., Meek, C., Quinlan, A., Raudsepp-Hearne, C., Robards, M. D., Schoon, M. L., Schultz, L., and West, P. C.: Toward
principles for enhancing the resilience of ecosystem services,
Annu. Rev. Env. Resour., 37, 421–448, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>Boysen et al.(2017)Boysen, Lucht, and Gerten</label><mixed-citation>
Boysen, L. R., Lucht, W., and Gerten, D.: Trade-offs for food production,
nature conservation and climate limit the terrestrial carbon dioxide removal
potential, Global Change Biol., 23, 4303–4317, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>Brondizio et al.(2016)Brondizio, O'brien, Bai, Biermann, Steffen,
Berkhout, Cudennec, Lemos, Wolfe, Palma-Oliveira et al.</label><mixed-citation>
Brondizio, E. S., O'Brien, K., Bai, X., Biermann, F., Steffen, W., Berkhout, F., Cudennec, C., Lemos, M. C., Wolfe, A., Palma-Oliveira, J., and Chen, C.-T. A.:
Re-conceptualizing the Anthropocene: A call for collaboration,
Glob. Environ. Change, 39, 318–327, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>Brugger et al.(2017)Brugger, Feulner, and Petri</label><mixed-citation>
Brugger, J., Feulner, G., and Petri, S.: Baby, it's cold outside: Climate model simulations of the effects of the asteroid impact at the end of the
Cretaceous, Geophys. Res. Lett., 44, 419–427, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>Brundtland(1987)</label><mixed-citation>
Brundtland, G. H.: Report of the World Commission on Environment and
Development: Our common future, United Nations,  New York,   374 pp., 1987.
</mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>Budyko et al.(1987)Budyko, Ronov, and Yanshin</label><mixed-citation>
Budyko, M. I., Ronov, A. B., and Yanshin, A. L.: History of the Earth's
atmosphere, Springer, Berlin, Germany, 1987.
</mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>Calder et al.(2018)Calder, Craig, Culley, de Cani, Donnelly, Douglas, Edmonds, Gascoigne, Gilbert, Hargrove et al.</label><mixed-citation>
Calder, M., Craig, C., Culley, D., de Cani, R., Donnelly, C. A., Douglas, R., Edmonds, B., Gascoigne, J., Gilbert, N., Hargrove, C., Hinds, D., Lane, D. C., Mitchell, D., Pavey, G., Robertson, D., Rosewell, B., Sherwin, S., Walport, M., and Wilson, A.: Computational
modelling for decision-making: where, why, what, who and how,
Roy. Soc. Open Sci., 5, 172096, <a href="https://doi.org/10.1098/rsos.172096" target="_blank">https://doi.org/10.1098/rsos.172096</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>Calvin and Bond-Lamberty(2018)</label><mixed-citation>
Calvin, K. and Bond-Lamberty, B.: Integrated human-earth system
modeling-state of the science and future directions, Environ. Res. Lett., 13, 063006, <a href="https://doi.org/10.1088/1748-9326/aac642" target="_blank">https://doi.org/10.1088/1748-9326/aac642</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>Caminade et al.(2014)Caminade, Kovats, Rocklov, Tompkins, Morse,
Colón-González, Stenlund, Martens, and Lloyd</label><mixed-citation>
Caminade, C., Kovats, S., Rocklov, J., Tompkins, A. M., Morse, A. P.,
Colón-González, F. J., Stenlund, H., Martens, P., and Lloyd, S. J.:
Impact of climate change on global malaria distribution, P. Natl. Acad. Sci. USA, 111, 3286–3291, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>Castellano et al.(2009)Castellano, Fortunato, and
Loreto</label><mixed-citation>
Castellano, C., Fortunato, S., and Loreto, V.: Statistical physics of social
dynamics, Rev. Mod. Phys., 81, 591–646, <a href="https://doi.org/10.1103/RevModPhys.81.591" target="_blank">https://doi.org/10.1103/RevModPhys.81.591</a>, 2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>Charney et al.(1977)Charney, Quirk, Chow, and
Kornfield</label><mixed-citation>
Charney, J., Quirk, W. J., Chow, S.-H., and Kornfield, J.: A comparative study of the effects of albedo change on drought in semi-arid regions, J. Atmos. Sci., 34, 1366–1385, 1977.
</mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>Colding and Folke(2001)</label><mixed-citation>
Colding, J. and Folke, C.: Social taboos: “invisible” systems of local
resource management and biological conservation, Ecol. Appl., 11,
584–600, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>Crutzen(2002)</label><mixed-citation>
Crutzen, P. J.: Geology of mankind, Nature, 415, p. 23, <a href="https://doi.org/10.1038/415023a" target="_blank">https://doi.org/10.1038/415023a</a>, 2002.
</mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>Cumming and Peterson(2017)</label><mixed-citation>
Cumming, G. S. and Peterson, G. D.: Unifying research on social-ecological
resilience and collapse, Trends Ecol. Evol., 32, 695–713, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>Dearing et al.(2014)Dearing, Wang, Zhang, Dyke, Haberl, Hossain,
Langdon, Lenton, Raworth, Brown et al.</label><mixed-citation>
Dearing, J. A., Wang, R., Zhang, K., Dyke, J. G., Haberl, H., Hossain, Md. S., Langdon, P. G., Lenton, T. M., Raworth, K., Brown, S., Carstensen, J., Cole, M. J., Cornell, S. E., Dawson, T. P., Doncaster, C. P., Eigenbrod, F., Flörke, M., Jeffers, E., Mackay, A. W., Nykvist, B., and Poppy, G. M.: Safe and just
operating spaces for regional social-ecological systems, Glob. Environ. Change, 28, 227–238, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>Di Baldassarre et al.(2017)Di Baldassarre, Martinez, Kalantari, and
Viglione</label><mixed-citation>
Di Baldassarre, G., Martinez, F., Kalantari, Z., and Viglione, A.: Drought and flood in the Anthropocene: feedback mechanisms in reservoir operation, Earth Syst. Dynam., 8, 225–233, <a href="https://doi.org/10.5194/esd-8-225-2017" target="_blank">https://doi.org/10.5194/esd-8-225-2017</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>Donges et al.(2015)Donges, Donner, Marwan, Breitenbach, Rehfeld, and Kurths</label><mixed-citation>
Donges, J. F., Donner, R. V., Marwan, N., Breitenbach, S. F. M., Rehfeld, K., and Kurths, J.: Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns, Clim. Past, 11, 709–741, <a href="https://doi.org/10.5194/cp-11-709-2015" target="_blank">https://doi.org/10.5194/cp-11-709-2015</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>Donges et al.(2017a)Donges, Lucht, Müller-Hansen,
and Steffen</label><mixed-citation>
Donges, J. F., Lucht, W., Müller-Hansen, F., and Steffen, W.: The
technosphere in Earth System analysis: A coevolutionary perspective,
The Anthropocene Review, 4, 23–33, 2017a.
</mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>Donges et al.(2017b)Donges, Winkelmann, Lucht, Cornell, Dyke, Rockström, Heitzig, and Schellnhuber</label><mixed-citation>
Donges, J. F., Winkelmann, R., Lucht, W., Cornell, S. E., Dyke, J. G.,
Rockström, J., Heitzig, J., and Schellnhuber, H. J.: Closing the loop:
Reconnecting human dynamics to Earth System science, The Anthropocene
Review, 4, 151–157, 2017b.
</mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>Donges et al.(2020)Donges, Heitzig, Barfuss, Wiedermann, Kassel,
Kittel, Kolb, Kolster, Müller-Hansen, Otto, Zimmerer, and
Lucht</label><mixed-citation>
Donges, J. F., Heitzig, J., Barfuss, W., Wiedermann, M., Kassel, J. A., Kittel, T., Kolb, J. J., Kolster, T., Müller-Hansen, F., Otto, I. M., Zimmerer, K. B., and Lucht, W.: Earth system modeling with endogenous and dynamic human societies: the copan:CORE open World–Earth modeling framework, Earth Syst. Dynam., 11, 395–413, <a href="https://doi.org/10.5194/esd-11-395-2020" target="_blank">https://doi.org/10.5194/esd-11-395-2020</a>, 2020.
</mixed-citation></ref-html>
<ref-html id="bib1.bib31"><label>Edenhofer et al.(2014)Edenhofer, Pichs-Madruga, Sokona, Farahani,
Kadner, Seyboth, Adler, Baum, Brunner, Eickemeier, Kriemann, Savolainen,
Schlömer, von Stechow, Zwickel, and Minx</label><mixed-citation>
Edenhofer, O., Pichs-Madruga, R., Sokona, Y., Farahani, E., Kadner, S.,
Seyboth, K., Adler, A., Baum, I., Brunner, S., Eickemeier, P., Kriemann, B.,
Savolainen, J., Schlömer, S., von Stechow, C., Zwickel, T., and Minx,
J. (Eds.): Climate Change 2014: Mitigation of Climate Change, in: Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, Cambridge University Press, Cambridge, United
Kingdom and New York, USA, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib32"><label>Farmer and Foley(2009)</label><mixed-citation>
Farmer, J. D. and Foley, D.: The economy needs agent-based modelling, Nature,
460, 685–686, 2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib33"><label>Fischer-Kowalski(2003)</label><mixed-citation>
Fischer-Kowalski, M.: On the history of industrial metabolism, in:
Perspectives on Industrial Ecology, edited by: Bourg, D.,  Erkman, S., and  Chirac, J., Routledge, London, 35–45, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib34"><label>Fischer-Kowalski and Erb(2006)</label><mixed-citation>
Fischer-Kowalski, M. and Erb, K.-H.: Epistemologische und konzeptuelle
Grundlagen der sozialen Ökologie, Mitt. Osterr. Geogr. G., 148, 33–56, 2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib35"><label>Fischer-Kowalski and Haberl(1993)</label><mixed-citation>
Fischer-Kowalski, M. and Haberl, H.: Metabolism and colonization, Modes of
production and the physical exchange between societies and nature,
Innovation-Abingdon, 6, 415–442, 1993.
</mixed-citation></ref-html>
<ref-html id="bib1.bib36"><label>Fischer-Kowalski and Hüttler(1998)</label><mixed-citation>
Fischer-Kowalski, M. and Hüttler, W.: Society's metabolism,
J. Ind. Ecol., 2, 107–136, 1998.
</mixed-citation></ref-html>
<ref-html id="bib1.bib37"><label>Flato et al.(2013)Flato, Marotzke, Abiodun, Braconnot, Chou, Collins, Cox, Driouech, Emori, Eyring, Forest, Gleckler, Guilyardi, Jakob, Kattsov, Reason, and Rummukainen</label><mixed-citation>
Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S., Collins, W.,
Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P.,
Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and Rummukainen, M.:
Evaluation of Climate Models, in: Climate Change 2013 – The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, USA, 741–866, <a href="https://doi.org/10.1017/CBO9781107415324.020" target="_blank">https://doi.org/10.1017/CBO9781107415324.020</a>, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib38"><label>Flato(2011)</label><mixed-citation>
Flato, G. M.: Earth system models: an overview, WIRES. Clim. Change, 2, 783–800, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib39"><label>Folke(2006)</label><mixed-citation>
Folke, C.: Resilience: The emergence of a perspective for social-ecological
systems analyses, Glob. Environ. Change, 16, 253–267, 2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib40"><label>Folke et al.(2011)Folke, Jansson, Rockström, Olsson, Carpenter,
Chapin III, Crépin, Daily, Danell, Ebbesson
et al.</label><mixed-citation>
Folke, C., Jansson, Å., Rockström, J., Olsson, P., Carpenter, S. R., Chapin, F. S., Crépin, A.-S., Daily, G., Danell, K., Ebbesson, J., Elmqvist, T., Galaz, V., Moberg, F., Nilsson, M., Österblom, H., Ostrom, E., Persson, Å., Peterson, G., Polasky, S., Steffen, W., Walker, B., and Westley, F.: Reconnecting to the biosphere, AMBIO, 40, 719–738, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib41"><label>Folke et al.(2016)Folke, Biggs, Norström, Reyers, and
Rockström</label><mixed-citation>
Folke, C., Biggs, R., Norström, A. V., Reyers, B., and Rockström, J.:
Social-ecological resilience and biosphere-based sustainability science,
Ecol. Soc., 21, 41, <a href="https://doi.org/10.5751/ES-08748-210341" target="_blank">https://doi.org/10.5751/ES-08748-210341</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib42"><label>Gabriel(2013)</label><mixed-citation>
Gabriel, M.: Warum es die Welt nicht gibt, Ullstein, Berlin, 270 pp., 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib43"><label>Gaines et al.(2010)Gaines, White, Carr, and
Palumbi</label><mixed-citation>
Gaines, S. D., White, C., Carr, M. H., and Palumbi, S. R.: Designing marine
reserve networks for both conservation and fisheries management, P. Natl. Acad. Sci. USA, 107, 18286–18293, 2010.
</mixed-citation></ref-html>
<ref-html id="bib1.bib44"><label>Ganopolski et al.(2016)Ganopolski, Winkelmann, and
Schellnhuber</label><mixed-citation>
Ganopolski, A., Winkelmann, R., and Schellnhuber, H. J.: Critical
insolation-CO<sub>2</sub> relation for diagnosing past and future glacial inception, Nature, 529, 200–203, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib45"><label>Garrett(2015)</label><mixed-citation>
Garrett, T. J.: Long-run evolution of the global economy – Part 2: Hindcasts of innovation and growth, Earth Syst. Dynam., 6, 673–688, <a href="https://doi.org/10.5194/esd-6-673-2015" target="_blank">https://doi.org/10.5194/esd-6-673-2015</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib46"><label>Geier et al.(2019)Geier, Barfuss, Wiedermann, Kurths, and
Donges</label><mixed-citation>
Geier, F., Barfuss, W., Wiedermann, M., Kurths, J., and Donges, J. F.: The
physics of governance networks: critical transitions in contagion dynamics on
multilayer adaptive networks with application to the sustainable use of
renewable resources, Eur. Phys. J.-Spec. Top., 228, 2357–2369, 2019.
</mixed-citation></ref-html>
<ref-html id="bib1.bib47"><label>Gerten et al.(2018)Gerten, Schönfeld, and Schauberger</label><mixed-citation>
Gerten, D., Schönfeld, M., and Schauberger, B.: On deeper human dimensions in Earth system analysis and modelling, Earth Syst. Dynam., 9, 849–863, <a href="https://doi.org/10.5194/esd-9-849-2018" target="_blank">https://doi.org/10.5194/esd-9-849-2018</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib48"><label>Gregory et al.(2009)Gregory, Jones, Cadule, and
Friedlingstein</label><mixed-citation>
Gregory, J. M., Jones, C., Cadule, P., and Friedlingstein, P.: Quantifying
carbon cycle feedbacks, J. Climate, 22, 5232–5250, 2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib49"><label>Haff(2012)</label><mixed-citation>
Haff, P. K.: Technology and human purpose: the problem of solids transport on the Earth's surface, Earth Syst. Dynam., 3, 149–156, <a href="https://doi.org/10.5194/esd-3-149-2012" target="_blank">https://doi.org/10.5194/esd-3-149-2012</a>, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib50"><label>Haff(2014)</label><mixed-citation>
Haff, P. K.: Humans and technology in the Anthropocene: Six rules, The
Anthropocene Review, 1, 126–136, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib51"><label>Hamilton(2015)</label><mixed-citation>
Hamilton, C.: Getting the Anthropocene so wrong, The Anthropocene Review, 2,
102–107, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib52"><label>Harfoot et al.(2014)Harfoot, Newbold, Tittensor, Emmott, Hutton,
Lyutsarev, Smith, Scharlemann, and Purves</label><mixed-citation>
Harfoot, M. B., Newbold, T., Tittensor, D. P., Emmott, S., Hutton, J.,
Lyutsarev, V., Smith, M. J., Scharlemann, J. P., and Purves, D. W.: Emergent
global patterns of ecosystem structure and function from a mechanistic
general ecosystem model, PLoS Biol., 12, e1001841, <a href="https://doi.org/10.1371/journal.pbio.1001841" target="_blank">https://doi.org/10.1371/journal.pbio.1001841</a>, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib53"><label>Heck et al.(2016)Heck, Donges, and Lucht</label><mixed-citation>
Heck, V., Donges, J. F., and Lucht, W.: Collateral transgression of planetary boundaries due to climate engineering by terrestrial carbon dioxide removal, Earth Syst. Dynam., 7, 783–796, <a href="https://doi.org/10.5194/esd-7-783-2016" target="_blank">https://doi.org/10.5194/esd-7-783-2016</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib54"><label>Heitzig and Donges(2021)</label><mixed-citation>
Heitzig, J. and Donges, J.: pycopandiscount v1.0,  Zenodo [code],  <a href="https://doi.org/10.5281/zenodo.4704936" target="_blank">https://doi.org/10.5281/zenodo.4704936</a>, 2021.
</mixed-citation></ref-html>
<ref-html id="bib1.bib55"><label>Heitzig et al.(2016)Heitzig, Kittel, Donges, and
Molkentin</label><mixed-citation>
Heitzig, J., Kittel, T., Donges, J. F., and Molkenthin, N.: Topology of sustainable management of dynamical systems with desirable states: from defining planetary boundaries to safe operating spaces in the Earth system, Earth Syst. Dynam., 7, 21–50, <a href="https://doi.org/10.5194/esd-7-21-2016" target="_blank">https://doi.org/10.5194/esd-7-21-2016</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib56"><label>Heitzig et al.(2018)Heitzig, Barfuss, and
Donges</label><mixed-citation>
Heitzig, J., Barfuss, W., and Donges, J. F.: A thought experiment on
sustainable management of the earth system, Sustainability-Basel, 10, 1947, <a href="https://doi.org/10.3390/su10061947" target="_blank">https://doi.org/10.3390/su10061947</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib57"><label>Herrmann-Pillath(2018)</label><mixed-citation>
Herrmann-Pillath, C.: The case for a new discipline: technosphere science,
Ecol. Econ., 149, 212–225, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib58"><label>Herrmann-Pillath(2020)</label><mixed-citation>
Herrmann-Pillath, C.: The art of co-creation: An intervention in the philosophy of ecological economics, Ecol. Econ., 169, 106526, <a href="https://doi.org/10.1016/j.ecolecon.2019.106526" target="_blank">https://doi.org/10.1016/j.ecolecon.2019.106526</a>, 2020.
</mixed-citation></ref-html>
<ref-html id="bib1.bib59"><label>Jarvis et al.(2015)Jarvis, Jarvis, and Hewitt</label><mixed-citation>
Jarvis, A. J., Jarvis, S. J., and Hewitt, C. N.: Resource acquisition, distribution and end-use efficiencies and the growth of industrial society, Earth Syst. Dynam., 6, 689–702, <a href="https://doi.org/10.5194/esd-6-689-2015" target="_blank">https://doi.org/10.5194/esd-6-689-2015</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib60"><label>Jax et al.(2013)Jax, Barton, Chan, De Groot, Doyle, Eser, Görg,
Gómez-Baggethun, Griewald, Haber et al.</label><mixed-citation>
Jax, K., Barton, D. N., Chan, K. M. A., de Groot, R., Doyle, U., Eser, U., Görg, C., Gómez-Baggethun, E., Griewald, Y., Haber, W., Haines-Young, R., Heink, U., Jahn, T., Joosten, H., Kerschbaumer, L., Korn, H., Luck, G. W., Matzdorf, B., Muraca, B., Neßhöver, C., Norton, B., Ott, K., Potschin, M., Rauschmayer, F., von Haaren, C., and Wichmann, S.:
Ecosystem services and ethics, Ecol. Econ., 93, 260–268, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib61"><label>Jentoft et al.(2007)Jentoft, van Son, and Bjørkan</label><mixed-citation>
Jentoft, S., van Son, T. C., and Bjørkan, M.: Marine protected areas: a
governance system analysis, Hum. Ecol., 35, 611–622, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib62"><label>Kates et al.(2001)Kates, Clark, Corell, Hall, Jaeger, Lowe, McCarthy, Schellnhuber, Bolin, Dickson, Faucheux, Gallopin, Grübler, Huntley, Jäger, Jodha, Kasperson, Mabogunje, Matson, Mooney, III, and Uno Svedin</label><mixed-citation>
Kates, R. W., Clark, W. C., Corell, R., Hall, J. M., Jaeger, C. C., Lowe, I.,
McCarthy, J. J., Schellnhuber, H. J., Bolin, B., Dickson, N. M., Faucheux,
S., Gallopin, G. C., Grübler, A., Huntley, B., Jäger, J., Jodha,
N. S., Kasperson, R. E., Mabogunje, A., Matson, P., Mooney, H., Moore III, B., O'Riordan, T., and Svedin, U.: Sustainability Science, Science, 292, 641–642, <a href="https://doi.org/10.1126/science.1059386" target="_blank">https://doi.org/10.1126/science.1059386</a>, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib63"><label>Kellie-Smith and Cox(2011)</label><mixed-citation>
Kellie-Smith, O. and Cox, P. M.: Emergent dynamics of the climate-economy
system in the Anthropocene, Philos. T. Roy. Soc. A, 369, 868–886, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib64"><label>Keys and Wang-Erlandsson(2017)</label><mixed-citation>
Keys, P. W. and Wang-Erlandsson, L.: On the social dynamics of moisture recycling, Earth Syst. Dynam., 9, 829–847, <a href="https://doi.org/10.5194/esd-9-829-2018" target="_blank">https://doi.org/10.5194/esd-9-829-2018</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib65"><label>Kleidon(2016)</label><mixed-citation>
Kleidon, A.: Thermodynamic foundations of the Earth system, Cambridge
University Press, Cambridge, UK, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib66"><label>Lade et al.(2015)Lade, Niiranen, Hentati-Sundberg, Blenckner,
Boonstra, Orach, Quaas, Österblom, and Schlüter</label><mixed-citation>
Lade, S. J., Niiranen, S., Hentati-Sundberg, J., Blenckner, T., Boonstra,
W. J., Orach, K., Quaas, M. F., Österblom, H., and Schlüter, M.: An
empirical model of the Baltic Sea reveals the importance of social dynamics
for ecological regime shifts, P. Natl. Acad. Sci. USA, 112, 11120–11125, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib67"><label>Lade et al.(2017a)Lade, Donges, Fetzer, Anderies, Beer, Cornell, Gasser, Norberg, Richardson, Rockström, and Steffen</label><mixed-citation>
Lade, S. J., Donges, J. F., Fetzer, I., Anderies, J. M., Beer, C., Cornell, S. E., Gasser, T., Norberg, J., Richardson, K., Rockström, J., and Steffen, W.: Analytically tractable climate–carbon cycle feedbacks under 21st century anthropogenic forcing, Earth Syst. Dynam., 9, 507–523, <a href="https://doi.org/10.5194/esd-9-507-2018" target="_blank">https://doi.org/10.5194/esd-9-507-2018</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib68"><label>Lade et al.(2017)Lade, Haider, Engström, and
Schlüter</label><mixed-citation>
Lade, S. J., Haider, L. J., Engström, G., and Schlüter, M.: Resilience offers escape from trapped thinking on poverty alleviation, Science Advances, 3, e1603043, <a href="https://doi.org/10.1126/sciadv.1603043" target="_blank">https://doi.org/10.1126/sciadv.1603043</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib69"><label>Latour(2017)</label><mixed-citation>
Latour, B.: Facing Gaia: Eight lectures on the new climatic regime, John  Polity Press, Cambridge, UK,  327 pp., 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib70"><label>Lenton et al.(2004)Lenton, Schellnhuber, and
Szathmary</label><mixed-citation>
Lenton, T., Schellnhuber, H., and Szathmary, E.: Climbing the co-evolution
ladder, Nature, 431,  913, <a href="https://doi.org/10.1038/431913a" target="_blank">https://doi.org/10.1038/431913a</a>, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib71"><label>Lenton and Latour(2018)</label><mixed-citation>
Lenton, T. M. and Latour, B.: Gaia 2.0, Science, 361, 1066–1068, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib72"><label>Lenton et al.(2016)Lenton, Pichler, and Weisz</label><mixed-citation>
Lenton, T. M., Pichler, P.-P., and Weisz, H.: Revolutions in energy input and material cycling in Earth history and human history, Earth Syst. Dynam., 7, 353–370, <a href="https://doi.org/10.5194/esd-7-353-2016" target="_blank">https://doi.org/10.5194/esd-7-353-2016</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib73"><label>Leontief(1936)</label><mixed-citation>
Leontief, W. W.: Quantitative input and output relations in the economic
systems of the United States, Rev. Econ. Statistics, 18,
105–125, 1936.
</mixed-citation></ref-html>
<ref-html id="bib1.bib74"><label>Lewis and Maslin(2015)</label><mixed-citation>
Lewis, S. L. and Maslin, M. A.: Defining the anthropocene, Nature, 519,
171–180, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib75"><label>Lewis-Beck and Ratto(2013)</label><mixed-citation>
Lewis-Beck, M. S. and Ratto, M. C.: Economic voting in Latin America: A general model, Elect. Stud., 32, 489–493, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib76"><label>Lovelock(1989)</label><mixed-citation>
Lovelock, J. E.: Geophysiology, the science of Gaia, Rev. Geophys.,
27, 215–222, 1989.
</mixed-citation></ref-html>
<ref-html id="bib1.bib77"><label>Lovelock and Margulis(1974)</label><mixed-citation>
Lovelock, J. E. and Margulis, L.: Atmospheric homeostasis by and for the
biosphere: the Gaia hypothesis, Tellus, 26, 2–10, 1974.
</mixed-citation></ref-html>
<ref-html id="bib1.bib78"><label>Lucht and Pachauri(2004)</label><mixed-citation>
Lucht, W. and Pachauri, R.: The mental component of the Earth system, in:
Earth system analysis for sustainability, edited by: Schellnhuber, H.-J.,
Crutzen, P., Clark, W., Claussen, M., and Held, H., Dahlem Workshop Reports,
Cambridge University Press, Cambridge, UK, 341–365, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib79"><label>Lutz and Skirbekk(2008)</label><mixed-citation>
Lutz, W. and Skirbekk, V.: Low fertility in Europe in a global demographic
context, in: Demographic Change and Intergenerational Justice,
Springer, Berlin, Heidelberg, 3–19, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib80"><label>Martin and Schlüter(2015)</label><mixed-citation>
Martin, R. and Schlüter, M.: Combining system dynamics and agent-based
modeling to analyze social-ecological interactions – an example from modeling restoration of a shallow lake, Front. Environ. Sci., 3, 66, <a href="https://doi.org/10.3389/fenvs.2015.00066" target="_blank">https://doi.org/10.3389/fenvs.2015.00066</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib81"><label>Masterson et al.(2017)Masterson, Stedman, Enqvist, Tengö, Giusti, Wahl, and Svedin</label><mixed-citation>
Masterson, V., Stedman, R., Enqvist, J., Tengö, M., Giusti, M., Wahl, D.,
and Svedin, U.: The contribution of sense of place to social-ecological
systems research: a review and research agenda, Ecol. Soc., 22,  49, <a href="https://doi.org/10.5751/ES-08872-220149" target="_blank">https://doi.org/10.5751/ES-08872-220149</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib82"><label>Mengel et al.(2018)Mengel, Nauels, Rogelj, and
Schleussner</label><mixed-citation>
Mengel, M., Nauels, A., Rogelj, J., and Schleussner, C.-F.: Committed sea-level rise under the Paris Agreement and the legacy of delayed mitigation action, Nat. Commun., 9, 601, <a href="https://doi.org/10.1038/s41467-018-02985-8" target="_blank">https://doi.org/10.1038/s41467-018-02985-8</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib83"><label>Millennium Ecosystem Assessment(2005)</label><mixed-citation>
Millennium Ecosystem Assessment: Ecosystems and human well-being, Island
Press, Washington, D.C., USA, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib84"><label>Milo et al.(2002)Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii, and Alon</label><mixed-citation>
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon,
U.: Network motifs: simple building blocks of complex networks, Science, 298,
824–827, 2002.
</mixed-citation></ref-html>
<ref-html id="bib1.bib85"><label>Mooney et al.(2013)Mooney, Duraiappah, and Larigauderie</label><mixed-citation>
Mooney, H. A., Duraiappah, A., and Larigauderie, A.: Evolution of natural and
social science interactions in global change research programs, P. Natl. Acad. Sci. USA, 110, 3665–3672, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib86"><label>Morton(2013)</label><mixed-citation>
Morton, T.: Hyperobjects: Philosophy and Ecology after the End of the World, University of Minnesota Press, Minneapolis, 240 pp., 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib87"><label>Müller-Hansen et al.(2017)Müller-Hansen, Schlüter,
Mäs, Donges, Kolb, Thonicke, and Heitzig</label><mixed-citation>
Müller-Hansen, F., Schlüter, M., Mäs, M., Donges, J. F., Kolb, J. J., Thonicke, K., and Heitzig, J.: Towards representing human behavior and decision making in Earth system models – an overview of techniques and approaches, Earth Syst. Dynam., 8, 977–1007, <a href="https://doi.org/10.5194/esd-8-977-2017" target="_blank">https://doi.org/10.5194/esd-8-977-2017</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib88"><label>National Research Council(1986)</label><mixed-citation>
National Research Council: Earth System Science: Overview: A Program for
Global Change, Washington, DC, The National Academies Press,
<a href="https://doi.org/10.17226/19210" target="_blank">https://doi.org/10.17226/19210</a>, 1986.
</mixed-citation></ref-html>
<ref-html id="bib1.bib89"><label>National Research Council(1988)</label><mixed-citation>
National Research Council: Earth System Science: A closer view, Washington, DC, The National
Academies Press, available at: <a href="https://doi.org/10.17226/19088" target="_blank"/>, 1988.
</mixed-citation></ref-html>
<ref-html id="bib1.bib90"><label>National Research Council(2007)</label><mixed-citation>
National Research Council: Models in Environmental Regulatory Decision
Making, The National Academies Press, Washington, D.C., USA, 286 pp., <a href="https://doi.org/10.17226/11972" target="_blank">https://doi.org/10.17226/11972</a>, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib91"><label>Nelson et al.(2014)Nelson, Valin, Sands, Havlík, Ahammad,
Deryng, Elliott, Fujimori, Hasegawa, Heyhoe et al.</label><mixed-citation>
Nelson, G. C., Valin, H., Sands, R. D., Havlík, P., Ahammad, H., Deryng, D., Elliott, J., Fujimori, S., Hasegawa, T., Heyhoe, E., Kyle, P., Lampe, M. V., Lotze-Campen, H., d’Croz, D. M., van  Meijl, H., van der  Mensbrugghe, D., Müller, C., Popp, A., Robertson, R., Robinson, S., Schmid, E., Schmitz, C., Tabeau, A., and Willenbockel, D.: Climate
change effects on agriculture: Economic responses to biophysical shocks,
P. Natl. Acad. Sci. USA, 111, 3274–3279, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib92"><label>Nitzbon et al.(2017)Nitzbon, Heitzig, and Parlitz</label><mixed-citation>
Nitzbon, J., Heitzig, J., and Parlitz, U.: Sustainability, collapse and
oscillations in a simple World-Earth model, Environ. Res. Lett., 12, 074020,  <a href="https://doi.org/10.1088/1748-9326/aa7581" target="_blank">https://doi.org/10.1088/1748-9326/aa7581</a>, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib93"><label>Nordhaus(1992)</label><mixed-citation>
Nordhaus, W. D.: An optimal transition path for controlling greenhouse gases,
Science, 258, 1315–1319, 1992.
</mixed-citation></ref-html>
<ref-html id="bib1.bib94"><label>Nordhaus(2017)</label><mixed-citation>
Nordhaus, W. D.: Revisiting the social cost of carbon, P. Natl. Acad. Sci. USA,  114,  1518–1523, <a href="https://doi.org/10.1073/pnas.1609244114" target="_blank">https://doi.org/10.1073/pnas.1609244114</a>,  2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib95"><label>Ostrom(2009)</label><mixed-citation>
Ostrom, E.: A general framework for analyzing sustainability of
social-ecological systems, Science, 325, 419–422, 2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib96"><label>Ostrom et al.(2007)Ostrom, Janssen, and Anderies</label><mixed-citation>
Ostrom, E., Janssen, M. A., and Anderies, J. M.: Going beyond panaceas,
P. Natl. Acad. Sci. USA, 104, 15176–15178, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib97"><label>Otto et al.(2017)Otto, Willner, Wenz, Frieler, and
Levermann</label><mixed-citation>
Otto, C., Willner, S. N., Wenz, L., Frieler, K., and Levermann, A.: Modeling
loss-propagation in the global supply network: The dynamic agent-based model
acclimate, J. Econ. Dyn. Control, 83, 232–269, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib98"><label>Otto et al.(2020a)Otto, Donges, Cremades, Bhowmik,
Hewitt, Lucht, Rockström, Allerberger, McCaffrey, Doe
et al.</label><mixed-citation>
Otto, I. M., Donges, J. F., Cremades, R., Bhowmik, A., Hewitt, R. J., Lucht, W., Rockström, J., Allerberger, F., McCaffrey, M., Doe, S. S. P., Lenferna, A., Morán, N., van  Vuuren, D. P., and Schellnhuber, H. J.:
Social tipping dynamics for stabilizing Earth's climate by 2050,
P. Natl. Acad. Sci. USA, 117, 2354–2365, 2020a.
</mixed-citation></ref-html>
<ref-html id="bib1.bib99"><label>Otto et al.(2020b)Otto, Wiedermann, Cremades, Donges,
Auer, and Lucht</label><mixed-citation>
Otto, I. M., Wiedermann, M., Cremades, R., Donges, J. F., Auer, C., and Lucht, W.: Human agency in the anthropocene, Ecol. Econ., 167, 106463, <a href="https://doi.org/10.1016/j.ecolecon.2019.106463" target="_blank">https://doi.org/10.1016/j.ecolecon.2019.106463</a>, 2020b.
</mixed-citation></ref-html>
<ref-html id="bib1.bib100"><label>Perman et al.(2003)</label><mixed-citation>
Perman, R., Ma, Y., McGilvray, J., and Common, M.:: Natural resource and environmental economics, Pearson Education, Harlow, England, 726 pp.
2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib101"><label>Phalan(2018)</label><mixed-citation>
Phalan, B. T.: What have we learned from the land sparing-sharing model?,
Sustainability-Basel, 10, 1760, <a href="https://doi.org/10.3390/su10061760" target="_blank">https://doi.org/10.3390/su10061760</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib102"><label>Purves et al.(2013)Purves, Scharlemann, Harfoot, Newbold, Tittensor, Hutton, and Emmott</label><mixed-citation>
Purves, D., Scharlemann, J. P., Harfoot, M., Newbold, T., Tittensor, D. P.,
Hutton, J., and Emmott, S.: Ecosystems: time to model all life on Earth,
Nature, 493, 295–297, <a href="https://doi.org/10.1038/493295a" target="_blank">https://doi.org/10.1038/493295a</a>, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib103"><label>Raworth(2012)</label><mixed-citation>
Raworth, K.: A safe and just space for humanity: can we live within the
doughnut, Oxfam Policy and Practice: Climate Change and Resilience, Oxfam International, available at: <a href="https://oxfamilibrary.openrepository.com/handle/10546/210490?show=full" target="_blank"/> (last access: 24 September 2021), 8, 1–26, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib104"><label>Reichler and Kim(2008)</label><mixed-citation>
Reichler, T. and Kim, J.: How well do coupled models simulate today's climate?, B. Am. Meteorol. Soc., 89, 303–311, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib105"><label>Renn(2018)</label><mixed-citation>
Renn, J.: The Evolution of Knowledge: Rethinking Science in the Anthropocene,
HoST-Journal of History of Science and Technology, 12, 1–22, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib106"><label>Robinson et al.(2017)Robinson, Di Vittorio, Alexander, Arneth,
Barton, Brown, Kettner, Lemmen, O'Neill, Janssen, Pugh, Rabin, Rounsevell,
Syvitski, Ullah, and Verburg</label><mixed-citation>
Robinson, D. T., Di Vittorio, A., Alexander, P., Arneth, A., Barton, C. M., Brown, D. G., Kettner, A., Lemmen, C., O'Neill, B. C., Janssen, M., Pugh, T. A. M., Rabin, S. S., Rounsevell, M., Syvitski, J. P., Ullah, I., and Verburg, P. H.: Modelling feedbacks between human and natural processes in the land system, Earth Syst. Dynam., 9, 895–914, <a href="https://doi.org/10.5194/esd-9-895-2018" target="_blank">https://doi.org/10.5194/esd-9-895-2018</a>, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib107"><label>Rocha et al.(2015)Rocha, Peterson, and Biggs</label><mixed-citation>
Rocha, J. C., Peterson, G. D., and Biggs, R.: Regime shifts in the
Anthropocene: drivers, risks, and resilience, PLoS One, 10, e0134639, <a href="https://doi.org/10.1371/journal.pone.0134639" target="_blank">https://doi.org/10.1371/journal.pone.0134639</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib108"><label>Rockström et al.(2009a)Rockström, Steffen,
Noone, Persson, Chapin, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et al.</label><mixed-citation>
Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F. S., Lambin, E. F., Lenton, T. M., Scheffer, M., Folke, C., Schellnhuber, H. J., Nykvist, B., de Wit, C. A., Hughes, T., van der Leeuw, S., Rodhe, H., Sörlin, S., Snyder, P. K., Costanza, R., Svedin, U., Falkenmark, M., Karlberg, L., Corell, R. W., Fabry, V. J., Hansen, J., Walker, B., Liverman, D., Richardson, K., Crutzen, P., and Foley, J. A.: A safe operating space for humanity, Nature, 461, 472–475,
2009a.
</mixed-citation></ref-html>
<ref-html id="bib1.bib109"><label>Rockström et al.(2009b)Rockström, Steffen,
Noone, Persson, Chapin III, Lambin, Lenton, Scheffer, Folke, Schellnhuber
et al.</label><mixed-citation>
Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F. S. I., Lambin, E., Lenton, T., Scheffer, M., Folke, C., Schellnhuber, H. J., Nykvist, B., de Wit, C., Hughes, T., van der Leeuw, S., Rodhe, H., Sörlin, S., Snyder, P., Costanza, R., Svedin, U., Falkenmark, M., Karlberg, L., Corell, R., Fabry, V., Hansen, J., Walker, B., Liverman, D., Richardson, K., Crutzen, P., and Foley, J.: Planetary Boundaries: Exploring the Safe Operating Space for
Humanity, Ecol. Soc., 14, 32, <a href="https://doi.org/10.5751/ES-03180-140232" target="_blank">https://doi.org/10.5751/ES-03180-140232</a>, 2009b.
</mixed-citation></ref-html>
<ref-html id="bib1.bib110"><label>Rockström et al.(2017)Rockström, Gaffney, Rogelj,
Meinshausen, Nakicenovic, and Schellnhuber</label><mixed-citation>
Rockström, J., Gaffney, O., Rogelj, J., Meinshausen, M., Nakicenovic, N.,
and Schellnhuber, H. J.: A roadmap for rapid decarbonization, Science, 355,
1269–1271, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib111"><label>Rounsevell et al.(2014)Rounsevell, Arneth, Alexander, Brown,
de Noblet-Ducoudré, Ellis, Finnigan, Galvin, Grigg, Harman
et al.</label><mixed-citation>
Rounsevell, M. D. A., Arneth, A., Alexander, P., Brown, D. G., de Noblet-Ducoudré, N., Ellis, E., Finnigan, J., Galvin, K., Grigg, N., Harman, I., Lennox, J., Magliocca, N., Parker, D., O'Neill, B. C., Verburg, P. H., and Young, O.: Towards decision-based global land use models for improved understanding of the Earth system, Earth Syst. Dynam., 5, 117–137, <a href="https://doi.org/10.5194/esd-5-117-2014" target="_blank">https://doi.org/10.5194/esd-5-117-2014</a>, 2014.
</mixed-citation></ref-html>
<ref-html id="bib1.bib112"><label>Schellnhuber(1998)</label><mixed-citation>
Schellnhuber, H.-J.: Discourse: Earth system analysis – The scope of the
challenge, in: Earth system analysis: Integrating science for
sustainability, edited by: Schellnhuber, H.-J. and Wenzel, V.,
Springer, Berlin, Germany, 3–195, 1998.
</mixed-citation></ref-html>
<ref-html id="bib1.bib113"><label>Schellnhuber(1999)</label><mixed-citation>
Schellnhuber, H. J.: Earth system analysis and the second Copernican
revolution, Nature, 402, 19–23, 1999.
</mixed-citation></ref-html>
<ref-html id="bib1.bib114"><label>Schill et al.(2019)Schill, Anderies, Lindahl, Folke, Polasky,
Cárdenas, Crépin, Janssen, Norberg, and
Schlüter</label><mixed-citation>
Schill, C., Anderies, J. M., Lindahl, T., Folke, C., Polasky, S., Cárdenas, J. C., Crépin, A.-S., Janssen, M. A., Norberg, J., and Schlüter, M.: A more dynamic understanding of human behaviour for the Anthropocene, Nature Sustainability, 2, 1075–1082, 2019.
</mixed-citation></ref-html>
<ref-html id="bib1.bib115"><label>Schlüter et al.(2012)Schlueter, McAllister, Arlinghaus, Bunnefeld,
Eisenack, Hoelker, MILNER-GULLAND, Müller, Nicholson, Quaas
et al.</label><mixed-citation>
Schlüter, M., McAllister, R. R. J., Arlinghaus, R., Bunnefeld, N., Eisenack, K., Hölker, F., Milner-Gulland, E. J., Müller, B., Nicholson, E., Quaas, M., und Stöven, M. T.: New horizons for managing the environment: A review of coupled
social-ecological systems modeling, Nat. Resour. Model., 25, 219–272,
2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib116"><label>Schlüter et al.(2017)Schlüter, Baeza, Dressler, Frank,
Groeneveld, Jager, Janssen, McAllister, Müller, Orach
et al.</label><mixed-citation>
Schlüter, M., Baeza, A., Dressler, G., Frank, K., Groeneveld, J., Jager, W., Janssen, M. A., McAllister, R. R. J., Müller, B., Orach, K., Schwarz, N., and Wijermans, N.: A
framework for mapping and comparing behavioural theories in models of
social-ecological systems, Ecol. Econ., 131, 21–35, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib117"><label>Schneider et al.(2004)Schneider, Miller, Crist, and
Boston</label><mixed-citation>
Schneider, S. H., Miller, J. R., Crist, E., and Boston, P. J. (Eds.): Scientists Debate Gaia: The Next Century, MIT Press, Cambridge, Massachusetts, USA, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib118"><label>Seitzinger et al.(2015)Seitzinger, Gaffney, Brasseur, Broadgate,
Ciais, Claussen, Erisman, Kiefer, Lancelot, Monks
et al.</label><mixed-citation>
Seitzinger, S. P., Gaffney, O., Brasseur, G., Broadgate, W., Ciais, P., Claussen, M., Erisman, J. W., Kiefer, T., Lancelot, C., Monks, P. S., Smyth, K., Syvitski, J., and Uematsu, M.:
International Geosphere-Biosphere Programme and Earth system science: three
decades of co-evolution, Anthropocene, 12, 3–16, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib119"><label>Sitch et al.(2003)Sitch, Smith, Prentice, Arneth, Bondeau, Cramer,
Kaplan, Levis, Lucht, Sykes et al.</label><mixed-citation>
Sitch, S., Smith, B., Prentice, I. C., Arneth, A., Bondeau, A., Cramer, W., Kaplan, J. O., Levis, S., Lucht, W., Sykes, M. T., Thonicke, K., and Venevsky, S.: Evaluation of
ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ
dynamic global vegetation model, Glob. Change Biol., 9, 161–185, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib120"><label>Steffen et al.(2007)Steffen, Crutzen, and
McNeill</label><mixed-citation>
Steffen, W., Crutzen, P. J., and McNeill, J. R.: The Anthropocene: are humans
now overwhelming the great forces of nature, AMBIO, 36, 614–621, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib121"><label>Steffen et al.(2015)Steffen, Richardson, Rockström, Cornell,
Fetzer, Bennett, Biggs, Carpenter, de Vries, de Wit
et al.</label><mixed-citation>
Steffen, W., Richardson, K., Rockström, J., Cornell, S. E., Fetzer, I., Bennett, E. M., Biggs, R., Carpenter, S. R., de Vries, W., de Wit, C. A., Folke, C., Gerten, D., Heinke, J., Mace, G. M., Persson, L. M., Ramanathan, V., Reyers, B., and Sörlin, S.: Planetary boundaries: Guiding human development on a changing planet, Science, 347, 1259855, <a href="https://doi.org/10.1126/science.1259855" target="_blank">https://doi.org/10.1126/science.1259855</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib122"><label>Steffen et al.(2018)Steffen, Rockström, Richardson, Folke,
Barnosky, Cornell, Crucifix, Donges, Fetzer, Lade, Lenton, Liverman,
Scheffer, Summerhayes, Winkelmann, and
Schellnhuber</label><mixed-citation>
Steffen, W., Rockström, J., Richardson, K., Folke, C., Barnosky, A. D.,
Cornell, S. E., Crucifix, M., Donges, J. F., Fetzer, I., Lade, S. J., Lenton,
T. M., Liverman, D., Scheffer, M., Summerhayes, C., Winkelmann, R., and
Schellnhuber, H. J.: Trajectories of the Earth system in the Anthropocene,
P. Natl. Acad. Sci. USA, 115, 8252–8259, 2018.
</mixed-citation></ref-html>
<ref-html id="bib1.bib123"><label>Steffen et al.(2020)Steffen, Richardson, Rockström, Schellnhuber, Dube, Dutreuil, Lenton, and Lubchenco</label><mixed-citation>
Steffen, W., Richardson, K., Rockström, J., Schellnhuber, H. J., Dube,
O. P., Dutreuil, S., Lenton, T. M., and Lubchenco, J.: The emergence and
evolution of Earth System Science, Nature Reviews Earth &amp; Environment, 1,
54–63, 2020.
</mixed-citation></ref-html>
<ref-html id="bib1.bib124"><label>Stocker et al.(2013)Stocker, Qin, Plattner, Tignor, Allen, Boschung, Nauels, Xia, Bex, and Midgley</label><mixed-citation>
Stocker, T., Qin, D., Plattner, G.-K., Tignor, M., Allen, S., Boschung, J.,
Nauels, A., Xia, Y., Bex, V., and Midgley, P. (Eds.): Climate Change 2013: The Physical Science Basis, in: Contribution of Working Group I to the Fifth
Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, United Kingdom and New York, USA,
<a href="https://doi.org/10.1017/CBO9781107415324" target="_blank">https://doi.org/10.1017/CBO9781107415324</a>, 2013.
</mixed-citation></ref-html>
<ref-html id="bib1.bib125"><label>Strnad et al.(2019)Strnad, Barfuss, Donges, and
Heitzig</label><mixed-citation>
Strnad, F. M., Barfuss, W., Donges, J. F., and Heitzig, J.: Deep reinforcement learning in World-Earth system models to discover sustainable management strategies, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29, 123122, <a href="https://doi.org/10.1063/1.5124673" target="_blank">https://doi.org/10.1063/1.5124673</a>, 2019.
</mixed-citation></ref-html>
<ref-html id="bib1.bib126"><label>Taylor et al.(2012)Taylor, Stouffer, and Meehl</label><mixed-citation>
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of CMIP5 and the experiment design, B. Am. Meteorol. Soc., 93, 485–498, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib127"><label>Traulsen et al.(2010)Traulsen, Semmann, Sommerfeld, Krambeck, and
Milinski</label><mixed-citation>
Traulsen, A., Semmann, D., Sommerfeld, R. D., Krambeck, H.-J., and Milinski,
M.: Human strategy updating in evolutionary games,, P. Natl. Acad. Sci. USA, 107, 2962–2966, 2010.
</mixed-citation></ref-html>
<ref-html id="bib1.bib128"><label>Turchin(2008)</label><mixed-citation>
Turchin, P.: Arise “cliodynamics”, Nature, 454,   34–35, <a href="https://doi.org/10.1038/454034a" target="_blank">https://doi.org/10.1038/454034a</a>, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib129"><label>UNFCCC(2015)</label><mixed-citation>
UNFCCC:
Paris Agreement (Dec. 13, 2015),  UNFCCC, COP Report No. 21, Addenum, at 21, U.N. Doc. FCCC/CP/2015/10/Add, 1 (29 January 2016), 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib130"><label>Van Dijk and Breedveld(1991)</label><mixed-citation>
Van Dijk, J. and Breedveld, P. C.: Simulation of system models containing
zero-order causal paths – I. Classification of zero-order causal paths,
J. Frankl. Inst., 328, 959–979, 1991.
</mixed-citation></ref-html>
<ref-html id="bib1.bib131"><label>van Vuuren et al.(2012)van Vuuren, Bayer, Chuwah, Ganzeveld,
Hazeleger, van den Hurk, Van Noije, O'Neill, and Strengers</label><mixed-citation>
van Vuuren, D. P., Bayer, L. B., Chuwah, C., Ganzeveld, L., Hazeleger, W.,
van den Hurk, B., Van Noije, T., O'Neill, B., and Strengers, B. J.: A
comprehensive view on climate change: coupling of earth system and integrated
assessment models, Environ. Res. Lett., 7, 024012, <a href="https://doi.org/10.1088/1748-9326/7/2/024012" target="_blank">https://doi.org/10.1088/1748-9326/7/2/024012</a>, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib132"><label>van Vuuren et al.(2016)van Vuuren, Lucas, Häyhä, Cornell, and
Stafford-Smith</label><mixed-citation>
van Vuuren, D. P., Lucas, P. L., Häyhä, T., Cornell, S. E., and Stafford-Smith, M.: Horses for courses: analytical tools to explore planetary boundaries, Earth Syst. Dynam., 7, 267–279, <a href="https://doi.org/10.5194/esd-7-267-2016" target="_blank">https://doi.org/10.5194/esd-7-267-2016</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib133"><label>Vaughan and Lenton(2011)</label><mixed-citation>
Vaughan, N. E. and Lenton, T. M.: A review of climate geoengineering proposals, Climatic Change, 109, 745–790, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib134"><label>Verburg et al.(2016)Verburg, Dearing, Dyke, van der Leeuw,
Seitzinger, Steffen, and Syvitski</label><mixed-citation>
Verburg, P. H., Dearing, J. A., Dyke, J. G., van der Leeuw, S., Seitzinger, S., Steffen, W., and Syvitski, J.: Methods and approaches to modelling the
Anthropocene, Glob. Environ. Change, 39, 328–340, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib135"><label>Vernadsky(1986)</label><mixed-citation>
Vernadsky, V. I.: The biosphere (An abridged version based on the French
edition of 1929), Synergetic Press, London, UK, 1986.
</mixed-citation></ref-html>
<ref-html id="bib1.bib136"><label>Waters et al.(2016)Waters, Zalasiewicz, Summerhayes, Barnosky,
Poirier, Gałuszka, Cearreta, Edgeworth, Ellis, Ellis
et al.</label><mixed-citation>
Waters, C. N., Zalasiewicz, J., Summerhayes, C., Barnosky, A. D., Poirier, C., Gałuszka, A., Cearreta, A., Edgeworth, M., Ellis, E. C., Ellis, M., Jeandel, C., Leinfelder, R., McNeill, J. R., Richter, D. deB., Steffen, W., Syvitski, J., Vidas, D., Wagreich, M., Williams, M., Zhisheng, A., Grinevald, J., Odada, E., Oreskes, N., Wolfe, A. P.: The Anthropocene is functionally and stratigraphically distinct from
the Holocene, Science, 351, aad2622, <a href="https://doi.org/10.1126/science.aad2622" target="_blank">https://doi.org/10.1126/science.aad2622</a>, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib137"><label>Watson(2008)</label><mixed-citation>
Watson, A. J.: Implications of an anthropic model of evolution for emergence of complex life and intelligence, Astrobiology, 8, 175–185, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib138"><label>Weiss and Bradley(2001)</label><mixed-citation>
Weiss, H. and Bradley, R. S.: What drives societal collapse?, Science, 291,
609–610, 2001.
</mixed-citation></ref-html>
<ref-html id="bib1.bib139"><label>Wiedermann et al.(2015)Wiedermann, Donges, Heitzig, Lucht, and
Kurths</label><mixed-citation>
Wiedermann, M., Donges, J. F., Heitzig, J., Lucht, W., and Kurths, J.:
Macroscopic description of complex adaptive networks co-evolving with dynamic
node states, Phys. Rev. E, 91, 052801, <a href="https://doi.org/10.1103/PhysRevE.91.052801" target="_blank">https://doi.org/10.1103/PhysRevE.91.052801</a>, 2015.

</mixed-citation></ref-html>
<ref-html id="bib1.bib140"><label>Williamson(1998)</label><mixed-citation>
Williamson, O. E.: Transaction cost economics: how it works; where it is
headed, De Economist, 146, 23–58, <a href="https://doi.org/10.1023/A:1003263908567" target="_blank">https://doi.org/10.1023/A:1003263908567</a>, 1998.
</mixed-citation></ref-html>
<ref-html id="bib1.bib141"><label>Winkelmann et al.(2015)Winkelmann, Levermann, Ridgwell, and
Caldeira</label><mixed-citation>
Winkelmann, R., Levermann, A., Ridgwell, A., and Caldeira, K.: Combustion of
available fossil fuel resources sufficient to eliminate the Antarctic Ice
Sheet, Science Advances, 1, e1500589, <a href="https://doi.org/10.1126/sciadv.1500589" target="_blank">https://doi.org/10.1126/sciadv.1500589</a>, 2015.
</mixed-citation></ref-html>
<ref-html id="bib1.bib142"><label>Woroniecki et al.(2020)Woroniecki, Wendo, Brink, Islar, Krause,
Vargas, and Mahmoud</label><mixed-citation>
Woroniecki, S., Wendo, H., Brink, E., Islar, M., Krause, T., Vargas, A.-M., and Mahmoud, Y.: Nature unsettled: How knowledge and power shape
“nature-based” approaches to societal challenges, Glob. Environ.
Change, 65, 102132, <a href="https://doi.org/10.1016/j.gloenvcha.2020.102132" target="_blank">https://doi.org/10.1016/j.gloenvcha.2020.102132</a>, 2020.
</mixed-citation></ref-html>
<ref-html id="bib1.bib143"><label>Yearworth and Cornell(2016)</label><mixed-citation>
Yearworth, M. and Cornell, S. E.: Contested modelling: a critical examination
of expert modelling in sustainability, Syst. Res. Behav. Sci., 33, 45–63, 2016.
</mixed-citation></ref-html>
<ref-html id="bib1.bib144"><label>Zalasiewicz et al.(2017)Zalasiewicz, Waters, Wolfe, Barnosky,
Cearreta, Edgeworth, Ellis, Fairchild, Gradstein, Grinevald
et al.</label><mixed-citation>
Zalasiewicz, J., Waters, C. N., Wolfe, A. P., Barnosky, A. D., Cearreta, A., Edgeworth, M., Ellis, E. C., Fairchild, I. J., Gradstein, F. M., Grinevald, J., Haff, P., Head, M. J., Ivar do Sul, J. A., Jeandel, C., Leinfelder, R., McNeill, J. R., Oreskes, N., Poirier, C., Revkin, A., Richter, D. deB, Steffen, W., Summerhayes, C., Syvitski, J. P. M., Vidas, D., Wagreich, M., Wing, S., and Williams, M.: Making the case for a formal Anthropocene Epoch: an analysis of
ongoing critiques, Newsl. Stratigr., 50, 205–226, 2017.
</mixed-citation></ref-html>
<ref-html id="bib1.bib145"><label>Zeebe and Zachos(2013)</label><mixed-citation>
Zeebe, R. E. and Zachos, J. C.: Long-term legacy of massive carbon input to the Earth system: Anthropocene versus Eocene, Philos. T. Roy. Soc. A, 371,
20120006, <a href="https://doi.org/10.1098/rsta.2012.0006" target="_blank">https://doi.org/10.1098/rsta.2012.0006</a>, 2013.
</mixed-citation></ref-html>--></article>
