LPJ-GUESS is a dynamic global vegetation model that simulates – here, at a spatial resolution of 0.5∘ – physiological, demographic, and disturbance processes for a variety of plant functional types (PFTs) on natural land . Hydrological and most physiological processes are modeled at daily temporal resolution; vegetation growth, establishment, disturbance (including land use change), and mortality happen annually. Agricultural land is also included, with cropland and pasture being restricted in the types of plants allowed and experiencing annual harvest. Transitions among land use types are given as an input, with LPJ-GUESS calculating the associated change in carbon pools and fluxes . Four crop functional types (CFTs) are represented: C3 cereals sown in winter, C3 cereals sown in spring, C4 cereals, and rice . Nitrogen limitation on plant growth is modeled, with cropland able to receive fertilizer applications . The mechanistic representation of wild plant and crop growth accounts for the CO2 fertilization effect, by which productivity can be enhanced due to improved water use efficiency and (in C3 plants) reduced photorespiration . In an intercomparison of eight vegetation models over 1981–2000 , LPJ-GUESS simulated a mean global gross primary productivity very close to the ensemble average, although with the second-steepest increasing trend. LPJ-GUESS has also been shown to realistically simulate the effects of elevated CO2 on temperate cereal yield , although the latter effect is stronger than in other crop models . Changes to irrigation, water demand, water supply, and plant water stress as described in the Supplement of were included. Most importantly, these changes include (a) increasing maximum irrigation to allow it to bring soil to moisture levels well above the wilting point, and (b) a factor reflecting how soil moisture extraction gets more difficult as the soil gets drier.

LPJ-GUESS simulates variables that can be used as indicators of a number of provisioning and regulating ecosystem services (see also Table 1 in ); these are described in Sect. .

PLUM is designed to produce trajectories of land use and management based on socioeconomic trends and grid-cell-level crop and pasture productivity at a resolution of 0.5∘ . Food demand is projected into the future based on external scenario projections of country-level population and gross domestic product (GDP), using the historical relationship of per capita GDP to consumption of each of six crop types – C3 cereals, C4 cereals, rice, oil crops, pulses, and starchy roots – plus ruminant and monogastric livestock . Demand of a seventh crop type – dedicated bioenergy crops such as Miscanthus – is specified based on an exogenous scenario. PLUM calculates the demand for food crops both for human consumption and feed for monogastric livestock, plus any ruminants not raised on pasture.

Demand is satisfied at the country level by either domestic production or imports, the balance between which is determined considering commodity prices, management costs (fertilizer, irrigation, land conversion, and “other management” such as pesticide use), and changing LPJ-GUESS-simulated productivity due to climate change and CO2 under a range of irrigation–fertilization treatments. The latter are assumed to produce diminishing returns, such that increasing them increases yield at low intensity levels, but less and less so at higher levels, approaching a yield asymptote.

To solve for land use areas and inputs that satisfy demand, PLUM uses least-cost optimization, which allows for short-term resource surpluses and deficits. Such imbalances can be significant in the real world: global supply of major cereal crops frequently swings 5 % to 10 % out of equilibrium on an annual aggregate basis, and more extreme imbalances can be seen at the scale of individual countries . These dynamics are not captured by equilibrium models, such as those used in other land use and integrated assessment models, which represent for each year the stable state that the economic system would move to eventually if the environment did not change. Because global agricultural markets are not in equilibrium, disequilibrium models are needed to capture the real-world process of moving towards – but not reaching – equilibrium in a constantly changing economic and physical environment. Disequilibrium models have received varying amounts of attention in the literature over time e.g.,, and to our knowledge PLUM is the first land use model to incorporate one.

The composition of livestock feed (in terms of which crops are used) is assumed to be flexible, which can result in large interannual fluctuations in demand and production of individual crops as their prices change relative to one another. This is seen, for example, in Fig. S10 in the Supplement, where oil crop demand in the US and Canada triples from one year to the next. This assumption is not expected to materially affect the results in terms of gross decadal trends in total agricultural area and management inputs.

As outputs (feeding into LPJ-GUESS for use in LandSyMM), PLUM produces half-degree gridded maps of land use area (cropland, pasture, and non-agricultural land), crop distribution (fraction of cropland planted with each crop type), irrigation intensity, and nitrogen fertilizer application rate. Land use areas are calculated as net change, which neglects certain dynamics – such as shifting cultivation – that can have significant impacts on modeled carbon cycling especially in some regions . Other ecosystem services could be affected as well. LandSyMM does not capture these dynamics, but this was considered an acceptable trade-off for computational efficiency.

This section and Fig.  provide an overview of how LPJ-GUESS and PLUM are combined in the LandSyMM runs presented in this work. More details on this coupling can be found in the Supplement.

The first step in running LandSyMM is to perform “yield-generating” runs in LPJ-GUESS. A simulation of the historical period generates a model state, which is needed so that vegetation and soil condition can be fed into subsequent runs (Fig. ). From that state, we perform a series of runs that generate “potential yields” in every grid cell for each crop under six different management treatments in a factorial setup: fertilization of 0, 200, and 1000 kgNha-1, and either no irrigation or maximum irrigation. Changing pasture productivity is accounted for using annual average net primary productivity; for simplicity, we include pasture when using the phrase “potential yields”. These potential yields account for changing productivity given changing climate and atmospheric CO2 concentration.

PLUM then combines the future potential yields from LPJ-GUESS (averaged over 5-year time steps) with its own estimates of future commodity demand to project land use areas, fertilizer application, and irrigation intensity (Fig. ). PLUM has been found to perform well in this coupled system; its recreation of historical patterns and projections into the future are discussed in . Here, PLUM's demand estimates are driven by scenario-specific population and GDP data (Sect. ).

The outputs of land use and management from PLUM for a given 2011–2100 scenario are fed into a final LPJ-GUESS run in order to produce projections of the ecosystem service indicators analyzed here (Fig. ). However, the PLUM outputs must be processed first, because at the beginning of the future period they do not exactly match the land use and management forcings used at the end of the historical period. Feeding the raw PLUM outputs directly into LPJ-GUESS – causing large areas of sudden agricultural abandonment and expansion between 2010 and 2011 – would thus complicate interpretation of the results, especially of carbon cycling. We developed a harmonization routine, based on that published for Land Use Harmonization v1 dataset (LUH1) (; http://luh.umd.edu/code.shtml, last access: 16 April 2020), that adjusts the PLUM outputs to ensure a smooth transition from the historical period to the future. While global totals are conserved in almost all cases, harmonization can produce notable differences at the regional scale. Details on this routine can be found in the Supplement (Sect. S3).

In addition to the LPJ-GUESS runs forced with harmonized PLUM-output land use and management trajectories, we perform several experiments to examine the impact of different factors on the land use and management projections generated by PLUM and thus the ecosystem service indicators simulated by LPJ-GUESS in the PLUM-forced runs. By holding either climate, atmospheric CO2, or land use and management constant (or for climate, looping through 30 years of temperature-detrended historical forcings) over 2011–2100, we can estimate the contribution of each to changing ecosystem service indicators in the future. Details regarding the inputs of these experimental runs can be found in Sect.  and the Supplement. The results of these experimental runs were used to inform interpretation of the results but are mostly not presented here. Instead, the Supplement contains figures supporting claims derived from the experimental runs, in addition to other figures that were not included here to conserve space. Runs are referred to using the naming convention described in Table . Note that all PLUM outputs consider LPJ-GUESS yields under changing climate and CO2 concentration, even when those outputs are fed into LPJ-GUESS runs with constant climate and/or CO2. Our analyses thus account only for the direct effects of changing climate and CO2 on ecosystem service indicators, rather than their indirect effects via land use and management.

The experiments treated here are based around combined future climate–socioeconomic scenarios. Future population growth and economic development are derived from the Shared Socioeconomic Pathways SSPs;. We use four of the five SSPs, which together cover a wide spectrum of possible storylines for the future evolution of the climate and society . SSP1 characterizes a world shifting to a more sustainable pathway, with low population growth and strong technological and economic developments. SSP3 describes a pathway with strong population growth and intensive resource usage, low technological development, and lessening globalization. SSP4 is a pathway of inequality with the potential for competition over resources and resource intensification. SSP5 is a pathway dependent on fossil fuels with low population growth, strong globalization, and high economic and technological growth. (SSP2, a “middle-of-the-road” pathway intermediate between the other four SSPs, is not considered here.)

Scenarios of future climate change and atmospheric CO2 concentrations are based on the Representative Concentration Pathways RCPs;. SSPs are paired with RCPs based on what sort of climate change could be expected under each SSP's storyline: SSP1 with RCP4.5, SSP3 and 4 with RCP6.0, and SSP5 with RCP8.5. RCP numbering refers to each scenario's average global radiative forcing (Wm-2) in 2100.

We use climate input data from the fifth Coupled Model Intercomparison Project CMIP5; outputs of the IPSL-CM5A-MR climate model . Maps of temperature and precipitation change over the simulation period for each RCP are presented in the Supplement (Fig. S4). The CMIP5 runs did include land use change but not the trajectories output by PLUM. As such, and as with all models that are not climate coupled but rather use offline forcings, we do not consider the effects of our simulated land use change on climate. We also use just one climate model, and as such the only uncertainty explored in this work is uncertainty related to scenario choice.

Future socioeconomic data – country-level population and GDP projections – are taken from version 0.93 of the SSP database . Demand of dedicated bioenergy crops such as Miscanthus is specified according to the SSP2 scenario from the MESSAGE-GLOBIOM model described by ; demand for bioenergy from food crops is specified to double from 2010 by 2030 and thereafter remain constant. The SSP narratives also affected parameters within PLUM. These included input and transport costs, tariffs, and minimum non-agricultural area (which places an upper limit on the total fraction of a grid cell that PLUM can allocate to cropland and pasture). Values were estimated for each SSP based on an interpretation of the storylines and can be found in Table S6. Because of these scenario-specific parameters, the raw PLUM outputs are not necessarily expected to match at the beginning of the period.

Historical land use areas (cropland and pasture fractions), irrigation, and synthetic nitrogen fertilizer application levels were taken from the LUH2 dataset . Historical manure application rates (simplified upon import to LPJ-GUESS as pure nitrogen addition) come from . Historical crop distributions (i.e., given LUH2 cropland area in a grid cell, what fraction was rice, starchy roots, etc.) came from the MIRCA2000 dataset and were held constant throughout the historical period.

LPJ-GUESS simulates a number of output variables that here serve as the basis for quantifying ecosystem services. The carbon sequestration performed by terrestrial ecosystems is measured as the simulated change in total carbon stored in the land system, including both vegetation and soil. Ecosystem nitrogen in LPJ-GUESS is lost in liquid form via leaching (a function of percolation rate and soil sand fraction), and in gaseous form through denitrification (1 % of the soil mineral nitrogen pool per day) and fire. Here, we combine these into a value for total N loss. LPJ-GUESS also simulates the emission of isoprene and monoterpenes – the most prevalent BVOCs in the atmosphere – and accounts for three important factors regulating their emission: temperature, CO2 concentration ([CO2]), and changing distribution of woody plant species due to climate and land use change .

LPJ-GUESS simulates basic hydrological processes such as evaporation, transpiration, and runoff. The latter is calculated as the amount of water by which soil is oversaturated after precipitation, leaf interception, plant uptake, and evaporation. We present change in average annual runoff as a general indicator of trend in water availability. After , we also use the difference between 1971–2000 and 2071–2100 in the 95th percentile of monthly surface runoff (P95month) as a proxy for changing flood risk (although note that those authors used daily values), and the difference in the 5th annual percentile (P5year) for changing drought risk. Note that we are referring to hydrologic drought, which can be contrasted with, e.g., meteorological drought (a long time with little or no precipitation) or socioeconomic drought water supply levels too low to satisfy human usage demand;. As note, these metrics do not translate directly into impacts due to the mitigation capacity and nonlinear effectiveness of reservoirs, flood control mechanisms, and other infrastructure, as well as changes in demand and mean climate. However, changes in streamflow extremes have served as rough indicators of changing risk in a number of previous global-scale studies e.g.,. While LPJ-GUESS does not model the physical flow of water within and between grid cells, the predecessor LPJ model has been shown to compare well to dedicated hydrological models when aggregated to basin scale . As such, where discussing geographic patterns, we will refer to basin-level results only.

Finally, we assess how much land is converted to agriculture within the Conservation International (CI) hotspots, a set of 35 regions covering less than 3 % of the Earth's land area but containing half the world's endemic plant species and over 40 % of the world's endemic vertebrate animal species . These regions each contain at least 1500 endemic vascular plant species and have already lost at least 70 % of their original natural vegetation, thus representing highly diverse areas presently at high risk of habitat loss. Note that our chosen metric does not consider areas where agricultural abandonment could lead to a long-term increase in biodiversity, because it is impossible to determine where and how soon, given enough newly available land, there would be sufficient vascular plant richness to qualify as a biodiversity hotspot.

LandSyMM simulates net global loss of natural land area over the 21st century in all scenarios (Fig. ), with SSP3 experiencing the greatest loss of area (10 %), SSP1 the least (3 %), and SSPs 4 and 5 an intermediate loss (6 %). These patterns are mostly reversed for pasture area change, in which all scenarios show an increase, although the trajectory for SSP5 is more similar to that of SSP3. PLUM also simulates net increased cropland area globally in all scenarios, with SSPs 1 and 5 showing the least increase, SSP4 more, and SSP3 the most.

Cropland expansion happens at a more or less constant rate in SSP3 and SSP4, but these scenarios experience very different trajectories of crop commodity demand: SSP4 approximately levels off around mid-century, whereas SSP3 experiences only a brief slowdown in growth followed by constantly increasing demand through 2100 (Fig. S5). The majority of the increased demand in the first half of the century is satisfied by fertilizer application, which increases by more than 75 % from the 2010s to the 2050s while crop area increases by less than 15 %. However, management inputs per hectare in SSP3-60 approximately plateau after mid-century (Fig. S6), while crop demand rises 16 %. Cropland area expands about 10 % between 2050 and 2100, with boosted productivity – thanks to climate change and/or CO2 fertilization – helping to satisfy the rest of the increased demand. Since SSP4-60 experiences the same climate and CO2 fertilization but with level crop demand during the second half of the century, management inputs decrease after about 2050. PLUM prescribes lower irrigation rates by the end of the century for most scenarios (Figs. , S6). This is enabled by higher global mean rainfall in all RCP scenarios, as evidenced by the bars for runoff in Fig. , as well as by improved water use efficiency for crops other than C4 cereals due to increased CO2 concentrations. Crop demand increase in SSP3-60 outweighs these effects, however, resulting in higher irrigation in that scenario.

Although population growth in SSP5-85 is more than twice that of SSP1-45, PLUM simulates very similar trajectories of global crop demand in both: an increase until about 2040 followed by a decrease for the rest of the century, with SSP5-85 crop demand ending slightly higher. SSP5-85 livestock demand increases about 20 % more than in SSP1-45, which explains the rest of the difference in global caloric needs between the two scenarios (Fig. S5). However, because SSP5-85 experiences much stronger climate change and CO2 increase, the two scenarios differ importantly in how they satisfy their crop demand over the century. Whereas cropland area increases more or less constantly in SSP1-45 (slightly slowing throughout), in SSP5-85 it decreases through about 2050, after which it increases slowly, ending at a slightly lower global extent than in SSP1-45 despite a jump in the early 2090s as feed becomes more important in raising ruminant livestock (Fig. S7). Crop production remains similar between the two scenarios, especially in the first half of the century, because SSP5-85 applies much more fertilizer and irrigation water per hectare (Fig. S6). This gap in these inputs narrows in the second half of the century as climate change and the CO2 fertilization effect become even stronger in SSP5-85 relative to SSP1-45, although the latter also begins to increase PLUM's “other management” intensity (representing, e.g., pesticide application).

Figure  presents the change in cropland and pasture area over 2010–2100 for each scenario after harmonization. It should be noted that the harmonization process, while preserving global changes in net area change for each land use type, produces more gross area change. Where relevant, in this section and in the rest of the results, we will point out where apparent strong regional effects of land use change result from changes that were not present pre-harmonization.

Several regional patterns in crop area change stand out in Fig. :

North America loses cropland in parts of the Great Plains (mainly C3 cereals; Fig. S8) and the midwestern US (mainly oil crops; Fig. S9) in all scenarios after harmonization. However, this is exaggerated relative to the original PLUM outputs by approximately 1500 %, 1700 %, 400 %, and 800 % for SSPs 1, 3, 4, and 5, respectively. Similarly, harmonization inflates projected cropland expansion in the temperate forests of the eastern US and Canada: by approximately 800 % for SSP1-45 and 100 % for the other scenarios. On the other hand, large-scale cropland expansion in Alaska in all scenarios except SSP3-60 was almost entirely present in the raw PLUM outputs. This new cropland is entirely planted with spring wheat (Fig. S8) and is most extensive in SSP5-85, which shows the largest increase in North American cereal demand – nearly 250 % by the end of the century (Fig. S10) – but also the largest potential yield increase in Alaska, thanks to high warming and CO2 fertilization. Indeed, by the end of the century, the potential yield of rainfed C3 cereals there is similar to or exceeds that of the parts of the Great Plains where cropland is lost (Fig. S11). It should be noted that while LPJ-GUESS includes several limitations on plant and soil processes based on air and soil temperature, the version used here does not represent permafrost dynamics, and so may be optimistic with regard to the increase in arable land area. However, permafrost extent is expected to decrease across parts of Alaska and the boreal zone as a whole, especially in high-temperature-increase scenarios such as RCP8.5 .

Pasture area is projected to expand significantly in the western Amazon in all scenarios (although in SSP1-45 this is strongly exaggerated by harmonization) and even more so in all scenarios in the African rainforest (Fig. ). This tropical deforestation is largely driven by the increasing consumption of ruminant products in those regions: as incomes increase in developing tropical countries, PLUM projects greater consumption of commodities such as meat and milk and a reduction in staples such as starchy roots and pulses . Depending on the SSP, ruminant products are simulated to account for 23 %–43 % of calories in central Africa by 2100, compared to only 4 %–7 % of calories consumed in 2010 caloric density derived from. Between 50 % and 98 % of the ruminant production increase in central Africa goes to this domestic consumption, with the rest being exported.

The African pasture expansion even occurs in SSP1-45, the “sustainability” scenario , in which LandSyMM simulates a net global pasture expansion of about 1 Mkm2. For comparison, five other land use models all projected SSP1 pasture area decrease: by an average of about 3.4 Mkm2 . While we do not expect LandSyMM's results to necessarily match those of other models, such a large, qualitative difference requires explanation. Several factors related to experimental setup and overall model structure likely contribute.

First, PLUM makes no assumption about changes in food production needs besides what occurs due to population and GDP changes. The storyline for SSP1, however, with its “low challenges to mitigation”, suggests that people will gradually shift to lower-meat diets than would be expected given GDP levels, at first at least in high-income countries. The Integrated Model to Assess the Global Environment (IMAGE) – which simulates a decrease in pasture area of about 7 Mkm2 by the end of the century – incorporates this dietary shift as a 30 % (global) reduction in meat consumption relative to what would have otherwise been simulated, and additionally includes a 33 % reduction in food supply chain losses to represent efficiencies from improved management and infrastructure . use the Model of Agricultural Production and its Impact on the Environment (MAgPIE) to show that, under a scenario like ours where historical differences in livestock production efficiency are maintained or exacerbated, a shift to lower-meat diets can reduce the expansion of pasture in sub-Saharan Africa by over 50 %.

Second, the land use modeling components of most integrated assessment models (IAMs) – for example, all those contributing to the LUH2 trajectories – include demand for timber and other products. The carbon value of forests (and land more generally) can also be included by some, even if forest products are not explicitly modeled e.g., MAgPIE;, which could come into play in scenarios with policy-based incentives designed to minimize emissions from deforestation and degradation and/or to maximize carbon sequestration. In contrast, PLUM includes neither forest products nor land carbon value. The only cost PLUM considers in converting a forest to agriculture is the cost of conversion, with the opportunity cost of lost forest products or services ignored. Similarly, the only incentive to replace existing agricultural land with forest would be to avoid costs associated with production. Including forest products, payments for carbon sequestration, and managed forestry into LandSyMM could result in more forest simulated over the course of the century. This is especially likely for SSP1, whose storyline specifies a gradual improvement in how the global commons are managed . As an example, IMAGE represented this improvement in SSP1-45 by (a) disallowing clearing of forests with carbon density greater than 200 tha-1 and (b) reforesting half of the world's degraded or former forest.

The spread in land use area projections between the most extreme scenarios is much higher in this work than in , by around 500 % for cropland and 700 % for pasture. The primary reason for this increase in inter-scenario variation is that used the SSP2 socioeconomic scenario for all RCPs, whereas here we compare different SSPs paired with appropriate RCPs. The wide variation among the SSPs in population and economic growth trajectories, along with SSP-specific PLUM parameters (Sect. ), contributes to this increased spread. Even so, the LandSyMM trajectories are more closely clustered than those from some other land use models. IMAGE, for example, projects a range of cropland area increase from 0.4 to 5.3 Mkm2 across the five SSPs, and pasture trajectories ranging from a decrease of 7.3 Mkm2 to an increase of 4.4 Mkm2 . As described above, IMAGE makes a number of assumptions (based on the SSP storylines) that PLUM does not regarding future deviations from historical “business-as-usual” trends and relationships, including dietary shifts, reductions in food losses during transport, and forest conservation.