Global Food Demand Scenarios for the 21st Century

Long-term food demand scenarios are an important tool for studying global food security and for analysing the environmental impacts of agriculture. We provide a simple and transparent method to create scenarios for future plant-based and animal-based calorie demand, using time-dependent regression models between calorie demand and income. The scenarios can be customized to a specific storyline by using different input data for gross domestic product (GDP) and population projections and by assuming different functional forms of the regressions. Our results confirm that total calorie demand increases with income, but we also found a non-income related positive time-trend. The share of animal-based calories is estimated to rise strongly with income for low-income groups. For high income groups, two ambiguous relations between income and the share of animal-based products are consistent with historical data: First, a positive relation with a strong negative time-trend and second a negative relation with a slight negative time-trend. The fits of our regressions are highly significant and our results compare well to other food demand estimates. The method is exemplarily used to construct four food demand scenarios until the year 2100 based on the storylines of the IPCC Special Report on Emissions Scenarios (SRES). We find in all scenarios a strong increase of global food demand until 2050 with an increasing share of animal-based products, especially in developing countries.


Introduction
Over the last 50 years, global food demand approximately trippled [1]. This rapid growth was caused on the one hand by the doubling of world population from about 3 to more than 6 billion people and on the other hand increased per-capita demand due to rising living standards. In this article, we define food demand as equivalent to food supply according to FAOSTAT [1]. It describes the daily average availability of food in households in kcal capita −1 d −1 , comprising both food intake and non-eaten household food waste. Detecting a basic rule of estimates. Other studies [19,22] create quantitative estimates based on computable general equilibrium or partial equilibirum models. However, these demand models are designed primarily to simulate shocks on markets. For long-term scenarios, the parameters in the models have to be adjusted based on assumptions in order to derive caloric estimates for the future that are not unrealistically high or low [22]. Often, the parameters are adjusted in a way that the model results become consistent with the numbers in the FAO report "World agriculture towards 2030/2050" by Alexandratos & Bruinsma [17] [22]. Consequently, there are no econometric model estimates yet available with the potential to challenge or support the expert estimates. Secondly, the available literature is not very transparent. It remains unclear how the expert-estimates were derived [17,18], or which exact parameters, functional relations and calibration steps were used to create the model-based projections. Thirdly, most studies provide only data for a single storyline and cover a time-horizon not beyond 2050. However, users of food demand projections have a strong need for multiple scenarios to explore the sensitivity of their analyses to changes in dietary patterns. Furthermore, climate impact research requires scenarios until 2100 [8], which will inevitably show a much wider range of uncertainties between different storylines. Fourthly, the results are not reproducible, and scenarios cannot be easily adapted to the needs of scientific communities that use the projections as input data.
Therefore, we provide a transparent method for creating specific food demand scenarios for total and animal-based calories, requiring only population and income projections as input, while no information on the food supply side is needed. This tool shall support the work of other scientists who require food demand scenarios as input for policy-relevant studies on food security, environmental assessments, or agricultural outlooks. The scenarios that can be created are flexible regarding the time horizon and provide information on the national level, which can be aggregated to regions of any size and location. Our method is exemplarily applied to the storylines of the SRES scenarios [8] to create country-based projections until the year 2100. The SRES storylines are broadly used in the literature and were further elaborated in the Millenium Ecosystem Assessments [23,24]. Beyond, our method could be applied to many other scenario projects: To the climate-related global IPCC storylines SA90 [25], IS92 [26] or the upcoming SSP [27] and SPA storylines [28]; to general long-term scenarios for sustainability research like the Club of Rome scenarios [29] or the Millenium Ecosystem Assessments [23,24]; or to scenarios on agriculture and land-use that are focussed on specific world regions like [30]. They could also help as a tool for participatory scenario-building processes like CCAFS [31].

Materials and Methods
Our approach uses country-specific historical data to fit regressions of food demand on income over time which we apply to scenarios of future income and population.

Data sources
We use data on historical food demand provided by the United Nations Organisation for Food and Agriculture (FAO) in the FAOSTAT database (Table 1). Demand is given in kcal capita −1 d −1 per country from 1961 to 2007 as total calorie (C T ) and animal-based calorie demand (C L ). The data include a wide range of unprocessed and processed agricultural and fishery products intended for food consumption.
Historical data on population and per-capita income are taken from the World Bank in the World Development Indicator (WDI) database (Table 1, [32]). Population (P c ) is given in capita per country c and income values (I c ) [gdp capita −1 year −1] in constant US$ 2000 from 1961 to 2007, based on market exchange rate (MER). For income (I) and calorie demand (C T ,C L ) there are 5889 complete data pairs from 162 countries.
Projections of per capita income (I Proj t;c ) and population (P Proj t;c ) are based on the SRES storylines [8]. Population scenarios were estimated with the UN (A2, B2) and the IIASA model (A1, B1). Four storylines (A1, A2, B1, B2) are distinguished based on diverging assumptions on the societal development concerning economical values as well as regional connectivity. We used the country-specific datasets from CIESIN database [33,34]. population projections (P Proj t;c ) are given in capita ( Figure

Functional relations between income and food demand
Different functional relations can be formulated between food demand, income I and time t. Here, we estimate the parameters of two functional relations for both total per capita demand and for the share of animal-based calories. These relations can subsequently be used to customize scenarios to their storylines.
Data preparation and analysis is performed using the programming language and statistical software R [35]. To select the necessary predictors, regressions are compared by an analysis of variance and stepwise reduction of the models is performed using the Akaike Information Criterion AIC (function step of package stats). The resulting models were tested against observed data with linear regressions using function lm of package stats.
Total calorie demand. For total calorie demand C T , we apply the Engel curve with an under-proportional increase with income I. The relation can be described by the power function g (Eq 1) with parameter β which can be interpreted as an elasticity (see review in [36]).
We model the parameters α and β to be time-dependent which represents the influence of other drivers than income. In order to provide appropriate functions for the scenario storylines, parameters α and β are determined in two alternative ways. For one parameter set we assume a linear temporal relation, and for the second set a decreasing time increment.
The first parameter set assumes a linear temporal relation and uses the linearized formulation of Eq (1) Parameters α Ã = ln(α) and β are estimated by a linear mixed-effect model (using function lmer of package lme4, [37]). Hereby, ln(C T ) is described with the fixed effect ln(I) and random effect time t. This results in time-dependent relations (exponential for α and linear for β) and is further on referred to as formulation g A (Eq 3).
The second parameter set assumes a decreasing time increment. Parameters α and β are estimated per year by a nonlinear least squares model fitted to Eq (1) (using function nls of package stats, [38]). Subsequently, the time series of parameters α and β are fitted to the asymptotic function m of Michaelis-Menten type (Eq 4) with intercept ω 1 , asymptotic value ω 2 , half-saturation constant ω 3 and base year t 1 = 1960.
With the resulting functions m α and m β , the alternative formulation for g can be written as This captures the dynamics with rapidly changing values during the first 20 years of observations and rather less increase in the last period and is referred to as formulation g B (Eq 5). Both functional relations g A and g B can be applied to the historical data in a way that assumptions on their future development can be chosen according to the storyline of the respective scenario.
Animal calorie share. To estimate the animal-based calorie demand C L , the share of animal-based calories C LS (Eq 6) in total calories C T is taken.
Again, two functional relations are used to estimate the demand according to the chosen storylines. First, the linear regression h A (Eq 7) on income I and time t is fitted on logarithmic values of C LS as This approach assumes that livestock products are a normal necessity good in accordance with Bennet's law [39]. Secondly, we assume that animal products are a normal necessity good at low incomes, but turn into inferior goods at high incomes. This can be justified e.g. by the ambition of better educated people for a more balanced, healthy or sustainable diet [36]. For the derivation of h B (Eq 8), the under-proportionally increasing square root function is multiplied with an exponential decline. Thus, the share of animal-based calories declines at high incomes but does not become negative.
The functional relations h A and h B will be chosen for the projections of C LS according to the storylines.

SRES scenario preparation
Generally, scenario construction is focussed on variables and assumptions that are both subject to the largest uncertainty and that have major impacts on the results. For our analysis, we vary the assumptions on population growth, on income growth, and on the functional relations between per-capita income and dietary consumption patterns. The latter reflects the process uncertainty of dietary dynamics, and highlights the ambiguity in the past data that is consistent with various model representations.
Choice of functional relations based on storylines of SRES scenarios. Storylines have the purpose to harmonize scenario parameters, as in our case the assumptions on population growth, income growth and functional relations. The four storylines used in this study were developed to analyze the impacts of global climate change and possible mitigation strategies [8]. The A1 and A2 scenarios describe worlds emphasizing economic growth with societies that are characterized by materialistic attitudes. In contrast, the B1 and B2 scenarios describe worlds developing towards a sustainable economy, and where the society has a stronger environmental awareness. Common features of the A1 and B1 scenarios are a globalized economy and increased cultural and social interactions, whereas A2 and B2 storylines emphasize more self-reliance and local solutions to economic and social problems. A1 and B1 are therefore assumed to have a higher level of education and labor productivity, which also translates into lower reproduction rates and therefore slower population growth or even decreasing population. The higher population growth in A2 and B2 scenarios results in relatively lower per-capita incomes as the available resources have to be shared by a larger population. With regard to dietary habits, the SRES storylines suggest that the A1 and A2 scenarios describe a society with an affluent, wasteful and materialistic consumption pattern, even though dynamics like increased health consciousness in rich countries might also here reduce the consumption of animalbased calories. In contrast, the B1 and B2 worlds have societies with high environmental awareness that translate into a de-materialization of consumption, a reduced intake of animal-based calories and lower rates of household waste.
In accordance with the storylines, population and income projections were selected from the SRES database. Moreover, to represent the differences in the materialistic A1 and A2 storylines and the sustainable B1 and B2 storylines, we assign different functional relations for A1 and A2 than for B1 and B2. The globalized worlds A1 and B1 and their fragmented counterparts A2 or B2 are only distinguished by different population and income growth paths. As selection criterion for the allocation of the functional relation, we used the level of consumption that will prevail in the long-run in high income countries. The levels of consumption are higher in the g A and h A functions, that were applied to the materialistic A1 and A2 scenarios (Eq 9). For the storylines with a focus on environmentally sustainable lifestyles (B1 and B2), the formulations g B and h B , that result in a much lower consumption in the long-run, were chosen (Eq 10). All functional relations are consistent with past data; the differences just reflect divergent interpretations of the data.
Calculating the demand scenarios. The data sources from FAOSTAT [1], Worldbank [32], and CIESIN [33,34] do not completely cover all countries and the full time-span. For the scenarios (not for the regression analysis), we harmonized the data sources and filled missing data with regional average values. We excluded all countries not listed in FAOSTAT [1], representing 2.1% of the world population according to Worldbank [32]. Historical GDP data was completed with estimates of UNSTATS [40] for the countries of the Eastern Bloc.
For the 4 SRES scenarios, we projected per-capita vegetal (C V Proj t;c , Eq 11) and animal-based calorie demand (C L Proj t;c , Eq 12) for time t and countries c based on income I Proj t;c . , we calibrated our estimates to the observed values C V cal 1990;c and C L cal 1990;c in the year 1990. There is evidence that heterogeneous national dietary patterns become more homogeneous through globalization (see e.g. [41][42][43]). Our regression being a plausible target for a globalized diet, we assume that the deviations of observed values from our regression function gradually disappear until 2100. For this purpose, we applied the function conv (Eq 13), for which calibrated demand X t meets historical values C 0 in an initial year y s and converges to the regression values until the final year y e . convðX t ; C 0 ; y s ; y e Þ ¼ t À y s y e À y s X t þ y e À t y e À y s C 0 8 t 2 ½y s ; y e X t 8 t > y e For regional aggregates, every country was assigned to one of ten world regions (S1 Fig) [44]. The validity of the projections was assessed by deriving trends for the transitional period from 1990 to 2007 using the partial Mann-Kendall test [45,46]. The trend itself is determined as median value of all differences between the values and their successors. Trends were considered to be significant for p < 0.05.

Sensitivity analysis of demand regression models
In order to provide information on the robustness of the estimated parameters, we performed a sensitivity analysis with respect to the underlying data. For each of the regression models, a random selection of 67% of the data pairs was chosen 1000 times and the respective regression parameters were estimated. The parameters were divided by the respective values derived from the entire dataset. For these relative factors, median and standard deviation were calculated. In order to evaluate the robustness of the regression models, the goodness of fit of dataset versus model estimates was calculated for the part of the dataset not used for the regression.

Results
For both total calorie demand and animal-based calorie shares, results are presented for the two alternative formulations. Subsequently, features of food demand projections following the SRES storylines are described. We concentrate on regional results, while country-level estimates are given in the Supplement (S4, S5, S6 and S7 Figs). An interactive web-application can be used to explore the regional results (given in the Supporting Information). Own scenarios can be generated using the package "CalorieDemand" in the open source programming language R [35] (Supporting Information).  (Table 2). Parameter β, the income elasticity of the demand, is estimated by the mixed model as 0.1002 ± 4.37 Á10 −4 (mean ± SE) and decreases from 0.101 in 1961 to 0.0995 in 2007. The overall fit of the model to observed data (Fig 1a) is highly significant with a coefficient of determination of 0.65 and slope 0.66 (Table 3). The temporal development of the model (Fig 2) at high income I = 60,000 US$ shows an increase from 3587 kcal capita −1 d −1 in 2000 to 4289 kcal capita −1 d −1 in 2100.

Regressions for total calorie demand from historical data
For the formulation g B , we use regression models (Eq 5) with diminishing time-dependence of the parameters α Ã and β of Michaelis-Menten type (Eq 4). Parameters were determined significantly (all p-values < 0.001, Table 4) ( Figure A in S3 Fig). Parameter β is estimated as 9.88 Á10 −2 ± 3.21 Á10 −3 (mean ± SE). The resulting demand values show a high correlation with observed data (Fig 1b, Table 3) with a comparable coefficient of determination as g A and a slightly higher slope of 0.68. The temporal change is similar to g A for the historical time span but nearly disappears for the projected years (Fig 2). At income values of I = 60,000 US$, total calorie demand after g B changes from 3661 kcal capita −1 d −1 in 2000 to 3805 kcal capita −1 d −1 in 2100.   Table 3) and 1:1 line (dashed). Note log scale of axes.
Regressions for the animal-based calorie share from historical data The animal-based calorie demand is determined by using the proportion of animal-based to total calories C LS and fitting the linear regression model h A (Eq 7) and the inverted U-shaped curve h B (Eq 8).
For the monotonically increasing function h A , anova results show that ln(I) and time t are significant predictors for ln(C LS ) as well as the interaction of both. The linear regression model (Eq 7, parameters in Table 5) is highly significant (Table 3) with a slope of 0.63 and intercept 0.04 (Fig 3a). Predictions with this model (Fig 4) decrease dramatically at higher incomes of 60,000 US$ from 0.42 in 2000 to 0.2 in 2100. Although the coefficients of income and time are positive, the negative coefficient for the interaction produces this decline ( Table 5).
The nonlinear function h B (Eq 8) is fitted for time-dependent parameters ρ and λ (Table 6). With the estimated values, parameter ρ = ρ 1 + ρ 2 Á t is decreasing and λ = λ 1 + λ 2 Á t is increasing over time ( Figure B in S3 Fig). Thus, for a given income level both parameters affect the values over time in a declining way. This model is highly significant (Fig 3b) with a slightly higher Table 3. Statistical properties of regression models on total calorie demand (C T ) and animal-based calorie share (C LS ). Significance levels for p-val-    coefficient of determination of 0.62 (Table 3) and less overestimated values than with the multiple regression (compare Fig 3a). Predictions in lower income ranges up to 20,000 US$ are comparable to the multiple regression model h A but give much lower values at higher incomes (Fig 4). At 60,000 US$, the animal-based calorie share drops from 0.28 in 2000 to 0.14 in 2100.
doi:10.1371/journal.pone.0139201.t005  Regionally aggregated values (population-weighted averages) show a strong increase in total calorie demand up to 2050 in all scenarios (Fig 5). In the second half of the century, the scenarios diverge with either a continuous increase (A2), a stagnation (B2) or a slight decrease (A1, B1). Population growth ( Figure A in S2 Fig), especially in developing countries, is the major driver for food demand throughout all scenarios. World population grows by 65% from 1990 to 2050 in the A1 and B1 scenarios, by 78% in the B2 scenario and by 114% in the A2 scenario. Compared to population growth, the increase in per-capita demand has a lower, yet substantial influence on total demand. It grows by 18% (A2), 21% (B2), 26% (B1) and 36% (A1) from 1990 to 2050. Here, the regions with the highest growth rates in per-capita demand are Sub-Saharan Africa, South, Central as well as South-East Asia.
The high per-capita demand values by far exceed plausible intake averages over the population of a country. As the Food Balance Sheets food availability also includes household waste, a substantial share of the food demand has to be interpreted as waste. Already today, high shares of the food demand can be attributed to waste in developed countries [1].
In order to compare our results with other studies [17,[19][20][21], we aggregated the countrybased values of the respective scenario to the same regions as given in the literature. These

Projections for the animal-based calorie demand
Animal-based calorie demand (S4, S5, S6 and S7 Figs) increases for all countries and scenarios only until the middle of the 21 st century. Here, some countries with a traditionally high share of meat in the diet (e.g. Mongolia or Hungary) reach a per-capita animal-based calorie demand of more than 2000 kcal capita −1 d −1 . Projections for the end of the century show similarities between A1 and A2 as well as between B1 and B2 caused by the application of the same function but are not identical because of differing income projections. The highest overall deviations between scenarios are projected for countries with traditionally high meat consumption (like Russia, eastern Europe or Northern America) with dramatic decreases of demand values for animal-based products. Also for countries with very low historical values (like most countries in Africa), the differences for 2100 are high both due to the income projections and the applied regression functions. The regionally aggregated demand for animal-based products increases in all four scenarios (Fig 7). With global growth rates of 176% (A2), 191% (B1), 194% (B2) and 233% (A1), it outpaces the average increase in total food consumption. The increase is strongest in Sub-Saharan Africa where total animal-based demand in 2050 reaches 7 to 9 times the value of 1990. In South Asia, demand also increases by a factor of 5 to 9. In contrast, animal-based demand stagnates in the OECD regions in the scenarios A1 and A2 or even declines in the environmentally oriented scenarios B1 and B2.
For animal-based demand in the A1 and B1 scenarios, the increase in per-capita demand by 106% (A1) and 80% (B1) becomes the dominant driver, compared to the increase in population. In the regionalized A2 and B2 scenarios, population growth still remains the dominant driver, but also per-capita demand grows by 31% (A2) and 68% (B2). Throughout all four animal-based demand projections, the increase in the share of animal-based calories is more decisive than the increase in total calorie demand per capita.
In the second half of the century, most regions already have a decreasing share of animalbased calories. Only in the least developed regions like Sub-Saharan Africa, South and South-East Asia, the animal-based share in some scenarios still slowly increases. At the same time, global demand for animal-based calories decreases in all but the A2 scenario (Fig 7). In the B scenarios this can be explained by a declining share and stagnating per-capita calorie consumption. In the globalized scenarios A1 and B1, a decreasing global population also contributes to the decline in the demand for animal-based products.
Comparing our results to those studies with projections for animal-based calories [19,20], the regional population-weighted means as well as global averages are also in good agreement (Fig 6, right and Tables 9 and 11).

Validation
The resulting demand values are examined from three different angles: their sensitivity towards the data used for building the regression models, their trends in the common period of data and projections and their comparison with values reported in the literature. Table 9. Comparison of projections in kcal capita −1 d −1 . Transforming the projections of Alexandratos et al. [18] for animal products into calorie values has been done by Valin et al. [19]. We aggregated our national values in order to match the FAO regions below. In comparison with values from FAOSTAT [1], we presume that ( Table 2, [19]) refers to total animal-based calories. The B2-Regional scenario of Valin et al. [19] takes population and income projections of the B2-scenario of Nakicenovic et al. [8] and assumes that food demand evolves according to strong regional specifications. DC = Developing Countries, IC = Industrial Countries (including Australia, Japan and New Zewland), TC = Transition Countries. The following subregions belong to DC: SSA = Sub-Sahara Africa (excluding South Africa), MEA = Middle East and North Africa (including Turkey and Afghanistan), LAM = Latin America, SAS = South Asia, EAS = East Asia.

Sensitivity of demand regression models
Each of the regression models was tested with regard to the sensitivity of the estimated parameters on the data used for the fit (as described in the Methods section). By randomly sampling a subset of the data for 1000 times and fitting the regression with this subset, the robustness of the models can be evaluated by two criteria. On the one hand, the parameters derived from the subset can be compared to those from the entire dataset, and on the other hand, the resulting estimates for total calorie demand and the animal-based calorie share can be compared to the residual data subset that were not used for the fit. For the first criterion, we divided the parameters determined from the respective subset of the data set through the parameters determined with the entire data set as the relative deviation from one can serve as criterion for the evaluation of model robustness. Our results show that for all parameters the relation between the parameters derived from the subset and those derived from the entire data set is close to one (Figures A and C in S11 and S12 Figs). Slight deviations can be seen for parameter ω 2 for model g B (Figure C S11 Fig). The second criterion is evaluated by using the residual third part of the dataset not used for the fit and calculating the coefficient of determination of the linear regression between models and data. The distribution of the respective coefficient of determination (Figures B and D in S11 and S12 Figs) is very close to the one determined from the entire data set. So, both criteria support the credibility of the chosen regression models.

Comparison of trends in overlapping period
The SRES projections start in 1990 and have an overlapping period of approximately 20 years with historical data. Within this period, population and income projections already diverge substantially from historical records (S1 Text). Nevertheless, we decided to keep the base year of 1990 in order to make our results consistent with other SRES-based studies. In order to evaluate the temporal trends of the historical data in comparison to those from the scenarios, we calculate trends from datasets from the FAO (1988 to 2007) and from regression results (1990 to 2010) (see description of Mann-Kendall test in Methods section).
For most of the regions, the reported data show significant trends as calculated by the Mann-Kendall test. For the total calorie demand (Table 7), regions with highest trends are best met by globally oriented scenarios (A1 or B1), whereas medium increases are mostly met by the regional scenarios (A2 or B2). Trends for the animal-based share have much lower values (Table 8) and are in most cases well represented by regional scenarios. Here, the higher positive trends follow mostly an economic storyline (A2) and the lower and negative trends are better met by an ecologic scenario (B2).

Comparison of calorie demand projections to other studies
In the following, we compare the projections of per-capita calorie demand to published estimates. Since the respective studies use world regions which partly differ from our geographical units, we aggregate our national values in order to make them comparable. For the comparison to Alexandratos [47], Valin et al. [19], Alexandratos and Bruinsma [17], and Kruse [21], we choose calorie projections of the B2 scenario (Table 9 and 10). For Valin et al. [19] this is a natural choice, since their assumptions on income and population are also based on the B2 scenario of Nakicenovic et al. [8]. The B2 scenario is also the most appropriate "middle of the road" for the comparison with Alexandratos [47], Alexandratos and Bruinsma [17] and Kruse [21], which have only one projection. To compare our calorie demand values to Dorin et al. [20] (Table 11), we choose the A1 scenario, which fits best to the Agrimonde Global Orchestration Scenario based on the Millenium Assessment report.
For global average per-capita calorie demand in the year 2000, other studies give values of 2789 kcal capita −1 d −1 [47], 2731 kcal capita −1 d −1 [19] and 2708 kcal capita −1 d −1 [21]. As these studies have the same base year, namely 2000, the difference between the studies is probably caused by different download dates from FAO food balance sheets on which their values are based. The base year of our study is 1990, values for 2000 are therefore projections, which at 2736 kcal capita −1 d −1 meet the global values of the other studies quite well.
Our global estimate for per-capita calorie demand in 2030 is within a range of 100 kcal capita −1 d −1 of Alexandratos [47], Valin et al. [19] and Kruse [21] for the B2 scenario. Valin et al. [19] also report global estimates for other scenarios which are comparable to our values. While they project 2995, 3095 and 3135 kcal capita −1 d −1 for the scenarios A1, B2 and B1, we predict 2949, 2990 and 3062 kcal capita −1 d −1 , respectively. In 2050, our scenario B2 lies at 3177 kcal capita −1 d −1 between the results of Kruse [21] at 3259 kcal capita −1 d −1 and Alexandratos [47] at 3130 kcal capita −1 d −1 . Our A1 scenario estimate for 2050 is only 20 kcal capita −1 d −1 lower than Dorin et al. [20]. On a regional level, the results of our B2 scenario for per-capita calorie demand are in between the estimates of Alexandratos [47], Kruse [21] and Valin et al. [19] for most regions. Only for Sub-Saharan Africa our estimates are lower, and for the transition countries of the Former Soviet Union we have slightly higher estimates.
Turning to animal-based demand, our global B2 estimate for 2030 is about 100 kcal capita −1 d −1 higher than in Valin et al. [19] and Alexandratos [47]. This is due to the temporal increase in animal-based demand in developing countries. The livestock share is 20.9% of the total demand in our study, while it is only 15.5% and 14.6% for Alexandratos [47] and Valin et al. [19]. On a regional level, we find that Valin et al. [19] and Alexandratos [47] project an increase in animal-based calories up to 2030 for the OECD regions, while our study projects a decrease.
When comparing our results for animal-based calorie demand in 2050 to Dorin et al. [20], we have considerably lower estimates for the OECD countries. Therewith, our projection is able to reproduce the historical trend in North America, Europe and Pacific OECD, where the share of animal-based calories fell since the 1960s, 1980s and 1990s, respectively, and where the absolute amount of livestock calories stagnates or decreases. This pattern is most predominant in our sustainable scenarios B1 and B2, while e.g. in our global and materialistic A1 scenario animal-based calories in OECD regions increase to 1181 kcal capita −1 d −1 in 2030. Only after reaching a peak value of 1235 kcal capita −1 d −1 in 2050 they do start to decline.
For countries in transition we project quite a steep increase in animal-based calorie demand until the year 2030 compared to other studies. Traditionally, countries in Central and Eastern Europe and Former Soviet Union had very high livestock demand in relation to their income [48]. Due to our calibration to the base year 1990, this regional peculiarity persists in our approach into the near future. Furthermore, for the B2 scenario we assume that the animalbased calorie share is highest for medium incomes (function h B ) which applies to Former Soviet Union countries.

Child mortality and children underweight
In order to relate food demand to food security, we refer to the independently estimated children mortality and children underweight indicators for children below 5 years. In countries reporting more than 2500 kcal capita −1 d −1 , child mortality and children underweight is comparatively low. Only less than 3% of these countries have child mortalities of more than 10% (Fig 8a) and children underweight of more than 20% (Fig 8b). On the other hand, countries with less than 2000 kcal capita −1 d −1 report at least a child mortality of 5% and children underweight of 10%. Although calorie availability seems to be a good indicator for the lower end of both aspects of food security, the highest values for child mortality and children underweight are not reported for countries with the lowest calorie demand values. More than every fourth child under five dies in African countries (Mali, Niger, Sierra Leone or Rwanda), where demand values between 1780 and 2200 kcal capita −1 d −1 are calculated. And nearly every second child (> 45%) under five is underweight in Asian countries (Bangladesh, India, Nepal or Cambodia) although demand values are above 2000 kcal capita −1 d −1 with one exception (between 1850 and 2300 kcal capita −1 d −1 ).

Interpretation of functional relations
Driving processes behind food demand dynamics are most likely different for the short-term and for the long-term. Major drivers of short-term dynamics include harvest failure, food storage capacities, expectation failures, policy interventions like trade regulations or biofuel targets, or business cycles and speculation. In contrast, major drivers of long-term dynamics include population, income, urbanization, demographic composition, market access, lifestyles, or the extent of physical labor. Long-term models should therefore consider other drivers and dynamics than short-term models. We decided to reduce the complexity to three major indicators that are representatives for these drivers, namely population, income and time.
Both sets of functions for per-capita consumption (g A and g B ) and the share of animalbased products (h A and h B ) give satisfactory results for the reproduction of historical data but assumptions on the form of the temporal development have a decisive effect on the projections. Especially the functional types for the share of animal-based products strongly diverge for high-income countries. As only 10 countries reach an average income above 40,000 US$ before 2005, the few observations do not allow to favor one of these functional relations.
Our statistical analysis cannot reveal the underlying causal relationship between income, time and food demand, which is open for debate. The strong increase of both total food demand and the share of animal-based products for low and medium income countries may be attributed amongst others to a higher purchasing power of consumers or a stronger economic development of food producers leading to falling prices for staple goods [5,50]. The positive non income-related time trend of total food demand could stem from a higher social alienation from the food production process due to urbanization, more single member households and increased openness to global markets [5,51]. Finally, the negative time-trend for the share of animal calories and the eventual negative connection to income could be attributed to a higher health consciousness among better-educated people [36] or to alternative lifestyles like vegetarianism becoming a status symbol.
At the same time, our empirical findings are not in line with the underlying assumptions of simple economic demand models that are based on a positive elasticity constant over time and income. The significant time trends in all our representations indicate that either elasticities should be adjusted over time, or that demand models should include other drivers than income. Additionally, our U-shaped regression even opens up the possibility to question a positive elasticity as such.
Our demand projections are influenced by our assumption, that national peculiarities, represented by the divergence of current demand from the regression results, disappear until the end of the 21 st century and that all values converge to the regression results (Eq 13). A contrasting hypothesis could be that these peculiarities are kept over time, such that the projections for 2100 deviate by the same percentage from the regression results as in the inital year (here 1990). Changing our assumption (Eq 13) accordingly leads globally to an increase of the total calorie demand of about 3.3% (2050) and 6% (2100). The alteration of the assumption would have larger consequences on the heterogeneity across countries. Whereas under the convergence assumption, the standard deviation across countries is about 704 kcal capita −1 d −1 ; this value increases to 833 kcal capita −1 d −1 when the peculiarities in national diets are maintained. Total demand is much higher than in the convergence estimates for the former Soviet Union members like Uzbekistan, Kosovo, Bosnia and Herzegovina, Serbia, Montenegro, or Ukraine, while it is lower for African countries like Angola, Chad, Eritrea, or Ethiopia. Nevertheless, the analysis of the FAO statistics of the past 50 years already reveals a convergence of food baskets [52] so that the assumption of convergent diets is most likely.

Interpretation of projection results
For long-term projections, data quality is still low and the understanding of socio-economic dynamics is weak. Future analysis has therefore to rely on the evaluation of multiple scenarios instead of best-guess forecasts. The benefit of such scenario analysis is to consistently deliberate the implications of a set of assumptions. We provide a tool that can be used for such scenario analysis. Even though the set of adjustable assumptions is limited (adjustable population and per-capita income, two sets of functional relations for per capita caloric demand and for the share of livestock-based calories, two types of calibration, exogenous values for long-term targets), this provides already considerable freedom to create own scenarios that can be adapted to a storyline consistently.
Exemplarily, we applied our method to the SRES storylines, which are characterized by the The resulting regional per-capita demand values remain in reasonable ranges given the strong income growth in the scenarios. The highest value for total calorie demand of 4700 kcal capita −1 d −1 for Northern America (S8 Fig) has to be seen in the context of the materialistic storyline of scenario A1 and a per-capita income which quadruples compared to current levels. For the sustainable scenarios B1 and B2, the projected per-capita demand exceeds only slightly the observed range of the past despite more than doubling per-capita income. Animal-based calorie demand on the regional level (S9 Fig) remains completely in the observed range. The increase of vegetal demand beyond observed ranges (S10 Fig) in scenarios B1 and B2 stems from the reduction of animal-based calorie demand due to the assumption of a more healthy diet in higher income ranges.
Some of our results seem surprising given the SRES storylines, but are consistent at a closer look.
First, one would not expect an increase of per-capita demand in high-income countries, as metabolic requirements are constant or even decline due to less physical labour in high-income groups [4]. Nevertheless, demand in these regions still increases, which has to be attributed to an increase in food waste at the household level.
Second, it seems plausible that food demand in the environmentally oriented scenarios (B1 and B2) (S6 and S7 Figs) is lower than in the materialistic oriented scenarios (A1 and A2) (S4 and S5 Figs) as people according to the latter storylines are likely to waste more food. A closer look reveals that a highly populated A2 world goes along with lower per-capita incomes in many developing regions. This leads to lower total per-capita demand values and, hence, people simply cannot afford to waste food.
Third, the animal-based share in developing countries increases faster in the environmental than in the materialistic scenarios. This occurs only for medium income countries with an income range that increases from 1,000-26,000 US$ in 1990 to 3,600-39,000 US$ in 2100. In this income range, the projected livestock share is smaller for function h A (applied to A1 and A2) than for h B (applied to B1 and B2). For the same income and year, results from function h A are up to 20% lower than values from h B . Especially for the regionalized scenario B2, income in many countries stays below 30,000 US$ so that their livestock share is higher than in scenarios A1 and A2. This peculiarity comes from the requirement that both models have to be consistent with past data. If the share of animal-based calories is assumed to fall with high incomes, the medium incomes need to have an even higher share in order to fit observations (compare blue curves in Fig 4 with red curves). We did not find a functional type fitting the same observation data that produces lower results for every possible combination of drivers.
Although using a single global approach for the estimation of food demand on the country level, trends of the projections in the overlapping period of data and projections compare well to those from observed data (Tables 7 and 8). Moreover, our estimates are well within the range of published projections by other authors (see results section). Finally, we showed with an analysis of regression models with random subsamples of two thirds of the observations that the other third can be predicted with a similar coefficient of determination as the model from the entire dataset (S11 and S12 Figs).

Food security prospects
The share of population which is undernourished declines with increasing per-capita demand at the country-level [49,53]. According to FAO [53], countries with more than 2500 kcal capita −1 d −1 do not observe undernourishment for more than 20% of the population. However, estimating the prevalence of undernourishment based on distribution corrected food availability as done by FAO [53] was criticized as being unreliable because it is a top-down approach that has to rely on poor statistical data [54]. Instead, Svedberg [54] proposes to use anthropometric bottom-up measurements like the prevalence of stunting and underweight. Unfortunately, global data on food security is still deficient and incomplete [55]. One of the few available global datasets that includes anthropometric measurements is the Global Hunger Index (GHI) [49] which is composed to equal shares of the prevalence of child underweight, child mortality and FAO's [53] top-down estimates. The GHI shows surprisingly strong correlation (Pearsons correlation coefficient of -0.84) with average per-capita demand per country [1] but it has to be considered that the data sources are not independent as undernourishment is estimated partly based on FAOSTAT [1].
According to our projections, the range of values between 2000 and 2500 kcal capita −1 d −1 will persist in some countries also in the coming decades (S4, S5, S6 and S7 Figs). While there is no country in 2050 that has a per-capita demand below 2000 kcal capita −1 d −1 , many people still live in countries with an average demand of 2000-2500 kcal capita −1 d −1 , ranging from 1.9 billion people in the A2 scenario to 0.3 billion people in the A1 scenario.
The major geographical areas of concern are clustered in the tropics. Most severely affected are the world regions Sub-Saharan Africa (< 2400 kcal capita −1 d −1 and 8% animal-based calories in the year 2005) and South Asia (< 2300 kcal capita −1 d −1 and 9% animal-based calories in 1990). According to our scenarios, per-capita demand will grow slowly in both regions. Comparing the demand in these least developed regions to the demand of a transition country like China in 1990 (% 2600 kcal capita −1 d −1 , 12% animal-based calories), Sub-Saharan Africa will reach a similar level only in 2030 (A1) or 2045 (B2). Also South Asia will reach this level only between 2020 (A1) and 2030 (A2). This suggests a time lag of 30 to 55 years to the development of China.
While food availability can be expected to increase, also obesity and related health problems are currently strongly rising. Already today, obesity is responsible for a similar extent of premature deaths as hunger [56]. It is of large interest to include the dynamics that determine overnourishment into future assessments.

Conclusions
This paper provides a simple method to create customized food-demand scenarios. It requires only information on gross domestic product and population which are the key indicators of many future scenarios. Despite this slim approach, the results of our projections are in good accordance with other studies.
Many investigations use scenarios that are adapted ex post to meet a certain storyline, e.g. by reducing the demand of livestock products by a certain share [10,11,57]. Our method is exceptional by adapting ex ante the core assumptions of the functional relations instead of changing the results ex post. In so doing, projections remain consistent with historical data. The results of our ex-ante customization sometimes seem unintuitive at the first glance, but at a closer look they are logical and more consistent with the overall storyline and history than an ex-post approach.
Our method has been applied exemplarily for constructing a set of food demand scenarios consistent with the SRES storylines, but could also be easily used for upcoming scenarios like the Shared Socio-economic Pathways (SSP, [58]). Applying our method or using our results may be of interest for different scientific communities. For investigations of food security aspects, our long-term scenarios suggest that food availability will rise above critical thresholds for wide parts of the currently developing countries. However, food availability in some countries, in particular in Sub-Saharan Africa, is likely to remain at critical levels in the coming decades such that long-term engagement is required. For health studies, the dynamics of excessive consumption of animal-based calories may be interesting, as it can be clearly linked to a number of heart and vascular health problems and colon cancer [59][60][61][62][63]. Finally, our longterm food demand scenarios can be valuable for the environmental science community. As our results suggest a doubling of food demand in all scenarios and an over-proportional increase of animal-based calorie demand, the pressure on environmental systems can be expected to increase strongly.
The model used in our study is provided as a package in the programming language R. We hope that other researchers will make use of and extend this open source project. For example, future research could try to split food demand projections into intake and waste. This could be done by estimating food energy requirements of a population based on body mass index, age structure, and physical activity, correcting for over-and under-consumption with estimates on stunting and obesity. Also, the model could be extended to include lifestyle-related drivers of food demand like urbanization or education for which historical panel datasets exist. (EPS) S1 Dataset. SRES scenario results of food calorie demand. Datasets of the historical period and SRES scenario projections are included in a Excel file. The data are available on country and regional resolution for total and animal-based food calorie demand as well as for income and population data. (ZIP)