An exploratory model of the impact of rapid climate change on the world food situation
Grechen C. Daily and Paul R. Ehrlich (1990)

Department of Biological Sciences, Stanford University, Stanford, California 94305-2020, U.S.A.

table of contents

SUMMARY

A simple, globally aggregated, stochastic-simulation model was constructed to examine the effects of rapid climatic change on agriculture and the human population. The model calculates population size and the production, consumption and storage of grain under different climate scenarios over a 20-year projection time. In most scenarios, either an optimistic baseline annual increase of agricultural output of 1.7% or a more pessimistic appraisal of 0.9% was used. The rate of natural increase of the human population exclusive of excess hunger-related deaths was set at 1.7% per year and climatic changes with both negative and positive impacts on agriculture were assessed.

Analysis of the model suggests that the number of hunger-related deaths could double (with reference to an estimated 200 million deaths in the past two decades) if grain production keeps pace with population growth but climatic conditions are unfavourable. If the rate of increase in grain production is about half that of population growth, the number of hunger-related deaths could increase about fivefold (over past levels); the impact of climatic change is relatively small under this imbalance. Even favourable climatic changes that enhance agricultural production may not prevent a fourfold increase in deaths (over past levels) under scenarios where population growth out paces production by about 0.8% per annum.

These results may foreshadow a fundamental change where, for the first time, absolute global food deficits compound inequities in food production and distribution in causing famine. The model also highlights the effectiveness of reducing population growth rates as a strategy for minimizing the impact of global climate change and maintaining food supplies for everyone.

1. INTRODUCTION

The conversion of land to agricultural use and exploitation of diverse other natural resources has generally increased the capacity of Earth to support human beings. In recent decades, however, the human enterprise has grown so large that it is seriously altering the global environment (SCEP 1970; Holdren & Ehrlich 1974; FAO, UNFPA and IIASA 1982; Keyfitz 1984, 1989; Sadik 1988). Humanity is now rapidly depleting fertile soils, fossil groundwater, biodiversity, and numerous other non-renewable resources, to support its growing population (Brown et al. 1990; Ehrlich & Ehrlich 1990; SCEP 1970). This resource depletion, coupled with other human pressures on the environment (e.g., production of toxic wastes, changing the composition of the atmosphere) is undermining the capacity of the planet to support virtually all forms of life (Ehrlich et al. 1989).

Possibly the most serious of human impacts is the injection of greenhouse gases into the atmosphere. The nature of climatic changes likely to result from greenhouse gas emissions is not yet clear in detail. The magnitude and pace of change that climatologists believe probable are unprecedented in human history (Abrahamson 1989; Cairns & Zweifel 1989; Lashof 1989; NAS 1987; Schneider 1989). Should such change occur, there will inevitably be wide-ranging effects on many facets of human societies. Current patterns and future plans of energy use and industrialization will require major revision (Chandler 1986; Chandler et al. 1988; Holdren 1990). International tensions are likely to heighten over claims on freshwater where scarce supplies are further reduced (Cooley 1984; da Cunha 1989; Gleick 1989; Myers 1989), transnational migration of environmental refugees Jacobson 1988), and ultimate responsibility for global warming and its effects (Gleick 1989).

The global production and distribution of food is inadequate for a large fraction of the rapidly expanding global population of 5.3 billion people under present and foreseeable economic systems (WRI 1987; Brown 1988; Brown & Young 1990; Ehrlich & Ehrlich 1990). The agricultural and food-distribution systems may be further stressed by shifting of temperature and precipitation belts, especially if changes are rapid and not planned for (see, for example, Adams et al. (1990)). There is also the alternative possibility, in our view much less likely, that climatic changes (or increased levels of CO2) will actually enhance global agricultural production.

In this paper we investigate the possible positive or negative effects of climate change on global food security by using a computer model. We focus on grain because it supplies over half of the calories in the average diet when consumed directly (and a substantial part of the remainder in the form of meat, eggs and dairy products (Brown 1988)) and accounts for the vast majority of the international trade in food (WRI, 1989). The model is a very simple, aggregate representation of global agricultural systems and human populations. Its results do not represent specific predictions, but offer insight into the relative impact on the growing human population of changes in agricultural production that may result from global warming. It does not consider many potentially important issues ranging from the chances of social breakdown accompanying large famines or the exhaustion of fuel wood needed for cooking grains before grain supplies run short to the possibility that bioengineering can enhance food production far beyond the trends envisioned here. In the following, we present the structure, results and limitations of the model, and then offer our interpretation of the results.

2. THE MODEL

The model simulates the effect of stochastic perturbations in food production (due to climate change) on population size. In yearly increments, the models calculates human population size, number of hunger related deaths, and the production, consumption and storage of grain under different climatic scenarios (see Appendix 1 for the equations). Parameters that may vary in each run of the model include the initial population size, the initial level of grain production and grain stores, the rate of change in population size and grain production, whether climate change has a net favourable or unfavourable impact on global agricultural production, the frequency and magnitude of changes in global harvest because of changed weather patterns, the projection time, and the desired number of simulations. The climate scenarios are described in terms of two parameters: the frequency and the magnitude of changes in global grain production caused by changing weather patterns. All of the parameters in the model represent aggregates for the world as a whole.

Global aggregation of the model is a serious limitation. Geographic variation in weather tends to make gluts or shortfalls of grain regional events whose consequences can, at least in theory, be compensated by trade. When the highly aggregated ''limit to growth' model (Meadows et al. 1972) was re-run at regional levels (Maarovic & Pestel 1974) it was found to have overestimated global disaster but underpredicted regional disasters. However, because of the uncertainties of modeling climate (especially at regional levels), the changing patterns of international grain trade, and the functioning of futures markets, disaggregating our model did not seem a wise course. Instead, we attempt to capture some of the complexities of regional variations in our parameterization of mortality relative to global grain stocks (described later).

In what follows, we define an iteration as a single execution of the core operations of the model (determining population size and the production, consumption and storage of grain for a single year; see figure 1). We define a simulation as the execution of the entire model once. To generate the output presented here, the model was iterated twenty-times per simulation (i.e., the projection time is 20 years). Finally, a run is a set of simulations done under the same initial conditions. Ten-thousand simulations were executed per run.

The manipulations of the input parameters are described next, in the order presented in figure 1. The initial values of input parameters for population and agricultural production were selected from recent but not extreme years.

The annual rate of natural increase of the population size (D N) is a constant percentage. For most runs, the initial population size and growth rate were set at 5.000 billion and 1.7% per year, respectively, figures that roughly reflect conditions in 1986, the year of peak grain harvest to date. Population size may be sharply reduced by grain shortages (which cause rapid increases in deaths by starvation). These periods of population decrease are assumed to be instantaneous. Following such periods, the. constant rate of increase is applied to the new lower population size. The between low or empty grain stocks and population is described below.

For most scenarios, initial production was set at 1.65 billion metric tons (T) grain, roughly the amount that was consumed in 1986. The underlying rate of change in grain production (the ' trend ') also remains constant. For reference, the average value of the trend was 2.6 % per year from 1969 to 1979, and 1.4% per year from 1980 to 1988 (FAO 1970-89). To simulate normal stochastic fluctuations in production, the amount harvested in a given year is caused to deviate from the trend bv one of five values (0.0, +2.0, -2.0, +4.0, or -4.0%) selected at random each year. These values were selected to create a pattern resembling a relatively favourable decade for global agriculture. The fluctuations in grain production generated by the model (expected variance 8.0%) are roughly comparable to those that actually occurred over the decade 1962-71 (observed variance 8.5%) a decade with little variation in the upward production trend. By contrast, the observed variances in grain production in the preceding (1952-61) and following (1972-81) decades were 51.0 and 20.4%, respectively. Thus the choice of the magnitude of 'normal' fluctuations was conservative.

Superimposed on these relatively small normal fluctuations are changes in global grain production caused by climatic events. Within a run, the changes are either all positive or all negative, i.e. unusual climatic events either increase or decrease production. These changes are made with a preset frequency and intensity (calculated as percent increase or reduction of potential harvest) within each run, but the actual years in which they occur are determined randomly. The grain production in a given year is completely independent of the random deviations, climatic events, and deaths occurring in all other years, and is calculated simply by adjusting the potential production expected from the trend in years in which a weather event occurs.

Regional patterns and the nature of events (e.g., drought, aseasonal frosts, extraordinarily favourable weather patterns, or possible yield enhancement through CO2 fertilization) that affect harvests are not simulated by the 'climatic' (production) parameters. Instead, the rapid changes in global climate patterns that many climatologists consider plausible as the concentration of greenhouse gases in the atmosphere increases (Abrahamson 1989; Lashof 1989; Schlesinger 1989; Schneider 1989) are simply subsumed within our production parameter as declines or increases in production. Though it is not clear whether the drought in North America in 1988 was related to global warming, it was the sort of event that climate models suggest will become more frequent and is thus simulated by runs of the model in which climatic events are deleterious (Schneider 1989). The amount of uncertainty in the implications of patterns of climatic change predicted by general circulation models for world agriculture (Golitsyn 1989) is very large. This, coupled with 'normal' regional climatic fluctuations (e.g. 20-year droughts; Mitchell et al. 1979) that can only vaguely be predicted, led us to conclude that we could not use the general circulation models to predict regional changes realistically. This is why our model is so highly aggregated.

The level of grain consumption in each year is calculated as the product of the current population size and the global average consumption per person per year. Our estimate of average consumption, 0.33 T grain per person-year, is equal to the average global per-capita production level over 1955-88 (FAO 195689; PRB 1988; UN 1987). Grain lost to wastage (estimated to be 40% between production and consumption; see notes in Kates et al. (1988) , diverted to livestock, and otherwise not consumed directly is subsumed under this global per-capita consumption.

The global grain carry-over stock is set at the beginning of each simulation. For most runs, the initial stock was set at 350 million T, an intermediate level equal to 21 % of consumption for the initial year. For reference, the record high carry-over stock is about 461 million T, achieved from the record grain harvest in 1986 (Lester Brown, personal communication), but the estimated stocks in 1990 are 293 million T, just 17 % of consumption and the lowest since 1981 (Lewis 1990). As each simulation proceeds, the stock is calculated as the carry-over stock from the previous year plus the current grain harvest minus the amount of grain consumed (as defined above). The global grain carry-over stock has a lower bound of zero T. We set no upper bound on carry-over stocks and assumed that any surplus grain can be stored for consumption in the subsequent year. (We ran the model with an upper bound on storage capacity of 750 million T, but this constraint did not influence the results under the conditions presented here.)

In the model, deaths from starvation occur because of both maldistribution and absolute shortage, as a function of global grain stock relative to consumption. It is difficult to estimate the baseline magnitude of this starvation-related mortality (see Discussion). We have assumed that distribution of food will not change significantly from past patterns over the decades of our runs. In the model, 2 million deaths occur per annum because of maldistribution at any level of grain stock. Additional deaths occur (per annum) as a linear function of stocks relative to consumption (see Appendix 1). In years when there are global grain deficits (production plus carry over insufficient to provide 0.33 T grain per capita), the model output presented here assumes that two people die for every 1 T grain deficit. The justification for this conversion factor is given in the Discussion.

The model iterates a set of equations describing this system for a projection time of twenty years for each scenario. We consider that period sufficiently long to reflect trends, but not so long that agricultural and economic systems are likely to change fundamentally. The mean and the standard deviation of several statistics are recorded on the completion of each run: the total number of deficits, the magnitude of the deficits, the total number of deaths and maximum that occurred, and the final population size.

3. RESULTS

The output of the model under a variety of scenario' is displayed in tables 1-7 and summarized in figure 2. These results are described briefly here and then interpreted in the Discussion. In most cases we contrast the output under different scenarios with reference to the average number of deaths produced in a run, a figure that reflects both the frequency and magnitude of changes in grain stocks. Generally, in what follows 'deaths' refers to hunger-related deaths in excess of those subsumed in the natural rate of increase. When there are no grain deficits, such deaths are caused by maldistribution; when there are deficits, both maldistribution and absolute shortages cause them.

To determine the validity of the model, we ran it simulating conditions approximating those that actually held over 1969-88. The initial population size was set at 3.616 billion people, the rate of natural increase was 1.8 % per annum, the initial level of grain production was 1.19 billion T, the grain production trend was 2.1% per annum, and variation about the trend was 21%. The probability of climatic events aside from those reflected in variation in the trend) was set to zero. Under this scenario, the mean number of grain deficits per 20-year simulation is 0.0 (± 0.8), about 100± 30 million people die of hunger-related causes in total, and the final population size for 1988 is 5.0 billion. The few deficits that occurred in simulations of this scenario result directly from the random fluctuation in production about the trend; the deaths result from those fluctuations as well as maldistribution. For reference, although no global grain deficits occurred over the period 1969-88, about 200 million people are estimated to have died of hunger or hunger related disease over that time (Dumont & Rosier 1969; WHO 1987; see discussion in WRI (1987). Results of the model thus appear, if anything, to be conservative.

Unless explicitly stated, the runs discussed next were done under initial conditions roughly matching those of 1986 as explained above. For comparative purposes, we ran the model in the absence of unfavourable climatic events and under the assumption that annual growth in grain production (D G)would keep pace with that of the population (D N), which was 1.7% in 1986 (D N is now 1.8% PRB 1989). Over the 20-year projection time under this scenario (run A, table 1), although there are no grain deficits (0.0± 0.0), 152± 39 million deaths occur because of maldistribution of food, leading to a final population size of 6.818 billion. The variance in the output statistics is quite high, as indicated by the occurrence of 304 million hunger related deaths in one of the 10000 simulations. The final population size at a constant growth rate of 1.7%, with no hunger-related reductions, would be 7.005 billion (5.000 x 10⁹ x (1.017)²⁰)

The model was run under several climatic scenarios with negative changes in harvest ranging from 3 to 10% per event. These seem reasonable values, because a reduction of about 5% (from the 1969-88 trend of 2.1% growth per annum) can be attributed to weather-caused harvest failure in 1988. The first set of the following runs assumes that D N = D G = 1.7% and that the initial carry-over stocks totaled 350 million T (table 1). Under these growth rates, a 5% reduction in harvest every five years (on average; probability of event, P_e = 20% causes 0.1 (± 0.3) deficits and 214 (± 59) million deaths per simulation, with a 57% chance of exceeding 200 million deaths ( run B). Doubling the magnitude of harvest reduction to 10%, increases the mean number of deaths to 326 (± 139) million (run C), and the probability of exceeding 200 million deaths rises to 85%. Increasing the average frequency of reductions to 1 in 3.3 years (P_e = 30%) causes 254 (± 72) million and 430 (± 154) million deaths under 5% (run D) and 10% (run E) reductions. respectively. Increasing the average frequency of reductions further to every other year (P_e = 50%) results in 248 (± 57), 338 (± 90), and 583 (± 121) million deaths under 3% (run F), 5% (run G), and 10% (run H) reductions, respectively.

Not surprisingly, reducing global grain harvests below the trend by 10% every year (run I) leads to the highest number of deaths (774± 42 million). The variance in the number of deaths under this latter scenario is especially low because there is no variance in the sequence of unfavourable years: each year is unfavourable.

Current trends in agriculture suggest that assuming grain production levels can increase by 1.7% annually is very optimistic. Growth averaged just 1.4% annually from 1980-88 (FAO 1982-89). In fact, the World watch Institute believes that the world's farmers will have difficulty expanding the average production at much more than 0.9% annually in the 1990s (Brown et al. 1990). Achieving either of these growth rates (1.7 or 0.9%) could well require substantial technological innovation, and maintaining productivity in the long run will clearly require major changes in farming practices. Therefore, we repeated the set of runs presented in table 1 under the assumption that D G = 0.9 % over the 20 year projection time. Table 2 displays the output of these simulations.

Even in the absence of unfavourable climatic conditions (run J, table 2), the imbalance between D N (1.7%) and D G (0.9%) leads to a staggering 891 (± 97) million deaths over the 20-year projection time. Under each scenario with climate-induced reductions (runs K-R), over 900 million people die on average and the probability of exceeding a billion deaths is usually 30% or more. However, imposing various deleterious climatic regimes (runs K-R) on grain production does not increase the resulting average number of deaths as much as when D G equals D N runs B-l, table 1). An explanation of this possibly counterintuitive result is given in the discussion.

To test the sensitivity of the model to different rates of increase in grain production relative to those of population growth, we ran an identical set of climate scenarios on both the conditions that D N = 1.7% and D G = 1.3% (runs S-U, table 3), and that D N = 1.7% and D G = 2.4% (runs V-X, table 3). The number of deaths that occur with D G = 1.3 is appreciably less than under the comparable scenarios with D G = 0.9 (runs K, M, and L, table 2). The number of deaths that occur when D G = 2.4% (runs V-X, table 3) is roughly comparable to that where D N = D G = 1.7 and no unfavourable weather patterns occur (run A, table 1). The model is similarly sensitive to changes in D N (holding D G and other parameters constant; table 4).

The number of deaths produced with D N = D G = 0 9 % is only slightly less (7%, on average) than under the same climatic scenarios with D N =D G = 1.7% ( runs B, D and C, table 1) . Scenarios AB-AD ( table 4) and S-U (table 3), all cases where the difference between D N and D G is 0.4, result in comparable numbers of deaths. Thus the critical factor is, not surprisingly, the difference between D N and D G, and not the absolute value of either (at least over the range of values presented here). This is in part because of our conservative assumption that a large population size (created by a large D N) does not itself cause more rapid climate change and thus more frequent extreme weather events.

The initial stock plays an important role under some conditions (see table 5). If the stock is set at zero to start, any initial fluctuations in grain production must be positive to avert immediate deaths. The influence of the initial stock on the final outcome is diminished when other factors come into play. For example, under relatively severe climatic conditions, the increase in mean number of deaths when initial stocks are set at 0 T (run AG) as opposed to 500 million T (run AH) is 67 % over the 20-year span. In contrast, when climate has no deleterious impacts on agriculture, the difference in mean number of deaths when initial stocks are set at 0 T (run AK) as opposed to 500 million T (run AF) is 123%. In the severe case, the climate parameters overwhelm the effect of initial stock.

It is unclear whether the recent climatic events deleterious to agriculture (e.g. the droughts in North America and China, the below-average rainfall in north-central Africa since the 1960s; Schneider & Londer 1984) are related to global warming. To test the sensitivity of the model to the timing of the onset of climatic changes caused by such warming, we ran it with an initial population size reflecting projections for 2020 (a date by which many climatologists believe the effects will be manifest). For these scenarios, we assumed that the rate of increase in grain production up to 2020 kept pace with that of population growth, such that per-capita production was 0.33 T grain per person to start. Initial population size was set at 8.330 billion people (as projected by the PRB (1989)) and initial grain production was set at 2.7489 billion T per year. We then ran the model under rates of population growth projected for 2020 (United Nations 1989), several annual rates of increase in production, and various climate scenarios (table 6).

The mean number of deaths per simulation under this set of scenarios (runs AI-AR, table 6) ranges from 135 million to 760 million, with the maximum in a simulation over 1.2 billion. Even when D G exceeds D N, reductions in harvest of 10% occurring with a mean frequency of once in three years (runs AL and AP) cause an average of 272 million and 237 million deaths. In contrast. when D N exceeds D G by 0.4% or more and 10% reductions occur every three years on average, over a billion people starve to death per simulation (runs AN, AQ, and AR).

Finally, we investigated the effect of a net positive impact of anthropogenic climate change on global agriculture (table 7). Under scenarios where growth in grain production keeps pace with population growth and favourable weather events increase production by 5 or 10% every 3.3 or 5 years (runs AS and AT, respectively), very few deaths occur. However, if growth in grain production is just 0.9% per annum while population size continues to expand at 1.7 % per annum then, even under the same very favourable climatic scenarios (runs AU and AV), over 800 million deaths occur on average.

4. DISCUSSION

The complexity of the systems that interface in this model, including population, agriculture, and climate, not to mention economics, trade, government policy and international relations, make it impossible to quantify accurately the interactions between them. None the less, the results of our relatively simple model have heuristic and perhaps some predictive value (see also Liverman (1983)). They offer insight to the vulnerabilities of our agricultural system and growing population, and provide a measure of the relative importance of key factors in the population-food-climate interaction.

(a) Limitations of the model

The model has several important limitations. First, it accounts for regional heterogeneity only by including deaths caused by maldistribution. This is a crude approximation because inequitable distribution of food (and wealth in general) and extreme heterogeneity in population density, in agricultural productivity (over space and time), in climate regimes, and in the variability of weather patterns are key factors in generating regional famine. For example, at least since 1966, the world has never experienced a global grain deficit (by our standard of 0.33 T per person per year; (FAO 1956-89; PRB 1988, 1989; United Nations 1987)), yet hunger has afflicted local and regional populations repeatedly throughout this period (Ehrlich et al. 1977; Murdoch 1990).

Secondly, the model does not include mechanisms whereby compensation for imminent food shortages could be made. Such mechanisms include (i) spurring research and development of new technology and crop strains to increase yields; (ii) intensifying crop production with increased inputs of water, fertilizer and pesticides; (iii) bringing set-aside and other marginal land in the U.S.A. and elsewhere into production; iv consuming more crops directly (as opposed to feeding livestock); (v) reducing herds by temporarily consuming more livestock (which represent a large food reserve); (vi) reducing wastage between farm and stomach; and (vii) development and implementation of emergency relief measures to minimize and contain the effects of local crop failures.

How likely are such ameliorating factors to make major impacts? The potential effectiveness of mechanism (i) is debatable: although no bright technological prospects lie on the immediate horizon (Brown & Young 1990), there is evidence in support of the hypothesis that crises stimulate innovation (Boserup 1981). Mechanisms (ii) and (iii) are likely to provide only short-term relief, and to be detrimental in the longer term; these traditional methods of expanding agricultural production are very resource intensive, generally not sustainable, and rapidly approaching physical constraints (Brown & Young 1990; Ehrlich 1989; Postel 1989). Mechanisms (iv)-(vii) are critical steps towards buffering over-large populations from the most devastating effects of insufficient production. All of these mechanisms may operate to reduce the number of deaths predicted by the model, but none represents a long-term solution to the problem of D N outstripping D G.

Thirdly, the model implicitly assumes that the underlying ' trend' (rate of change) in grain production will remain constant even in the face of the social and economic turmoils sure to result from massive crop failures, severe famine, loss of habitable land in coastal areas and other impacts of unfavourable climate change. Furthermore, maintaining a growth rate in agricultural output of 1.7% per year embodies a series of optimistic assumptions of success in the development and implementations of better agricultural practices and technologies (vide Brown et al. 1990). In addition, the effects of climate change are assumed to be constant, when really they may intensify. These assumptions would all have the effect of underestimating the number of deaths that may result from the impacts of deleterious climate change.

Fourthly, the number of deaths produced by the model under different scenarios depends to a large degree on the factor used to convert grain deficits to deaths. Currently, three people are supported on average by each tonne of grain produced per year (PRB 1989; FAO 1989). However, 1 T grain per year delivered to the mouth can provide four adults with 'adequate' diets and five adults with 'subsistence' diets (Lester Brown personal communication). The brunt of any deficits is likely to be borne by the world's poorest people; in response to the same decrease in supply, the poor reduce their grain consumption more than tentimes as much as the wealthy, who simply forego luxury items (Mellor & Gavian 1987). At one extreme, a few tonnes deficit in a rich country would probably not cause any deaths, whereas at the other, a one-tonne deficit in a poor country might cause the deaths of four subsistence-diet adults and two children. Considering these various factors and uncertainties, we feel an estimate of two deaths per tonne deficit is conservative.

Finally, a few comments relative to our validation of the model must be made. It is very difficult to quantify the actual number of people that have starved to death over the past two decades. Aside from poor censusing in famine-stricken areas, malnutrition compromises the immune system FAO 1987; UN 1987; WRI 1987) and the immediate cause of death of severely malnourished people is thus usually reported as disease. The rough estimate of 200 million deaths ((Dumont & Rosier 1969: WHO 1987; see discussion in WRI 1987) is considerably higher than the average of 100 (± 30) million deaths per simulation produced in our test scenario that approximates conditions over those decades. The numbers of deaths produced by the distributional aspects of the model are therefore probably conservative.

(b) Conclusions

Four general conclusions can be drawn from the model regarding the number of people at risk of starvation and the importance of the relation between D N and D G to both the creation of deficits and the relative impact of unfavourable climatic conditions. First, the model suggests that several hundreds of millions to a billion or so people could die of hunger in future decades. Examinations of the pattern of deaths within runs suggest that such numbers of people are not likely to die in a single large famine. The model generally indicates that unfavourable trends or climatic changes (or both) could multiply current deaths from hunger on the order of two-fivefold. Those additional deaths would not, however, be primarily 'distributional', as have been those of the past two decades. Instead, the vast majority of them could be due to absolute global shortage.

Furthermore, runs beginning with different population sizes but otherwise identical initial conditions (e.g. run AB, table 4 and run AK, table 6) result in a mean number of deaths equivalent to about a tenth of the initial population size, suggesting that the fraction of the population at risk of starvation is not greatly affected by how much the population has grown before the onset of unfavourable climatic change. The number of deaths could be much higher if the rate of increase in food production could not be maintained during major periods of shortfall. Serious social breakdown or widespread epidemics, both grim prospects that seem increasingly likely as societies become more crowded and strained (Ehrlich & Ehrlich 1990), could also greatly increase the death toll.

The second primary conclusion from the model is that seemingly small (on the order of 0.3%) differences in the annual rates of growth in population and agricultural production can have a large impact on global food security. This is an important point because land degradation (in the form of soil erosion, waterlogging and salinization of irrigated land, and decline in soil fertility), scarcity of freshwater in many parts of the world (Myers 1989; Postel 1989), and the in creasing cost of fertilizer and pesticide inputs threaten to constrain growth in grain production (Brown & Young 1990). The model highlights the effectiveness of declines in population growth toward minimizing the impact of deleterious global climate change and providing food for everyone. Initiation of the socioeconomic changes required to reduce birth rates is critical to bringing the human population to a size compatible even with the short-term carrying capacity of Earth (Ehrlich et al. 1989).

Thirdly, the model produced the interesting result that climate change contributes proportionally much less to food deficits when population growth outpaces growth in agricultural production (table 2), than when growth in each is equal (table 1). This is because deficits and great increases in mortality occur early in simulations with D N > D G that reduce population size and thereby increase per-capita production, creating grain reserves that serve as buffers against the impact of climate-reduced harvests occurring later. The increase in per-capita production results from the assumption that the production 'trend' remains constant despite reductions in population size.

Though the results under scenarios leading to high mortality may appear roughly the same (hundreds of millions of deaths) the distribution of deficits between rich and poor nations may be quite different. If the main cause of deficits is that growth in population size exceeds 'trend' growth in grain production, then the swelling populations of the Third World will be most directly affected. On the other hand, if climate change is the main contributor to deficits, then the direct impact is likely to be felt more evenly. Leading grain producers in the industrialized world such as North America, the Soviet Union, Europe and Australia (which account for about 43% of global grain production; FAO 1989) could incur relatively more severe climatic changes in grain-growing areas, with serious consequences for their economies and populations.

Finally, it is conceivable that CO2 fertilization and concomitant reduced transpiration (Easterling et al. (1989) but see Lincoln et al. (1986); Lincoln & Couvet (1989); Fajer et al. (1989)) will enhance global agricultural productivity. In our view, however, the potential benefits of CO2 fertilization are likely to be outweighed by the negative impact of changing temperature belts, reduced water availability in major grain-growing regions, possible unfavourable changes in crop-pest relations, and social and economic disruptions. In addition, we point out that the coolest years of the past decade were also the best for global agriculture (FAO 1989; Spencer & Christy 1990). None the less, the results of running the model under a net positive impact of climate change on agriculture (table 7) are interesting. As to be expected, when production keeps pace with population growth, relatively few deaths occur (and those as a result of maldistribution). However, if population growth outpaces production by 0.8% per year or so, then even very favourable climatic scenarios (e.g. with 5 or 10% increases in production every three-five years), do not prevent the deaths of over 800 million people on average over a 20-year period.

The model highlights the delicate balance between the nutritional needs of a rapidly growing human population and the ability of Earth to sustain the food production required to meet those needs. The odds that climate change will produce a net benefit to global agriculture seem small. But even if the odds of favourable and deleterious impact were even, the model suggests trying to slow the climatic change, since if D N = D G, many more lives would be lost if the changes were harmful than would be saved if they were beneficial, especially as the climatic impact (probability of event times magnitude of change) increases.

Analysis of the model further suggests that humanity may face a situation unprecedented in the modern era: absolute global food shortage. The political, economic and social consequences of such a situation in a 'global village' are difficult to imagine. That possibility presents itself at a time when conventional methods of expanding food production may be reaching physical and economic limits (Brown & Young 1990).

For the immediate future, global food security could be increased by minimizing the amount of food wasted between harvest and consumption, by strengthening the agricultural sectors of poor nations, and by improving the equity of food distribution. Long-term food security can ultimately be achieved only by initiating the socioeconomic changes necessary to bring about reduced birth rates. In addition, the model reinforces the prudence of striving to reduce the emission of greenhouse gases into the atmosphere (which in turn is strongly driven by population growth; Ehrlich & Ehrlich 1989, 1990). It also supports the view that providing everyone with adequate diets will remain a tremendous challenge even without the threat of global climatic change.

We greatly appreciate the helpful comment) on earlier drafts of this manuscript provided by the other members of the Stanford Carrying Capacity Croup, Anne Ehrlich, Pamela Matson and Peter Vitousek. Susan Alexander, John Baughman, Carol Boggs, Lester Brown, Roman Dial, Marcus Feldman, John Harte, Cheryl Holdren, Robert May, Sandra Postel, Jonathan Roughgarden and Lee Schipper were also kind enough to review the manuscript. John Holdren and Stephen Schnieder provided especially detailed and useful critiques. The Center for Conservation Biology and the Morrison Institute for Population and Resource Studies generously provided support for this project.

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(Received 13 June 1990; accepted 27 June 1990, Proc. R. Soc. Lond. B.)

APPENDIX 1

The following calculations are made in each time step (one year). The equations are presented in slightly expanded form for the sake of clarity:
N_t+1 = (1 + 0.01 x DN) x N_t,
where N = population size and D N = annual percentage rate of increase of the population:
G_p,t+l = (1 + 0.01 x DG) x G_p,t,
G_nf,t+l = G_p,t+l + 0.01 x v x G_p,t+l,
G_a,t+l = G_nf,t+l + 0.0l x m x G_nf,t+l,
where G_p = potential grain production and DG = annual percentage rate of increase of grain production; G_nf = potential grain production modified by 'normal fluctuations'; v is a number selected randomly (and uniformly) from the set (-4.0, -2.0, 0, 2.0, 4.0) to produce an expected variance of 8%; G_a. = actual production for the given year; m = the amount by which grain production is enhanced or reduced in years where climatic events affect agriculture (determined stochastically).

Grain consumption (C) is calculated as
C_t = (0.33 T per capita) x N_t.

Grain stock (S) is calculated as follows, and has a lower bound of zero T: S_t+l = S_t + G_a,t+1 - C_t+l

The number of hunger-related deaths (D) occurring in a year is a function of grain stocks and distribution. In the case of a huge grain surplus, where stocks constitute greater than 40% of consumption (i.e. S x 100/C > 40), 2 million hunger-related deaths occur in a year because of maldistribution of food. If there is a grain surplus (i.e. S > 0) but stocks constitute no more than 40% of consumption (i.e. S x 100/C £ 40), then D_t = 2 x 10⁶ + d - (d/40) x x, where d = number of deaths per year when stocks equal zero, and is set at 20 million here; x = 5 x 100/C. If there is a grain deficit, then D_t, = 2 x 10⁶ + d + 2 x (deficit).

Close approximations to the mean results of this model can be obtained via an analytical solution to these equations.

To determine the number of simulations required per run. we produced multiple sets of runs consisting of 100, 1000 and 10000 simulations each using initial conditions with high variance in output parameters (run E, table 1). The coefficient of variation of the mean number of deaths was 2.4, 1.3 and 0.3 respectively. We therefore considered 10000 simulations per run sufficient to produce reasonably consistent results.

Table 1. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

Table 2. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

Table 3. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

Table 4. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

Table 5. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

Table 6. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 8.330 billion.

Table 7. Each run represents 100,000 simulations of the same conditions: the projection time was 20 years; the initial population size is 5 billion.

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