Abstract Influential demographic projections suggest that the global human population will stabilize at about 9–10 billion people by mid-century. These projections rest on two fundamental assumptions. The first is that the energy needed to fuel development and the associated decline in fertility will keep pace with energy demand far into the future. The second is that the demographic transition is irreversible such that once countries start down the path to lower fertility they cannot reverse to higher fertility. Both of these assumptions are problematic and may have an effect on population projections. Here we examine these assumptions explicitly. Specifically, given the theoretical and empirical relation between energy-use and population growth rates, we ask how the availability of energy is likely to affect population growth through 2050. Using a cross-country data set, we show that human population growth rates are negatively related to per-capita energy consumption, with zero growth occurring at ∼13 kW, suggesting that the global human population will stop growing only if individuals have access to this amount of power. Further, we find that current projected future energy supply rates are far below the supply needed to fuel a global demographic transition to zero growth, suggesting that the predicted leveling-off of the global population by mid-century is unlikely to occur, in the absence of a transition to an alternative energy source. Direct consideration of the energetic constraints underlying the demographic transition results in a qualitatively different population projection than produced when the energetic constraints are ignored. We suggest that energetic constraints be incorporated into future population projections.

Citation: DeLong JP, Burger O, Hamilton MJ (2010) Current Demographics Suggest Future Energy Supplies Will Be Inadequate to Slow Human Population Growth. PLoS ONE 5(10): e13206. https://doi.org/10.1371/journal.pone.0013206 Editor: Henry Harpending, University of Utah, United States of America Received: March 17, 2010; Accepted: September 10, 2010; Published: October 5, 2010 Copyright: © 2010 DeLong et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: MJH and OB were supported by grants from NSF. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction Over human evolutionary history, the global human population has grown from an initial small size to ∼7 billion today. Recent global population growth rates peaked in the 1950's and 1960's but are now declining [1], and it is widely believed that the world's population size is approaching a steady-state. Demographic studies suggest that we can expect a leveling-off of the human population at about 9–10 billion by the middle of this century [2], [3]. Such projections are made by extrapolating recent trends in the relationship between time and vital rates. The key phenomenon invoked is the “demographic transition”, which is the reduction in fertility that follows the development-induced reduction in mortality [4], [5]. In essence, growth rates decline as a result of economic development, which brings benefits that increase lifespan and reduce infant mortality [6], [7]. Stimulated by these development benefits, fertility rates decline until they reach replacement levels or lower. Economic development requires energy [7]–[11]. An expanded, energetic view of the demographic transition is that increasing energy use yields increasing development, thus decreasing mortality, and eventually decreasing fertility. Most projections have assumed that energetic inputs are either irrelevant for the demographic transition or that global energy supplies will be sufficient to fuel the economic growth that underlies the demographic transition [1], [3]. Such assumptions should be scrutinized for empirical reasons, but also because they contradict basic ecological theory. We submit that understanding the connection between energy and population growth in humans has the potential to shed light on the mechanisms of population regulation in the human species [12]. Energy-dependent population growth Energy is related to population growth via its effects on birth, death, and migration rates. When energy increases in supply, a population may grow [13], but energy supply may be approximately fixed over some time scales. This latter state is the basis for much classic theory in ecology, which suggests that as a population grows, per-capita access to energy declines, leading to declines in birth rates and increases in death rates and ultimately to a steady-state population size [14]. Indeed, recent studies show that metabolic rates (i.e., rates of energy use) are directly linked to birth and death rates [15]. The majority of biological populations experience some level of density-dependent population growth that is a function of intra-specific competition for available food energy [16], although other factors, such as predation and abiotic stressors, are also involved [17]. For our purposes here, we define an ecological path to zero growth as that in which individuals become energetically constrained to the point where birth rates equal death rates. This is the steady state that occurs in the classic logistic model of population growth, for example. Importantly, however, modern humans use a considerable amount of energy in addition to that required to support their biological metabolism [18]. This extra-metabolic energy use has increased through time hand-in-hand with economic development [19]. Extra-metabolic energy is fundamentally different from the food energy that constrains the ecological path to zero growth, in terms of how it is acquired, the amounts that are involved, and the activities it fuels. Nonetheless, relaxing energetic constraints with the addition of extra-metabolic energy to the biological energy budget stimulates changes in energy allocation patterns, such that increased energy use results in fewer offspring. The use of extra-metabolic energy also increases survivorship [7], so it is possible that a high-energy steady-state could arise if there is an intersection of the curves relating energy use to fertility and energy use to mortality. The industrial path to zero growth is the trajectory in which the continued addition of extra-metabolic energy to the total energy use of individuals drives birth rates and death rates toward a steady state characterized by relatively large amounts of per-capita energy use [20]. The demographic prediction of a stabilized global population by mid-century rests on the ability of the global population to increase per-capita energy use and follow the industrial path to zero growth. Such a steady-state does not represent an ecological carrying capacity. It is a state where individuals with access to relatively large amounts of energy reproduce only at replacement levels. In this paper we ask whether future energy supplies are projected to be sufficient to allow the global population to follow the industrial path to zero growth. We quantify the empirical relationship between per-capita energy use and growth rate and use this relation to assess how future energy scenarios may affect the size of the human population through mid-century.

Discussion All attempts to project the future size of the global human population are subject to considerable, and unavoidable, uncertainty [23]. For most projections, the bulk of this uncertainty pertains to the rate and timing of the demographic transition. However, there is also much uncertainty in future energy supplies, and this energy is essential to fueling the economic development that results empirically in the demographic transition. It is therefore essential to understand how energy use patterns affect the growth and structure of the global human population [1]. By examining this relationship explicitly, we have identified a major, unrealistic assumption of previous population projections. Given the unequivocal relation between energy use and fertility, stabilizing the global population by mid-century will require vastly more energy than is currently projected to be available (Figure 2A, “Implicit UN assumption”). As the population grows, increasing amounts of energy are needed to bring more and more people to demographic equilibrium. Current average rates of energy use across the globe are much lower than equilibrium levels of ∼13 kW. Demographic projections assume that the demographic transition is both inevitable and irreversible. We submit that both of these assumptions are problematic. This is because the demographic transition requires substantial amounts of energy, and if energy supplies decline, then growth rates will very likely rise. The potential for reversal of the demographic transition follows directly from conventional theory in population ecology and from the empirical relation we show here between energy consumption and fertility. In the event of such a reversal, growth rates will likely follow the current growth rate – energy relation. It is also possible that a new relation will emerge as time progresses [24]. The growth rate – per-capita energy use relation has developed through recent human history as human societies have increased access to finite pools of energy stored in the geosphere, namely fossil fuels [18]. Not surprisingly, then, there are interesting historical and cultural patterns embedded in this relationship. Some countries with shared histories cluster, including Arabian peninsula oil-exporters that have high growth rates for their energy use, and former Soviet states in Eastern Europe that have low growth rates for their energy use (Figure 1A). Some of this variation may have to do with recent migration patterns and world energy trade networks, and we suggest that further evaluation of historical effects on these relations may help us to better understand these patterns. We also point out that the variation around the general relationship indicates that there is scope for a reduction in the amount of energy needed to fuel the demographic transition. The drop in growth rate with increasing per-capita energy use occurs because birth rates drop with energy use more quickly than death rates. How energy use induces a decline in death rates is fairly straightforward: energy is used to develop medical knowledge and technology and produce and distribute medical services [7], as well as support increased quantity and diversity of food that improves the nutritional state of people. In contrast, how the availability of extra-metabolic energy induces a change in birth rates is less clear. One possible explanation is that increases in the costs of raising children in more-developed countries forces the reduction in offspring number due to the constraint imposed by the time and energy available to allocate to total offspring number [5], [18], [25]. Currently, it is unclear why the introduction of extra-metabolic energy to the total energy budgets of industrial humans alters their reproductive allocation patterns, which in natural-fertility populations follow energy-based life history rules [26]. However, it is clear that understanding the energetic basis for reproductive decisions in humans could substantially contribute to our ability to affect future growth. Today, it is widely assumed that the global human population will follow an industrial path to zero growth [2], [27], [28]. Our results suggest that the total quantity of energy will be insufficient to facilitate this outcome, given current demographics. Other constraints on birth and death rates may come into play at some point, but this would be very difficult to predict at this time. Shortages of water, disease, or violent conflicts could all play a role in limiting population size, or the population could become limited by food [29] and begin, again, to follow an ecological path to zero growth. Our analysis indicates that it is crucial to determine how those limits will come into play, as we can only expect the global human population to follow the industrial path to zero growth if future energy supplies turn out to be much greater than currently projected, and a greater balance among rich and poor nations in access to energy is achieved. In conclusion, by failing to consider the fundamental theoretical and empirical relation between human reproduction and energy use, current demographic predictions of human population growth over the near future are at best questionable. Our analysis shows that by considering these relations as rigorously as possible, using empirical data and fundamental principles of ecological energetics, the global human population is likely to continue growing, due to energetic constraints that limit our ability follow the industrial path to zero growth under any reasonable prediction of future energy availability.

Methods Data We extracted data on per-capita energy use, growth rate, and crude birth and death rates from the World Resources Institute (WRI) database on country-level demographics and energy use [30], and we fit nonlinear models to the data to provide an empirical connection between energy and growth to use in the population model. Per-capita extra-metabolic energy use is defined as the total annual energy use for a country divided by the population size. The crude birth and death rate data from WRI are used only to show the intersection of birth rates and death rates at a unique value of per-capita energy use, illustrating why growth rates decline with per-capita energy use and how a high-energy zero-growth state exists for humans. Using the WRI data, we also tested for a relationship between per-capita energy use and growth rate through time, where growth rate was independently estimated as the average annual percent change of that country at mid-year. Data for Middle Eastern oil producing states were excluded as outliers, as they uniformly have far higher growth rates for their energy use, and this may be a function of the amount of energy used at a national scale in oil development. We produced four scenarios of future energy supply, E, that bracket pessimistic to optimistic possibilities. For the “pessimistic” scenario we used an estimate of the future total primary energy supply from [11], which predicts continued growth of primary energy supplies followed by declines beginning after mid-century, and is consistent with other estimates [31]. We suspect, however, that this projection underestimates future renewable energy supplies, as the demand for alternative sources of energy will be quite large, spurring additional energy production. Therefore, the “realistic”, “linear”, and “optimistic” scenarios project larger future energy supplies than those predicted by [11]. The optimistic scenario represents increasing energy use consistent with recent decades. The four future energy scenarios are: Population model In the model, changes in population size are given by rN, where growth rate r = f(E pc ). E is given by the future energy scenarios, and E pc is calculated as E/N. The function f is given by the empirically determined relationship in Figure 1A. The growth equation takes the form where a and c are fitted constants and b is the proportion of the global E available to a group. We divided the global population into the developed and the developing world because of the large imbalance in energy use between them (85% of global energy use in the developed world [30] and the large difference in population size (e.g., 5.32 billion in the developing and 1.35 billion in the developed in 2007 [30]. Thus, b is 0.85 in the developed world and 0.15 in the developing world. Global population sizes at year t are given as the sum of the developed and developing worlds. We applied the model to past and future trajectories of global energy supply. Estimated energy use for the years 1950–2007 were provided by [11]. The four future energy scenarios for the years 2007 to 2050 were used to produce four energy-dependent future population trajectories. Initial conditions for 1950 were E = 2.5×1012 W [11], with population size in the developed world = 0.81 billion, and population size in the developing world = 1.72 billion [6]. The growth trajectories produced by the model were sensitive to the value of c, and conformity to past growth required slight alterations this parameter. The fitted value of c was 0.055 (+/−0.07), but a match to the growth pattern from 1950–1990 was achieved when c was set at 0.057. From 1990–2007, a value of 0.051 produced a match to the observed growth. For the years after 2007, the fitted value of c was used. To assess the robustness of our overall conclusion from the model output, we reran the model with the 95% confidence intervals for the parameters. We obtained three curves using the optimistic future energy scenario, which we show as providing a best-case scenario. We calculated the future energy supply scenario implicitly assumed by the UN medium population growth trajectory using the following steps. We first broke the projection down into developed and developing worlds, given the endpoints of 2009 and 2050. We fitted a linear growth curve to the developed country growth curve and a quadratic function to the developing country growth curve. Sums of these two curves provided a close approximation to the UN medium projection. For each group, we calculated the growth rate for each year by (N t+1 −N t )/N t from the smoothed function. Third, we solved the fitted equation in Figure 1A for E pc , and used the calculated growth rate to estimate E pc for each year. Finally, we multiplied E pc for each year by N t to produce E, the assumed global energy supply needed for the developed and developing nations to follow their respective curves, and then summed them to get the total global supply needed to propel the global population along the industrial path to zero growth. This procedure allowed us to compare the assumed global energy supply with the predicted energy scenarios, as well as to assess the assumed distribution of energy among developed and developing nations.

Acknowledgments We thank Colin Butler, John Hawks, Henry Harpending, Melanie Moses, Shripad Tuljapurkar, David Vasseur, and Gur Yaari for helpful comments and modeling advice.

Author Contributions Conceived and designed the experiments: JPD OB MJH. Analyzed the data: JPD MJH. Wrote the paper: JPD OB MJH.