Introduction

All leading global population projections expect the size of the human population to peak in the second half of the 21st century and then decline. But quantitative projections past 2100 are rare, and none quantify the possibility of a rebound from low fertility to replacement-level fertility. Over a decade ago, Basten et al. (2013) [1] presented deterministic “Very long range global population scenarios.” In the years since, global fertility has declined faster than demographers expected. This new information has revised demographers’ expectations. For example, in 2014, Gerland et al. (2014) [2] reported that it was unlikely that the size of the world population would peak within the 21st century, but the most recent United Nations’ central scenario projects a peak in the 2080s.

Approximately two-thirds of the global population now live in a country with a fertility rate that is below replacement level [3]. Declines in fertility to sub-replacement levels can be at least partially explained by improvements in the alternatives to having a child. In many countries, women’s pursuit of higher education and participation in the labor force led to delays in marriage and childbearing that contributed to fertility decline [4, 5]. However, in some countries, like India, fertility has declined to sub-replacement levels despite women having children at young ages [6] and low female labor force participation [7]. In these countries, parents’ desire to invest more in the human capital of fewer children may partially explain fertility decline [8].

An important open question is how likely it is for low fertility to persist. The forces that have led to sub-replacement fertility are unlikely to go away: the alternatives to having a child will likely only improve in almost all countries. Lutz et al. (2006) [9] have influentially suggested that sustained experience with low fertility could result in a “low fertility trap,” once cultural norms, social structures, economies, and policies adapt to low fertility as normal. Quantitatively, Raftery and Ševčíková (2023) [10], estimate a 90% chance that global fertility is below replacement in 2250 and in 2300. Of course, it is not certain that fertility will continue its global downwards trend, nor that fertility must stay below replacement indefinitely. At a minimum, sustained low fertility is plausible enough that it is important to understand it.

Given the prospect of global sustained sub-replacement fertility, this paper presents a series of deterministic, long-term cohort-component projections of the size and age structure of the population under various hypothetical scenarios for future population decline, and potential subsequent rebound. In our first set of scenarios, we consider possible futures in which the world sustains below-replacement-fertility. Then, in our second set of scenarios, we provide what to our knowledge are the first long-term cohort-component projections of global population size that quantify the possibility of a reversal of fertility decline towards replacement-level fertility. All the scenarios that we investigate assume that global fertility stays below replacement for decades at least—consistent with the central projections of nearly all population scientists.

There is substantial uncertainty around how humanity would respond if depopulation persisted for decades. The scenarios we study are not predictions for the future. Rather, they illustrate how the global population could become small quickly, and remain that way despite future rebounds in fertility.

We find that the global population could shrink fast for a range of plausible levels of below-replacement fertility that are already common today. If global fertility rates continue to decline and remain below replacement, we would be living in a brief, unusual spike in human history. A world of many billions of people is an historical anomaly, relative to humanity’s past. It may also be an anomaly, if fertility rates stay low, relative to humanity’s future. We then quantify the consequences for long-run population dynamics of various possible future transitions to replacement fertility. By construction, these scenarios result in stabilization of the period population size. But that size depends radically on when the transition begins, which determines how much depopulation precedes it. For example, if the transition towards replacement fertility begins in 2125, the stationary population size would be about 8 billion, but if the transition begins just fifty years later in 2175, the stationary population size could be between 2 and 4 billion, depending on how low fertility initially falls. And if no transition to replacement fertility happens within the next few centuries, the size of the global population would become very small.

Our findings update and extend the literature on long-run population projections. In 2004, the United Nations Population Division published long-range population projections to 2300 that projected long-run stabilization of the global population at about 9 billion [11]. Nine years later, Basten et al. (2013) [1] called into question the assumption of long-run population stabilization, recognizing that fertility rates in Europe were below replacement and had been there for several decades. Since then, global fertility has declined faster than demographers predicted and many more people live in countries with sub-replacement level fertility. The UN, however, has not updated its long-run projections to reflect the most recent two decades of data. This paper builds on the work of Basten et al. (2013) [1] by incorporating and extending population science’s updated expectations for future fertility rates. We also quantitatively explore the consequences of any hypothetical future reversal towards replacement fertility, which no other long-term population projections explore.

Materials and methods

We construct deterministic, cohort-component method population projections for each of the “countries or areas” of the 2022 United Nations World Population Prospects (WPP) and aggregate these to worldwide totals. We use the demographic rates of the WPP Medium projection that omits migration, until it ends in 2100. Beyond 2100, we make assumptions for long-run fertility and mortality.

The core independent variable of our study is a long-run total fertility rate towards which the entire world converges after the end of the WPP projection in 2100. In our first set of results, we use a range of long-run future global fertility rates that are below replacement level. Our deterministic projections are intended to produce conditional results, answering the hypothetical question “What would happen to the global population if fertility in the future takes these possible paths?” Although it is not certain that long-run fertility will remain below replacement level in the long run, it is plausible enough that it is worth understanding.

The long-run fertility scenarios that we study are based on several broad patterns of the past decades and centuries. These include: the fact that the global average birth rate has fallen significantly over the past two centuries; the fact that countries that have fallen below replacement fertility have in almost all cases remained below replacement; the fact that in regions where fertility is currently high it is currently falling; and the fact that more than two-thirds of people in the world now live in a country with below-replacement fertility. These broad patterns motivate the conditional projections we present. We do not assign confidence intervals to these outcomes or derive a single projection from a more complicated mathematical extrapolation, because to do so would communicate false precision about the probability of what is a fundamentally conditional exercise.

In each five-year time step, each country’s age-specific fertility rates either increase or decrease by 3% until the country’s total fertility rate (TFR) reaches the specified long-run TFR. Because all countries approach the long-run TFR, the world does, too. In the limit, each country retains a slightly different age pattern of fertility because each has a different age pattern of fertility in 2100 at the end of the UN projection. Although fertility decline in many countries has been accompanied by a delay in childbearing, there is precedence for countries reaching low fertility yet maintaining different age-patterns of fertility. For example, India’s TFR is now 2.0 births per woman, yet women continue to begin childbearing at young ages [6], a pattern which is in stark contrast to what has occurred in high-income countries. S2 Fig shows scenarios for age-specific fertility rates globally and for selected countries.

The result of this procedure is that in the limit each country has the same average completed cohort fertility. Our 3% assumption for the pace of fertility convergence is conservatively slow compared to the change in global TFR, which decreased by roughly 7% over the five years from 2017–2022. However, the actual future rate of change could be faster or slower, so we show in S1 Fig that our descriptive results are robust to other plausible speeds. The Supporting Information describes the fertility assumptions in further detail.

Population projections also require assumptions for future mortality rates. After the WPP projections end in 2100, we assume that mortality rates everywhere converge to a life expectancy at birth of 100 years. We implement this high life expectancy as a demonstration that our depopulation main results are robust to mortality reductions. There is considerable uncertainty regarding future declines in mortality, however, and results shown in Supporting Information (S5 and S6 Figs) demonstrate that our results are robust to alternative assumptions for mortality. S4 Fig shows the assumed age-pattern of mortality in various periods until life expectancy at birth of 100 years is reached globally, and the Supporting Information describes the mortality assumptions in further detail.

Our cohort-component projections provide age-specific quantification for each five-year time step of births, deaths, and the age pyramid of the population. All results below reflect this methodology, and it is the basis of the Spike diagram in Fig 1. Because our dependent variable of interest is the size and age structure of the global population, we ignore migration. This focuses on our independent variable of interest: possible futures for global fertility. In this we follow Basten et al. (2013) [1] who “assume a slow phasing out of international migration,” summarizing that “this is clearly unrealistic,… but has little effect on global population size, which is the main point of interest here.” Indeed, the difference in global population size between the WPP Medium no-migration variant and the WPP Medium variant with migration is only 12 million people by 2100, or about 0.12%. This is a very small difference.

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Fig 1. Global population as a spike in world history.

Historical data are taken from Kaneda and Haub (2022) [12]. Projections from the present to 2100 are the Medium projection of the 2022 UN World Population Prospects. Projections from 2100 are produced by the authors as described in the Methods. “TFR → 1.66,” “TFR → 1.8,” and “TFR → 1.2” indicate three hypothetical scenarios for long-run global fertility rates towards which the world converges.

https://doi.org/10.1371/journal.pone.0298190.g001

Our second set of results describes possible hypothetical scenarios for future fertility increases up to the replacement level. A fertility increase scenario has two phases: first, the initial convergence after 2100 towards a long-run fertility rate (as described above); and second, a transition in a specified year towards replacement fertility. In the long-run the second phase approaches a stationary population with fixed fertility and mortality rates and zero growth. Therefore, a fertility increase scenario is described by two independent variables: the initial long-run TFR (such as 1.5) and the year in which the long-run TFR changes to replacement (such as 2150). This allows us to quantify long-run consequences—that is, path dependency—of the date at which fertility reverses and begins increasing. How, we ask, does the long-run size and structure of the population depend upon the year in which fertility rates reverse towards replacement levels? Methods are described in further detail in the Supporting Information.

Results

Fig 1 presents our main results. The figure plots the size of the global population a long way into the past (from 10,000 BCE) and a shorter way into the future. Historical data are taken from Kaneda and Haub (2022) [12]. Projections from the present to 2100 are the Medium projection of the 2022 UN World Population Prospects. Projections beyond 2100 make various assumptions on global average fertility, as indicated. The figure shows that, according to our projections (which follow the UN central scenario for the years of overlap), we would be living in a brief, unusual spike in human history. Population sizes that are familiar today are an exception, relative to both the past and the future.

To make these ideas concrete, consider the post-2100 projection in Fig 1 that assumes global fertility converges to a total fertility rate (TFR) of 1.66, which is selected for familiarity because it is the period TFR of the US in 2020. About a third of people alive now live in a country with a lower period TFR than 1.66. So Fig 1 assumes that fertility in those places would increase—despite that the trend in all large regions of the world, including where fertility is already below replacement, is stable or falling fertility. The other dashed lines, tracing scenarios after 2100, alternatively assume that the world converges to the period TFR of present-day East Asia (1.2) or present-day Mexico (1.8). We present these three alternatives not as predictions for future fertility, but to illustrate that, while the differences among these possible fertility rates are important, they are not very important for the shape of the spike in Fig 1. In all cases, we now would be living through a brief and sharp peak in population size.

Although population momentum bounds the population sizes that would be feasible in the coming few decades, global depopulation in the 22nd century and beyond could be rapid—just as rapid as the population explosion of the last 200 years—because exponential growth and decay are governed by the same compounding dynamics. Fig 1 shows scenarios in which only 26 billion human births would remain to happen in the future (interpreting the projection literally). 120 billion births have already occurred. This would imply that four-fifths of all the people who will ever live have already been born. (Such a scenario assumes no fertility rebound at any point, an assumption we alter for the second set of scenarios we evaluate).

Fig 2 is an expansion on the same family of population projections shown in Fig 1. Whereas Fig 1 considered hypothetical scenarios for total fertility converging to 1.20, 1.66, and 1.80, Fig 2 displays the implications of convergence to any long-run TFR between 1.00 and 1.80, as indicated along the horizontal axis.

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Fig 2. Longest-term consequences for population size of alternative long-run global fertility rates.

(a) plots iso-population curves and (b) plots iso-births curves. Each line indicates the combination of global fertility rates and dates that result in the indicated population or annual birth milestone. For example, if global fertility converges to 1.4 births per woman, then there are projected to be 1 billion people in 2370 and 1 million births per year in 2495.

https://doi.org/10.1371/journal.pone.0298190.g002

Panel (a) of Fig 2 traces a set of iso-population lines, indicating which combinations of global fertility rates and dates would yield the indicated population milestones. It demonstrates the delay in falling below a particular population milestone associated with increases in long-run TFR. A steeper curve indicates a longer delay, and a flatter curve indicates a shorter delay.

For example, what would happen if the world converges to a TFR of 1.2, the average fertility rate that East Asia, taken as a whole, exhibits today? A vertical line traced up from TFR = 1.2 crosses the (short dashed, green) iso-population curve for 1 billion people in 2340. Thus, within 250 years of the lifetime of most children born today, there would be fewer than 1 billion people alive. Panel (b) tells us that by 2280, there would be only about 10 million babies born each year, compared to about 135 million births in 2022. Only four decades after the global population reached 1 billion, by 2380, it would further halve to 500 million; this halving time of 40 years would be comparable to the world population’s doubling time of 37 years in the mid-20th century. If, instead, global fertility converges to 1.5 babies per woman (like in today’s Europe), these milestones would be delayed by only 25 and 95 years, for the 1 billion and 500 million thresholds, respectively.

Figs 1 and 2 present population projections under the assumption that fertility rates for each country change by 3% each five-year period, and that mortality rates decline such that long-run life expectancy at birth is 100 years. S1 Fig shows that the main findings on the speed of depopulation are qualitatively similar under different assumptions for the pace of change in fertility rates. Similarly, S5 Fig shows that the depopulation results are very similar even if we assume an even higher long-run life expectancy at birth of 120 years.

Fig 3 documents the consequences for the total number of humans who ever live; it is equivalent to the integral under panel (b) of Fig 1. So far, there have been about 120 billion people born [12]. If fertility stays below replacement—if global TFR indeed asymptotes to the levels that we consider—then Fig 3 shows that this count would never exceed about 150 billion, and could be less. In that case, at the time that we are writing, 80% of births would be in the past. As panel (b) demonstrates, low fertility would not have to continue for very many centuries (or decades) for humanity’s count of births to approximately reach its cumulative limit.

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Fig 3. Cumulative count of humans ever born, as a function of long-run global fertility.

Fig 3 uses the same set of population projections as Figs 1 and 2, but tabulates the projection as a cumulative count of human births. If fertility rates stay below replacement, then the total number of human births is projected to stay below 150 billion, or 26 billion more than have so-far occurred. (a) shows cumulative births in the very long-run, and (b) zooms in on cumulative births in the next couple of centuries.

https://doi.org/10.1371/journal.pone.0298190.g003

Of course, the further that future population sizes fall away from the sizes that are familiar to the population science community, the less informative these results can be about what might happen. These are merely deterministic population projections, conditional on our hypothetical scenarios. They are intended only to illustrate the consequences of sustained low fertility rates. Population science’s cohort-component model was not created to specify what exactly would happen when humanity’s numbers become very small, so that situation is outside the scope of our research. What the model can tell us is that if low fertility is sustained for just a few centuries, then the population size could be quite small.

Fig 4 describes consequences for the age structure of the population that the world would converge to. The youth dependency ratio would fall, because there would be few births. The old-age dependency ratio would become quite large under the fertility rates that are common today in Europe: There would be six or more times the number of older adults per working-age adult as there are now. In 2019, the highest country-level old-age dependency ratio in the world was Japan’s, with about half an older adult per working-age adult; if the world converges to a TFR of 1.2, like East Asia today, then it would converge to an old-age dependency ratio of 150, or three times that in Japan in 2019. Marois et al. (2021) [13], Galor (2022) [14], and others have emphasized that improving human capital and changing labor markets could soften the economic consequences of these changes in the dependency ratio. This is true; and yet, some forms of social interaction or in-person care work may not have good substitutes within a few centuries. It is also possible that in the far future, health improvements might contribute to longer working lives. This would imply lower dependency ratios than displayed in Fig 4. It is beyond the scope of this article, however, to predict how future societies will define the working ages. Fig 4 simply displays future dependency ratios if people continued to stop working at age 65, on average.

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Fig 4. Consequences of long-run fertility for long-run dependency ratios.

Fig 4 uses the same set of population projections as Figs 1 and 2, but presents the consequences for dependency ratios as a function of the assumed scenario for long-run, asymptotic fertility.

https://doi.org/10.1371/journal.pone.0298190.g004

Our second set of future fertility scenarios assumes that, at some point in the 22nd century, the global long-run fertility rate changes to replacement fertility. Here the research question is how long-run outcomes depend on when this transition occurs. Fig 5 plots three scenarios for when the reversal towards replacement fertility begins, crossed with a range of possible 22nd century global fertility rates (from 1.0 to 2.0) towards which the world converges before fertility begins to increase back to replacement. The left vertical axis of panel (a) indicates the stationary population size, in the long run after the world has converged to replacement rates. The right vertical axis indicates the annual number of births worldwide, again in the long run after the world has converged to replacement rates.

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Fig 5. Future stationary population size depends on when fertility increases to replacement.

(a) displays global population size (left) and annual births (right) after the population has stabilized. TFR first falls toward the given level after 2100 and then rises to replacement at either 2125, 2150, or 2175. (b) displays population size over time if the long-run TFR before increasing to replacement level is 1.66, demonstrating how even a few decades change in timing of this hypothetical transition could alter long-run population sizes by billions.

https://doi.org/10.1371/journal.pone.0298190.g005

Panel (a) of Fig 5 shows that the timing matters, because decades or centuries spent depopulating would shape the population size that future replacement fertility would eventually stabilize to. Notice that, unlike in our main results of continuing depopulation, here we describe convergence to a stationary population; as a result, the ratio of the population size to the annual number of births in the limit is fixed at the life expectancy at birth, as the two vertical axes of Fig 5 Panel (a) demonstrate.

The results reveal an interaction between the initial, pre-increase long-run target fertility level, on the one hand, and the year that the fertility increase towards replacement begins, on the other. If the increase starts early (in 2125) then not much time is spent at low fertility, so the initial fertility rate does not make as large a difference to the long-run size of the population. But if the increase starts even fifty years later (in 2175), then the long-run size of the population would be as low as 2 to 4 billion, if the initial fertility rate was low, rather than around 8 billion if either the initial fertility level was higher or the increase started earlier. So, even if depopulation is halted by a future increase in global fertility, the time spent depopulating could make a permanent difference in the size of the population, depending on how long fertility was low. A few decades of timing could result in a multi-billion difference in a permanent, stationary population size. S6 Fig shows that this result is robust to alternative mortality assumptions.

Panel (b) of Fig 5 examines our central case of TFR initially converging to 1.66. Here, a one-year delay in the initiation of a fertility rebound would cause an approximately 0.7% permanent reduction in the stationary size of the long-run population. Equivalently, delaying the rebound by one generation (30 years) reduces stabilized population size by about 19%. Despite its significant implications for the long run population size, the timing of a fertility rebound to replacement would have no impact on the long-run age structure or dependency ratios of the population in these scenarios, because these quantities (in the assumed stationary populations) are invariant to population size.

Discussion

This article contributes long-run population projections under future scenarios in which global fertility converges and remains at below-replacement levels, or increases to replacement levels. If fertility remains below replacement in the long-run, then the population spike of this century will be a brief anomaly relative to humanity’s past and future. If, instead, global fertility rates reverse course to increase towards replacement level at some point in the future, the length of time spent depopulating has important implications for the long-run global population size.

Returning to Fig 1, if these projections are informative, then the year with the greatest count of births would already be in the past. Panel (a) of Fig 1 tallies population size. Its peak occurs slightly to the right of the vertical line indicating 2023: The demographic consensus is that world population will peak between 2060 and 2090 [3, 9, 10, 15]. Panel (b) counts births per year. There, the peak has already occurred. The UN estimates it happened in 2014.

The most important limitation of this study is that its projections are deterministic; they are conditional statements that would describe the world if it followed a path similar to one of the stylized scenarios. No formal method could accurately predict what would happen once the world population size, in fact, became small. Instead, our study should be read narrowly as a quantification of how quickly the global population size could change under sustained below-replacement fertility, and how much timing matters for any future rebound to replacement.

This limitation suggests a question, beyond the scope of our study: Is sustained below-replacement fertility plausible? The population science literature suggests so. In a survey, many population scientists expected low future fertility [16]. In the Human Fertility Database (Max Planck Institute for Demographic Research (Germany) and Vienna Institute of Demography (Austria)), the completed cohort fertility of cohorts born since 1950 has fallen below 1.9 for 27 countries; so far, in none of these has it ever subsequently risen to 2. Arenberg et al. (2022) [17], pooling data from many recent Demographic and Health Surveys, emphasize that fertility decline is found in essentially every population and sub-population, including, for example, sixteen informative subdivisions of India, a country now emerging as a below-replacement-fertility population. Vogl (2020) [18] shows that the aggregate consequences of intergenerational correlations between parents’ and children’s fertility is quantitatively insufficient to meaningfully increase overall, population-level fertility rates [cf. 19]. Gietel-Basten (2019) [20] and others document that pro-natalist policies in low-fertility countries have generally done little to sustainably increase cohort completed fertility (although, of course, population control polices have often done considerable harm while achieving little [21–23]).

Though it is not the aim of this paper to consider the implications of a small and shrinking population for global well-being, other than in terms of implications for the old-age dependency ratio, we note that a substantial literature has linked the population size and growth rate to macroeconomic growth and average living standards—see Jones and Romer (2010) [24] for an overview.

Taken together, this collage of social science evidence suggests the importance of considering scenarios of sustained low fertility. We contribute new quantitative scenarios to better understand this possible future.

Supporting information

Acknowledgments

For helpful comments and suggestions, we are grateful to Mark Budolfson, Diane Coffey, Kevin Kuruc, and participants in the 12th Oxford Workshop on Global Priorities Research.