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A Representation of the World Population Dynamics for Integrated Assessment Models

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Abstract

Using the gross world product (GWP) as the only exogenous input variable, we design a model able to accurately reproduce the global population dynamics over the period 1950–2015. For any future increasing GWP scenarios, our model yields very similar population trajectories. The major implication of this result is that both the United Nations and the Intergovernmental Panel on Climate Change assume future decoupling possibilities between economic development and fertility that have never been witnessed during the last 65 years. In case of an abrupt collapse of the economic production, our model responds with higher death rates that are more than offset by increasing birth rates, leading to a relatively larger and younger population. Finally, we add to our model an excess mortality function associated with climate change. Estimates of additional climate-related deaths for 2095–2100 range from 1 million in a +2°C scenario to 6 million in a +4°C scenario.

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Notes

  1. For a summary of the 31 IAMs used in the Fifth Assessment Report of the Working Group III, see Table A.II.14 in Annex II of the Edenhofer et al.’s [20] report.

  2. Akaev and Sadovnichii [1] is a good introduction to this class of models.

  3. Aral [2] has introduced climate change into an information-based model of this kind.

  4. More precisely, two time series are used in this section: (i) File POP/7–1 (total population (both sexes combined) by 5-year age-group, region, subregion, and country, 1950–2100 (thousands)) and (ii) File MORT/4–1 (deaths (both sexes combined) by 5-year age-group, region, subregion, and country, 1950–2100 (thousands)).

  5. As a consequence of this modeling choice, we ignore the fact that some individuals, especially men, can have children after 49.

  6. Of course, in many countries there are now indications to push the retirement age further than 65. But here we are constrained by the United Nations data, which only has one age-group above 65.

  7. Logically, the transferred population of a given group, Ti, i + 1, should be strictly equal to the population number of the next group after taking into account the number of deaths, \( {N}_{i+1}-{N}_{i+1}^d \). However, we observed in the data a mismatch between those variables. We argue that this discrepancy comes from the fact that death numbers in each 5-year age-groups are estimated every 5 years by the UN from midyear to midyear.

  8. Regarding birth, our approach is in line with Becker [3] who suggests that the rise in income induces a fertility decline, because the positive income effect on fertility is dominated by a negative substitution effect induced by the rising opportunity cost of raising children.

  9. The minimization procedure consists in finding the parameters that minimize the sum of squared residuals. In practice, we selected the model that minimizes a BFGS algorithm employed with various initial points. More details are available upon request. Best-fit values of parameters are reported in Tables 2 and 3 of Appendix 2.

  10. Except for a very particular combination of variables that we do not have in our analysis and calibration

  11. An quantitative assessment of the propagation errors of the calibrated model is provided in Appendix 3.

  12. Another sensitivity analysis of the model under scenario SSP2 is provided in Fig. 13 of Appendix 3 using ad hoc birth and death rates.

  13. At midlatitudes increasing temperature may reduce the rate of diseases related to cold temperatures (such as pneumonia, bronchitis, and arthritis), but these benefits are unlikely to counter balance the global risks associated with warming that low latitudes regions will suffer the most [24].

  14. This initial formulation made Malthus both famous and infamous, but in later life, he took a much more nuanced attitude to the balance between production and population. In particular, Malthus came to appreciate that nuptiality played a very important role in determining population trends, influencing both fertility levels and, indirectly, also mortality levels ([63], pp. 24–25).

  15. This controversy is well illustrated by the I = PAT equation, where I is the impact of human activity on the environment (i.e., the pollution level), P is the population level, A stands for affluence (i.e., the level of per capita consumption), and T represents the technical level. See Chertow [9] for an historical analysis of the various forms; the IPAT equation has taken since its formulation in the 1970s.

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Acknowledgments

We thank Emmanuel Bovari and Antoine Godin for their helpful comments on an earlier version of this article. We are also grateful to two anonymous referees for their fruitful comments and suggestions. Many thanks to Noah Ver Beek for correcting the spelling and grammar of this text. All remaining errors and opinions are our own.

Funding

This work benefited from the support of the Chair Energy and Prosperity, under the aegis of the Risk Foundation.

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Correspondence to Victor Court.

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Appendices

Appendix 1

1.1 Overpopulation: Old Concerns Die Hard

Until approximately 300 years ago, world population growth has been very low, at around 0.04% per year, from four million people in 10,000 BCE to 610 million in 1700. However, the Industrial Revolution drastically changed this pattern of long-lasting limited growth, and global population reached 1.2 billion individuals by 1850, which corresponds to an annual increase of 0.45% during the period 1700–1850 ([33], and Fig. 11). Several classical economists of the time raised concerns about such rapid population growth. By considering exponential growth for the population dynamics, while food production followed a linear increase due to decreasing returns on land, Malthus [36] predicted that the English population would ultimately lack food supply, which could only result in unavoidable deaths by hunger and disease.Footnote 14 This prediction proved to be erroneous because Malthus did not reckon the massive yields increases that took place in the agricultural sector at the time ([50], p. 114) .

Fig. 11
figure 11

Historical and projected world population level (left axis) and annual growth rate (right axis), 1700–2100. Data source: Kremer [33] from 1700 to 1950, United Nations’ [59] medium estimate from 1950to 2100

From 1850 to 1920, the growth rate of the world population has slightly increased by about 0.55–0.60% per year, resulting in a global population of 1.8 billion. After 1920, another order of magnitude change can be observed. Exceeding 1% in the 1940s, the annual growth rate of the world population steadily increased and reached its peak at 2.2% in 1962–1963 with a global population of 3.15 billion (Fig. 11). At this point, the fear of overpopulation came back in several scholars’ writing, and, exactly 170 years after Malthus, Ehrlich became famous for his (pessimistic) predictions in The Population Bomb [21]. Again, those forecasts of impending world famines proved inaccurate due to an increase in food production from the conversion of forests to agricultural lands [25] and agricultural yield improvements ([50], p. 312).

As of 2015, the world population was about 7.4 billion, and its annual growth rate was approximately 1.15%. Considering the United Nations’ [59] medium projection of a growth rate reaching 0.09% per year at the end of this century, the global population would be just below 11.2 billion in 2100 (Fig. 11). Accordingly, in November 2017, the concern about overpopulation was renewed in a statement of 15,364 scientists from 184 countries who indicated that humanity is jeopardizing its future by not reining in its “intense but geographically and demographically uneven material consumption and by not perceiving continued rapid population growth as a primary driver behind many ecological and even societal threats” ([47], p. 1026). The strong warning of Ripple et al. [47] ends with thirteen proposed steps that mankind should undertake to transition toward a more environmentally sustainable alternative to the so-called business as usual. Among them, Ripple et al. [47] suggest “estimating a scientifically defensible, sustainable human population size for the long term while rallying nations and leaders to support that vital goal.”

Of course, for a given level of pollution, it is not the population level per se that represents a problem but rather a combination of population with the level of per capita consumption and the technical level defining the pollution by unit of consumption.Footnote 15 Since technical change is not more foreseeable than before, one could argue that, once again, future innovations are going to alleviate the human population burden on Earth in the coming decades. For technical optimists, the current overpopulation concern will add to the list of failed overpopulation predictions of the past. However, no one can deny that food supply is heavily supported by the use of fossil fuels, either directly through fertilizers or mechanization, but also indirectly through the general use of transport, industry, and services ([50], pp. 306–313). Harchaoui and Chatzimpiros [29] even suggest that modern agriculture hardly generates net energy surpluses, which means that an energy transition from fossil fuels that would not be compensated by enough net energy from renewable energy could jeopardize global agricultural production, and thus world population.

Appendix 2

1.1 Best-fit Parameters of the Global Birth Rate and Death Rate Sigmoid Functions of Our Model

Table 2 Best-fit parameters of the global birth rate sigmoid function
Table 3 Best-fit parameters of the global death rate sigmoid function for each 5-year age-group

Appendix 3

1.1 Model Sensitivity to Changes in the Death Rate of the Fragile Population and Propagation Errors

To test the sensitivity of the model without climate change, we modify the death rate of the fragile population, defined as the first and the last groups (i.e., N1 and N14), ceteris paribus in 2100 (i.e., keeping the GWP from the SSP2 scenario and the birth rate constant). The results are displayed on the heatmap of Fig. 12. For instance, this figure indicates that in order to observe a global population of about 4.5 billion people in 2100, as found in the standard run of the (in)famous study of Meadows et al. [37], the death rate of group N1 (0–4 years old) would have to be multiplied by about fifteen.

We note that an increase in the global mortality rate of N1 mimics the dynamics a similar decrease in BR for all age-groups, except for the first age-group that would be overestimated. Therefore, model sensitivity to birth rate would lead to similar results of Fig. 12 although N1, which is relatively small with respect to the sum of all other age-groups, will be lower than the one used to construct the heatmap.

Fig. 12
figure 12

Sensitivity of global population level in 2100 as a function of groups N1 (0–4 years old) and N14 (+65 years old) specific death rates D1 and D14. The black dot represents the population of about 12 billion attained in the SSP2 GWP scenario

To test propagation errors of the model due to wrongly assessed initial conditions, we add one member per age-group, and then we run the simulation ceteris paribus until 2100 and report the total addition in population with GWP from the SSP2 scenario. The results are shown in the graph of Fig. 13. For instance, this graph indicated that if the cohort 4 is wrongly assessed by one unit, the difference in total population at the end of the century will be roughly three units. In other words, if cohort four happens to have one additional million people than the original simulation, the world will be populated by an additional three million individuals in 2100, which is a total increase of population of about 0.0083% with respect to the original results.

Fig. 13
figure 13

Total population difference in 2100 for an additional unit of an age-group at in 2015

Appendix 4

1.1 Impacts of Economic Recessions on Birth Rate and Death Rate

Table 4 Impacts of economic recessions on birth rate (BR) and death rate (DR)

Appendix 5

1.1 Calibration of Excess Mortality Function Associated with Climate Change

To calibrate the αi, j, we borrow the methodology of Pottier et al. [45]. We note that calibrating the βi ≔∑j ∈ Jαi, j is sufficient to have the correct assessment of \( \overset{\sim }{D{R}_i} \) without identifying each elements of the set J for a given age-group. We start by simulating the model without climate feedback under SSP2 scenario and compute the number of deaths between 2045 and 2050 for each group. Then, assuming that the increase in temperature T within this period equals T0 (i.e., the temperature change of +2.5C in 2050 for the A1b used in the WHO [61] study), we add the number of death induced by climate change in 2050 estimated by the WHO [61] study (Table 5). As the number of deaths induced by climate change is not evenly distributed over the age-groups, we assume the distribution provided by the WHO [61] study and reproduced in Table 6. Finally, Table 7 provides the fitted values for parameters βi.

Table 5 Global additional deaths in 2030 and 2050 attributable to climate change for five mortality risks. Source: WHO [61]
Table 6 Proportion of the additional deaths provided by WHO [61] assigned to each age-group
Table 7 Calibrated parameter value for all βi (scale 102)

Appendix 6

1.1 Sensitivity Analysis of the Excess Mortality Function Associated with Climate Change

Table 8 Calibrated parameter value for all βi (scale 102) using Springmann et al.’s [53] estimates for nutrition-related climate-induced deaths
Fig. 14
figure 14

Climate change induced deaths every 5 years with exogenous ab SSP2 and cd GWP scenarios and Springmann et al.’s [53] estimates for nutrition-related climate-induced deaths

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Court, V., McIsaac, F. A Representation of the World Population Dynamics for Integrated Assessment Models. Environ Model Assess 25, 611–632 (2020). https://doi.org/10.1007/s10666-020-09703-z

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