Low Total Fertility in Simple Economic Systems

TL;DR

The paper analyzes how low total fertility interacts with wealth accumulation in a minimal agent-based model of a simple foraging economy. It uses a Sugarscape-inspired 2D torus with resource growth $g$, landscape size $row \times col$, metabolism $m$, birth cost $bc$, infertility $f$, and finite lifespan, mapping population dynamics to both continuous and discrete forms such as $dN(t)/dt = r N(t)\left(1-\frac{N(t)}{K}\right)$ and $N(t+1)=[1+r-\frac{N(t-\tau)}{K}]N(t)$. The results show that higher infertility or birth costs can drive populations below carry capacity, producing higher wealth per capita but unstable trajectories with a non-negligible extinction risk, while estate-tax funded birth-cost subsidies can stabilize populations near the carry capacity. The findings highlight the importance of explicitly modeling stochastic population trajectories in policy design to mitigate declining fertility and its ecological-economic feedbacks. The work also points to a potential low-fertility trap where wealth gains reinforce fertility reductions, underscoring the role of targeted fiscal mechanisms in sustaining demographic and economic stability.

Abstract

Low total fertility rates throughout the world have lead to concerns about economic growth, military security, international political power, environment impacts, and quality of life. Overall total fertility rates of today's societies are complex emergent functions of culture, biology, and economic policies that are notoriously difficult to forecast. In order to study the dynamic, stochastic nature of total fertility rates, population and wealth trajectories as functions of infertility and birth cost are generated from a minimal, endogenous, agent-based model of a simple foraging economy. A harvesting model from mathematical ecology is added to reflect death by "natural causes". With these added limits of finite lifespans, decreasing total fertility rates are shown to lead to population levels consistently below the actual carry capacity of the landscape. These below carry-capacity population levels generate higher total and per capita wealth. The stochastic population trajectories generated demonstrate instabilities that significantly increase the likelihood of extinction within reasonable time frames. Society may possibly be encouraged by this increasing wealth (and perhaps reduced environmental degradation) to continue decreasing total fertility rates, further increasing the extinction risk. Conversely, the additional wealth might increase total fertility rates through relatively lower birth costs. Tax-funded subsidies are added to the model to determine if directly reducing birth costs can significantly increase total fertility rates to escape these stochastic instabilities. This research demonstrates that understanding attempts to mitigate the consequences of declining total fertility rates must include modeling of the dynamic and stochastic nature of these population trajectories.

Figures (7)

• Figure 1: Stochastic population trajectories showing the chaotic, oscillatory, and stable regimes for 20 differently seeded runs of the foraging model for each critical infertility. The labels 'Fnnn' refer to the infertility value (nnn) in the foraging model. The continuous Verhulst process of Eq.(\ref{['contInV']}) and the discrete process of Eq.(\ref{['discretV']}) (labeled Hutch-W) are also provided for comparison and reference to the intrinsic growth rates of the Verhulst and Hutchinson-Wright processes.
• Figure 2: Annualized death rates for geographic regions of the world ciaDeathR and for the model with various values of infertility. A relatively high infertility of F500 was necessary to bring the simulations' death rates in line with these data on human societies. F500D and F790D refer to age-structured configurations.
• Figure 3: Actual and FL models' death distributions. a) Each agent at birth samples an age of death by natural causes from the indicated FL model. The census data arias2023united presented are actual ages of death for the referenced cohort (100,000 people). The FL model's mean frequency of ages of death over 10 differently seeded runs for a length of 1000 years is scaled to the size of the census cohort. b) The mean frequencies of ages of death over 10 differently seeded runs of the skewed Gaussian and linear FL modes over 1000 years. The actual number of deaths in the simulation exceed the census and Gompertz distributions by the approximate 50,000 actual deaths in the first three months after birth.
• Figure 4: Evolution pressures on the finite lifespan model's minimum age (FD) in a steady state environment select for the oldest possible lifespans. Models without inheritance (a) have the strongest pressure on the FD allele though, even without inheritance (b), the selection pressure on the FD allele is strong.
• Figure 5: a) Dynamic age-structured population trajectories for 20 differently seeded runs at various high values of infertility. As the infertility increases, at first the stable populations decrease slightly. At some point (F800), the dynamics transition to a decay regime with extinction inevitable. b) Total surplus trajectories for these same 20 differently seeded runs at high values of infertility. The corresponding total surplus substantially increases with lower but stable population levels until transition to decay. At transition, at first a remarkable spike in total surplus occurs but stochastic extinction awaits, slowly for the F800 case but much more quickly for F900.