Ellis et al. write, “High extrinsic mortality (EM) discounts the value of future reproduction, resulting in tradeoffs favoring earlier onset of reproduction.” This may be true, but the devil is in the details. Williams (Reference Williams1957) predicted that high EM would be associated with greater RE; however, Hamilton (Reference Hamilton1966) showed that an equal increase in mortality hazard across ages leaves the selection gradient on life-cycle transitions unaffected.

The theoretical foundation for Ellis and colleagues’ model is André & Rousset (Reference André and Rousset2020). This work is laudable, as it provides some desperately needed formalism to a field all too prone to strategic ambiguity (Frankenhuis et al. Reference Frankenhuis, Panchanathan and Smaldino2023). However, there are clear limitations of this approach to the current case. Most importantly, their model does not account for the age-specificity of vital rates.

It is a fact that infant and juvenile mortality are generally higher than adult mortality (Jones, Reference Jones2009) – see Figure 1a. Infants and small children are less physiologically buffered from the environment (e.g., lower fat depot, less muscle mass). They have incompletely developed immune systems and are reliant on adults for their energetic needs. Importantly, high juvenile mortality has robust effects in models of RE. In a remarkably simple formulation, Charnov and Schaffer (Reference Charnov and Schaffer1973) showed that optimal RE is controlled not by overall background mortality, but by its age-specificity. Simply put, high juvenile mortality relative to adults favors reduced RE.

Figure 1.

Demographic data for three countries with dramatically different mortality and fertility from Goodman et al. (Reference Goodman, Keyfitz and Pullum1974) included in the demogR package (Jones, Reference Jones2007) and related calculations. (a) Logarithm of the central death rate against age. (b) Fitness sensitivities of age-specific survival probabilities. (c) Elasticity of substitution for investment in improving infant survival compared to investment in improving subsequent survival. (d) Elasticity of substitution for investment in improving infant survival with respect to age-specific survival.

Human life cycles are age-structured, that is, vital rates change with age. The force of selection, measured by fitness sensitivities of age-specific vital rates, is highest in humans for infant survival and declines to zero with reproductive cessation (Jones, Reference Jones2009). Early mortality thus creates a powerful constraint on the evolution of life histories. Trade-offs involving infant, juvenile, and adolescent survival are steep and mean that the returns to any strategy that compromises them must be very high indeed – on the order of 5-20x (Jones & Tuljapurkar, Reference Jones and Tuljapurkar2015). The fitness premium of early survival clearly favors parental investment. This fact of the human life cycle casts substantial doubt on any age-independent explanation for human reproductive decisions.

In a footnote, the authors indicate that they don’t literally mean extrinsic mortality. Following André & Rousset (Reference André and Rousset2020), they suggest that decreasing the marginal efficacy of investments in survival could mimic EM. Their model is unstructured, so the same mortality rate applies to all members of the population. Moreover, the marginal reduction in mortality does not appear to depend on the level of mortality. The demographic reality is that investment in survival is characterized by strongly diminishing marginal returns (Preston, Reference Preston2007), particularly so for infant survival (Mejía-Guevara et al., Reference Mejía-Guevara, Zuo, Bendavid, Li and Tuljapurkar2019).

Suppose that survival is a function of investment, $\theta $ . Effort spent on increasing survival at any given age $i$ might trade off with either fertility or survival at some age $j \gt i$ (possibly both). Let the survival probability at age $i$ be ${P_i}\left( \theta \right)$ . Assume that this is an increasing, decelerating function. A Holling Type III functional response, which is sigmoid but decelerating for most of its domain, is a convenient representation:

(1) $${P_i}\left( \theta \right) = {{\theta _i^2} \over {b_i^2 + \theta _i^2}}.$$

Here, ${b_i}$ is an age-specific parameter measuring the value of the age-specific effort, ${\theta _i}$ . We can pick values of the two parameters that correspond to curves matching the observed survival probabilities and the assumption that the marginal improvement of adult survival is higher than for infants, reflecting the increasing difficulty of ensuring infant survival.

Following Jones & Tuljapurkar (Reference Jones and Tuljapurkar2015), measure the constraints on investment in mortality-reduction by first calculating the fitness elasticity to some value of $\theta $ :

(2) $${e_\theta } = {\theta \over \lambda }{{\partial \lambda } \over {\partial \theta }} = {\theta \over \lambda }\sum\nolimits_{i,j} {{{\partial \lambda } \over {\partial {a_{ij}}}}} {{\partial {a_{ij}}} \over {\partial \theta }},$$

where $\lambda $ is the mean fitness of a life cycle and ${a_{ij}}$ is a life-cycle transition (i.e., demographic rate) from the $j$ th to the $i$ th age/stage. The terms represented by $\partial \lambda /\partial {a_{ij}}$ are the fitness sensitivities and represent the selection gradient on the life cycle (Caswell, Reference Caswell2001).

The constraint on selection on that trait with respect to some other trait is then simply the ratio of their respective elasticities (Jones & Tuljapurkar, Reference Jones and Tuljapurkar2015).

A full analysis of this model is beyond the scope of this brief comment, but we can see some representative results in Figure 1 using demographic data from three populations with very different mortality and fertility schedules (Goodman et al., Reference Goodman, Keyfitz and Pullum1974). The elasticity of substitution is always greater than one for investment in improving infant survival compared to improvements of survival for any other age (Figure 1c). That is, investment in improving infant survival is always favored over improvements in survival at other ages. The elasticity of substitution is less than one for most reproductive ages for improving infant survival compared to survival elasticities at those ages, meaning survival is valued more than increased improvements to it.

Abrams (Reference Abrams1993) noted that density-dependence could potentially lead to increased EM favoring greater RE. The problem is that density-dependent population regulation – and therefore fitness – has been highly elusive in human populations. Wood & Smouse (Reference Wood and Smouse1982) found no evidence for density-dependence in fertility, where it is traditionally assumed to act, and weak evidence of density-dependence in mortality. The Gainj population that they studied was what might be the best-case scenario for finding it: natural fertility, very high population density, and limited opportunities for livelihood diversification. Human populations manage to avoid density-dependent effects on vital rates because of their remarkable capacity to intensify, innovate, and diversify when faced with population pressure (Boserup, Reference Boserup1965, Lee, Reference Lee, Coleman and Schofield1986, Netting, Reference Netting1993).

Historically, mortality regimes were more likely a result of episodic, extrinsic causes (e.g., crop failure, pestilence) than density per se (Hayward et al., Reference Hayward, Holopainen, Pettay and Lummaa2012; Zhang et al., Reference Zhang, Lee, Wang, Li, Pei, Zhang and An2011). On the one hand, this suggests that EM is an important phenomenon to understand for human (particularly agrarian) populations. On the other hand, it means that we are likely in a Hamiltonian regime, where an overall increase in EM will have no effect on selection unless it is age-specific (Moorad et al., Reference Moorad, Promislow and Silvertown2019).

Any adequate theory of adaptive plasticity in RE must account for the dramatically different forces of selection working on different parts of the human life cycle. We also desperately need data on the relative value of juveniles and adults in changing mortality regimes. Finally, we need to acknowledge – and measure – the contribution of social environments to human reproductive strategies. A 13-year-old girl who detects she is maturing in a harsh environment will not leave much of an evolutionary legacy if she immediately matures, gives birth, and dies young and alone. An essential element of a high-effort reproductive strategy surely involves allo-parents who can invest in offspring even when the mother cannot (Geronimus, Reference Geronimus2003).