Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering

Abstract

We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits. We use this formula to examine the effect of grandmothering, whereby post-fertile females subsidise their daughter's fertility by provisioning grandchildren. Grandmothering can drive a shift towards increasingly male-biased mating sex ratios due to a post-fertile life stage in females, while male fertility continues to older ages. Our fitness landscapes show a net increase in fitness for both males and females at longer lifespans, and as a result, we find that grandmothering alone provides an evolutionary trajectory to higher longevities.

Hunter‐gatherer studies and human evolution: A very selective review

“…All this modeling points to a switch from multiple mating to mate guarding as a great ape-like life history evolves into a human-like one. The grandmothering models (Kim et al 2012, 2014, Chan et al 2016, 2017) do not include evolution of male strategies. Incorporating that might give something other than the two equilibria that is a robust result so far.…”

The evolution of menopause in toothed whales

“…In addition, we test the explicit mechanism that some models have proposed by which the costly intergenerational help of older females can benefit their younger kin. These models propose that, by ceasing reproduction, older females can invest in increasing the reproductive rate of their daughters 30 , 33 . We test this by comparing the observed baseline fecundity in species with menopause, derived from the kinship demography models, compared to the predicted baseline reproductive rate of their non-menopausal rate.…”

“…In some models of intergenerational help and reproductive lifespan, the benefit provided by older females has been modelled as an increased reproductive rate in the daughters of postreproductive females 30 , 33 . Under this mechanism, the observed reproductive rate of species with menopause is predicted to be higher than in their ancestors without menopause.…”

Cognitive consequences of our grandmothering life history: cultural learning begins in infancy

“…Fitness benefits from continued baby production on one hand trading off with more grandmothering subsidies on the other seemed likely. Subsequent modelling [16][17][18] took up that trade-off. Using similar assumptions about life-history trade-offs and allowing both longevity and the end of female fertility to evolve, both partial differential equations that allow easier exploration of parameter values and simulations found that when grandmothering subsidies are added to an initial chimpanzee-like life history those subsidies drive populations to human-like longevities while holding the end of female fertility below 50.…”

“…Still-fertile females could invest less in each offspring and bear next babies sooner. More robust older females could subsidize more descendants, favouring mutations that increased allocation to somatic maintenance and propelling the evolution of postmenopausal longevity [11][12][13][14][15][16][17][18]-with some of the consequences to be noted below [5,[19][20][21][22][23][24].…”