A mathematical model for the effects of grandmothering on human longevity

Abstract

<abstract> <p>Although females in human and the great ape populations reach the end of fertility at similar ages (approximately 45 years), female humans often live well beyond their post-fertile years, while female primates typically die before or shortly after the end of fertility. The grandmother hypothesis proposes that the care-giving role provided by post-fertile females contributed to the evolution of longevity in human populations. When post-fertile females provide care for weaned infants, mothers are able to have their next baby sooner without compromising the chances of survival of their previous offspring. Thus, the post-menopausal longevity that is unique to human populations may be an evolutionary adaptation. In this work, we construct, simulate, and analyze an ordinary differential equations mathematical model to study the grandmother hypothesis. Our model describes the passage of the individuals of a population through five life stages in the cases with and without grandmothering. We demonstrate via numerical simulation of the mathematical model that grandmothering care is sufficient to significantly increase adult life expectancy. We also investigate the relationship between the number of weaned infants that a post-fertile female can care for at a given time and the steady-state age distributions of a population.</p> </abstract>

Reevaluating the grandmother hypothesis

“…Mathematical models of the grandmother hypothesis have had mixed results: Kachel, Premo, and Hublin (2011) found that the inclusive fitness benefits were too small to change human life history variables, but Kim, Coxworth, and Hawkes (2012), Kim, Mc-Queen, Coxworth, and Hawkes (2014), Chan, Hawkes, and Kim (2016), Hawkes (2019), andPaquin, Kato, andKim (2020) found that grandmothering was sufficient to do so. However, some of the assumptions used in these previous models are problematic.…”

“…All of these models found that grandmothering was sufficient to cause the emergence and maintenance of menopause in female life histories. However, some of these assumptions are unrealistic: namely, that grandmothers can care for any child, not just their progeny, which is present in Kim et al (2012Kim et al ( , 2014 and Paquin et al (2020), but also, for example, a constant weaning age and inability to reproduce while caring for weaned dependents, which is present in all models. Although the authors argue that these assumptions would actually make it less likely for grandmothering to lead to the evolution of menopause, I would prefer a model that just did not incorporate these objectionable assumptions.…”

Predictable increase in female reproductive window: A simple model connecting age of reproduction, menopause, and longevity

“…This eventually promotes the diffusion of grandmother genes and is sufficient to significantly increase adult life expectancy. [ 11 ]…”

“…This eventually promotes the diffusion of grandmother genes and is sufficient to significantly increase adult life expectancy. [11] Genetics and epigenetics are expected to influence the average age at menopause (AAM). The impact of the genetic component is supported by heritability estimates of AAM from twin studies as high as 63%.…”