A mathematical model for the effects of grandmothering on human longevity

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.