title: Grandmothering drives the evolution of longevity in a probabilistic model.
abstract: We present a mathematical model based on the Grandmother Hypothesis to simulate how human post-menopausal longevity could have evolved as ancestral grandmothers began to assist the reproductive success of younger females by provisioning grandchildren. Grandmothers׳ help would allow mothers to give birth to subsequent offspring sooner without risking the survival of existing offspring. Our model is an agent-based model (ABM), in which the population evolves according to probabilistic rules governing interactions among individuals. The model is formulated according to the Gillespie algorithm of determining the times to next events. Grandmother effects drive the population from an equilibrium representing a great-ape-like average adult lifespan in the lower twenties to a new equilibrium with a human-like average adult lifespan in the lower forties. The stochasticity of the ABM allows the possible coexistence of two locally-stable equilibria, corresponding to great-ape-like and human-like lifespans. Populations with grandmothering that escape the ancestral condition then shift to human-like lifespan, but the transition takes longer than previous models (Kim et al., 2012). Our simulations are consistent with the possibility that distinctive longevity is a feature of genus Homo that long antedated the appearance of our species.
authors.affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Electronic address: pkim@maths.usyd.edu.au.
authors.forename: Peter S
authors.initials: PS
authors.lastname: Kim
authors.affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Electronic address: john.mcqueen@sydney.edu.au.
authors.forename: John S
authors.initials: JS
authors.lastname: McQueen
authors.affiliation: Department of Anthropology, University of Utah, Salt Lake City, UT 84112, USA; Utah Population Database, University of Utah, Salt Lake City, UT 84112, USA. Electronic address: james.coxworth@anthro.utah.edu.
authors.forename: James E
authors.initials: JE
authors.lastname: Coxworth
authors.affiliation: Department of Anthropology, University of Utah, Salt Lake City, UT 84112, USA. Electronic address: hawkes@anthro.utah.edu.
authors.forename: Kristen
authors.initials: K
authors.lastname: Hawkes
mesh_terms: D000328:Adult; D000367:Age Factors; D005075:Biological Evolution; D005190:Family; D005260:Female; D005298:Fertility; D006801:Humans; D008136:Longevity; D008297:Male; D008954:Models, Biological; D015233:Models, Statistical; D012741:Sexual Maturation; D013997:Time Factors; D014886:Weaning
keywords: Agent-based modeling; Human evolution; Human longevity; Life history; Sexual conflict