Increased longevity evolves from grandmothering

Abstract

Postmenopausal longevity may have evolved in our lineage when ancestral grandmothers subsidized their daughters' fertility by provisioning grandchildren, but the verbal hypothesis has lacked mathematical support until now. Here, we present a formal simulation in which life spans similar to those of modern chimpanzees lengthen into the modern human range as a consequence of grandmother effects. Greater longevity raises the chance of living through the fertile years but is opposed by costs that differ for the sexes. Our grandmother assumptions are restrictive. Only females who are no longer fertile themselves are eligible, and female fertility extends to age 45 years. Initially, there are very few eligible grandmothers and effects are small. Grandmothers can support only one dependent at a time and do not care selectively for their daughters' offspring. They must take the oldest juveniles still relying on mothers; and infants under the age of 2 years are never eligible for subsidy. Our model includes no assumptions about brains, learning or pair bonds. Grandmother effects alone are sufficient to propel the doubling of life spans in less than sixty thousand years.

Figure 1.

Female reproductive output as a function of expected adult life span. Plots of net growth rate, r, versus expected adult life span, L, for populations with and without grandmothering. (In this simulation, the time step, Δt, was taken to be 1/12 years to generate a smoother plot. Such a small time step proved to be too computationally demanding for other simulations.)

Figure 2.

Three male weighting functions, α(L), versus expected adult life span, L.

Figure 3.

Evolution of populations from lower to higher expected adult life spans in the presence of grandmothering. The starting points (1) 25.4, (2) 24.9 and (3) 24.6 years correspond to equilibria without grandmothering of the three male trade-off curves in figure 2. Mean expected adult life spans over the population converge to (1) 49.43, (2) 49.40 and (3) 49.37 years in the presence of grandmothering. The population crosses the human threshold of L = 43 within (1) 24 000, (2) 30 000 and (3) 56 000 years.