Chaotic population dynamics and the evolution of ageing

Problem: Genetic and demographic studies suggest that ageing is an adaptive genetic program, but population genetic analysis indicates that the benefit of ageing to the group is too slow and too diffuse to offset its individual cost. Premise: Demographic homeostasis is a major target of natural selection at the group level, with a strength that can compete with the imperative to higher individual reproductive value. Hypothesis: Ageing has evolved based on its contribution to stabilizing population dynamics, helping prevent population growth overshoot, exhaustion of ecological resources, and local extinction. Model: Asexual individuals carrying a mutable ageing gene are tracked on a geographic grid with slow migration between neighbouring sites. Birth rate is constant; death probability for individuals is the sum of two terms: (1) a logistic crowding term proportional to the local site population and (2) a Gompertz ageing term, in which mortality increases exponentially with age at a rate that is governed by the individual’s gene. The logistic crowding term is computed with a time delay that simulates the momentum of population growth, and causes solutions to undergo chaotic population fluctuations if net growth rates are excessive. Results: Within each site, individual selection pushes life spans progressively longer. Once life spans have increased at a site, its population may fluctuate to extinction. Shorter-lived individuals re-seed it from neighbouring sites. The result is a dynamic steady state in which ageing is selected without pleiotropy.