A Darwinian Dynamic Model for the Evolution of Post-Reproduction Survival

Abstract

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role. © 2021 World Scientific Publishing Company.