Synchronisation of fertility with carrying capacity; an investigation using classical and agent based modeling

Abstract

A generalized Verhulst model subject to seasonal change in both fertility rate and carrying capacity is outlined. Numerical solutions to the Verhulst equations are employed to obtain optimal fertility rate phase shift with respect to carrying capacity. Possible natural selection for a preferred season of conception is investigated using agent based simulations. Both experiments indicate that synchronization of fertility rate to environment carrying capacity is beneficial to species survival.

Keywords

• population dynamics
• differential equations
• agent based model