Stochastic population dynamics driven by mutant interactors

Abstract

Spontaneous random mutations are an important source of variation in populations. Many evolutionary models consider mutants with a fixed fitness chosen from a certain fitness distribution without considering any interactions among the residents and mutants. Here, we go beyond this and consider \"mutant interactors\", which lead to new interactions between the residents and invading mutants that can affect the carrying capacity and the extinction risk of populations. We model microscopic interactions between individuals by using a dynamical payoff matrix and analyze the stochastic dynamics of such populations. New interactions drawn from invading mutants can drive the population away from the previous equilibrium, and lead to changes in the population size -- the population size is an evolving property rather than a fixed number or externally controlled variable. We present analytical results for the average population size over time and quantify the extinction risk of the population by the mean time to extinction.