Dynamics of Populations in Extended Systems

Abstract

Two models of spatially extended population dynamics are investigated. Model A describes a lattice model of evolution of a predator -prey system. We compare four different strategies involving the problems of food resources, existence of cover against predators and birth. Properties of the steady states reached by the predator-prey system are analyzed. Model B concerns an individual-based model of a population which lives in a changing environment. The individuals forming the population are subject to mutations and selection pressure. We show that, depending on the values of the mutation rate and selection, the population may reach either an active phase (it will survive) or an absorbing phase (it will become extinct). The dependence of the mean time to extinction on the rate of mutations will also be discussed. These two problems illustrate the fact that cellular automata or Monte-Carlo simulations, which take completely the spatial fluctuations into account, are very useful tools to study population dynamics.