Effect of aggressive behaviour on age-structured population dynamics

Abstract

In this work, we present an age-structured population model that incorporates individual behaviour. A classical Leslie matrix model is used to describe the population demography. Adults acquire resources required to survive and reproduce by using two contrasted behavioural tactics (hawk versus dove). Individual survival depends on the average cost of fights while individual fecundity depends on the average gain in the competition to access the resource. We investigated variation in fecundity according to the amount of resources available by using two functions: a Holling type function and a threshold function. We aimed to assess the long-term effects of conflicting tactics of resource acquisition on population dynamics. Our model includes two parts: a fast part that describes the encounters and fights involves a game dynamic model based upon the replicator equations in discrete time; and a slow part that describes the long-term effects of conflicting tactics on the population growth rate. The use of aggregation methods allowed us to reduce the proposed initial model into an aggregated model that describes the dynamics of the population (a Leslie matrix model). We analysed the effects of gain and cost parameters on the asymptotic growth rate of the total population.