The ideal free distribution and evolutionary stability in habitat selection games with linear fitness and allee effect

Abstract

Fretwell and Lucas [3] introduced the Ideal Free Distribution (IFD) to predict how birds establish themselves among habitats. It has been shown that the IFD is an evolutionarily stable strategy (ESS) of the habitat selection game when fitness is a decreasing function of patch density. We develop a formula for the IFD when there are an arbitrary number of habitats, and fitness functions are linearly decreasing in the population size (i.e., density) in each habitat. We also explore the IFD when fitness functions increase with population size until some maximum threshold is reached (Allee Effect) and examine whether an IFD still is an ESS in this case.