Evolution of dispersal and the ideal free distribution - Robert Stephen Cantrell; Chris Cosner; Yuan Lou (Mathematical Biosciences and Engineering)
A general question in the study of the evolution of dispersalis what kind of dispersal strategies can conveycompetitive advantages and thus will evolve.We consider a two species competition modelin which the species are assumed to have the same population dynamics but different dispersal strategies.Both species disperse by random diffusion and advection along certaingradients, with the same random dispersal rates but different advectioncoefficients.We found a conditional dispersal strategy which results in the ideal free distribution of species,and show that it is a localevolutionarily stable strategy.We further show that this strategyis also a global convergent stable strategyunder suitable assumptions, and our resultsillustrate how the evolution of conditional dispersal can lead to an ideal free distribution.The underlying biological reason is thatthe species with this particular dispersal strategy can perfectly match the environmentalresource, which leads to its fitness being equilibrated across the habitats.