Ideal Free Distribution of Multiple Species in a Time-Periodic and Patchy Habitat

Abstract

Dispersal strategies that lead to the ideal free distribution (IFD) were shown to be evolutionarily stable in various ecological models. In this paper, we investigate this phenomenon in time-periodic environments where $N$ species – identical except for dispersal strategies – compete. We extend the notions of IFD and joint IFD, previously established in spatially continuous models, to time-periodic and spatially discrete models and derive sufficient and necessary conditions for IFD to be feasible. Under these conditions, we demonstrate two competitive advantages of ideal free dispersal: if there exists a subset of species that can achieve a joint IFD, then the persisting collection of species must converge to a joint IFD for large time; if a unique subcollection of species achieves a joint IFD, then that group will dominate and competitively exclude all the other species. Furthermore, we show that ideal free dispersal strategies are the only evolutionarily stable strategies. Our results generalize previous work by construction of Lyapunov functions in multi-species, time-periodic setting.