A spatial model of interspecific competition and selective predation: The case of the two Hippolais

Mutual exclusion between congeneric species has been observed such as the case of the grey and red squirrels in Great Britain and the case of the twoHippolais warbler speciesHippolais icterina andH. polyglotta in Europe. This process can lead to the formation of an extinction wave which propagates. Two main assumptions are tested, competition and selective predation. The aim of this work is to present spatial models of these two processes. The animals of two species are assumed to move on a two dimensional array of spatial patches with local interactions of competition or of selective predation between them. We focus on the case of mutual exclusion. Initially, the two competing species occupy complementary areas in an array of spatial patches with a small common zone. Numerical simulations show that under particular conditions, one species gets extinct and the other invades the whole set of spatial patches. These simulations show that with time, the length of the overlapping zone stabilizes and moves at a constant velocity. The limit length of the overlapping band and the velocity of the extinction wave are found to be functions of the parameters of the models. We relate this general model to the case of two sibling species of birds:H. icterina andH. polyglotta.