Random dispersal versus fitness-dependent dispersal

This work extends previous work (Cantrell et al., 2008 [9], ) on fitness-dependent dispersal for a single species to a two-species competition model. Both species have the same population dynamics, but one species adopts a combination of random and fitness-dependent dispersal and the other adopts random dispersal. Global existence of smooth solutions to the time-dependent quasilinear parabolic system is studied. When a single species has a strong tendency to move up its fitness gradient, it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution (Cantrell et al., 2008 [9]). For the two-species competition model, if one species has strong tendency to move up its fitness gradient, such approximately ideal free dispersal is advantageous relative to random dispersal. Bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate.