Population dynamics with resource-dependent dispersal: single- and two-species models

In this paper, we consider the population models with resource-dependent dispersal for single-species and two-species with competition. For the single-species model, it is well-known that the total population supported by the environment is always greater than the environmental carrying capacity if the dispersal is simply random diffusion. However, we find that the total population supported can be equal or smaller than the environmental carrying capacity when the dispersal depends on the resource distribution. This analytical finding not only well agrees with the yeast experiment observation of Zhang et al. (Ecol Lett 20(9):1118-1128, 2017), but also indicates that resource-dependent dispersal may produce different outcomes compared to the random dispersal. For the two-species competition model, when two competing species use the same dispersal strategy up to a multiplicative constant (i.e. their dispersal strategies are proportional) or both diffusion coefficients are large, we give a classification of global dynamics. We also show, along with numerical simulations, that if the dispersal strategies are resource-dependent, even one species has slower diffusion, coexistence is possible though competitive exclusion may occur under different conditions. This is distinct from the prominent result that with random dispersal the slower diffuser always wipes out its fast competitor. Our analytical results, supported by the numerical simulations, show that the resource-dependent dispersal strategy has profound impact on the population dynamics and evolutionary processes.