The effects of density-dependent dispersal on the spatiotemporal dynamics of cyclic populations

Density-dependent dispersal occurs throughout the animal kingdom, and has been shown to occur in some taxa whose populations exhibit multi-year population cycles. However, the importance of density-dependent dispersal for the spatiotemporal dynamics of cyclic populations is unknown. We investigated the potential effects of density-dependent dispersal on the properties of periodic travelling waves predicted by two coupled reaction-diffusion models: a commonly used predator-prey model, and a general model of cyclic trophic interactions. We compared the effects of varying the gradient of both positive and negative density-dependent dispersal rates, to varying the ratio of the (constant) dispersal rates of the two interacting populations. Our comparison focussed on the possible range of wave properties, and on the waves generated by landscape obstacles and invasions. In all scenarios that we studied, varying the gradient of density-dependent dispersal has small quantitative effects on the travelling wave properties, relative to the effects of varying the ratio of the diffusion coefficients.