Continuous Traveling Waves for Prey-Taxis

Abstract

Spatially moving predators are often considered for biological control of invasive species. The question arises as to whether introduced predators are able to stop an advancing pest or foreign population. In recent studies of reaction-diffusion models, it has been shown that the prey invasion can only be stopped if the prey dynamics observes an Allee effect.In this paper, we include prey-taxis into the model. Prey-taxis describe the active movement of predators to regions of high prey density. This effect leads to the observation that predators are drawn away from the leading edge of a prey invasion where its density is low. This leads to counterintuitive result that prey-taxis can actually reduce the likelihood of effective biocontrol.

A user’s guide to PDE models for chemotaxis

“…Modelling the role of chemotaxis in pathological processes is a large field: Luca et al [61] considered whether the chemotactic aggregation of microglia may provide a mechanistic basis for senile plaques during progression of Alzheimer's disease, while chemotaxis has been incorporated into the modelling of a number of distinct stages of tumour growth, including the migration of invasive cancer cells [88], tumour-induced angiogenesis (see the reviews [16,63]) and macrophage invasion into tumours [79]. Finally, we should not neglect the modelling of taxis in the context of spatial ecological processes, including "prey-taxis" [43,58], herd grazing [31] and the spatial dynamics of mountain pine beetle attacks [60].…”

Global solutions and uniform boundedness of attractive/repulsive LV competition systems

“…It is worthwhile to mention that besides the competition model, the advection, which is referred to as the prey-taxis, has been studied in predator-prey models by various authors. See [7][8][9][10][11][12][13][14].…”

Complex Population Dynamics in Heterogeneous Environments: Effects of Random and Directed Animal Movements

“…Lee et al [5,6] investigate the necessary conditions for pattern formation in prey-taxis systems. They have also detected continuous travelling wave for prey-taxis in a model with Allee effect.…”

“…Spatial heterogeneities [15][16][17][18][19] such as prey density gradients, give rise to prey-taxis. This phenomenon has been found to have a stabilizing effect on the dynamics [6] although these authors employ a different modeling approach.…”