The effect of predator avoidance and travel time delay on the stability of predator-prey metacommunities

Abstract

The stability conditions for an isolated specialist predator-prey community are fairly well understood. The spatial coupling of several such systems through dispersal of individuals can generate new dynamic behavior that is not yet completely understood. Many factors are known to be stabilizing or neutral, e.g., random dispersal or time delays, while others may induce instabilities in some cases but not others, e.g., density-dependent movement. We study the combination of two stabilizing mechanisms in a two-patch Rosenzweig-MacArthur model with a novel density-dependent movement term. Specifically, we assume that prey move between patches according to their perceived predation risk, and we include travel time between patches as a time delay. We show that the combination of mechanisms may be destabilizing even though each mechanism by itself is stabilizing. Our results show that a detailed knowledge of mechanisms and their temporal scales is necessary to correctly predict the stability of a metacommunity.

How robust is dispersal-induced spatial synchrony?

“…2,33 Previous studies had revealed the importance of differences in the temporal scales of demographic processes between predator and prey species, 13 which can be characterized by the time to capture of prey. 35 Our results show how density-dependent movement and travel time introduce additional key interactions between temporal scales of movement. The effect of density-dependent movement generates fluctuations in movement rate (time until movement), and its effect on synchrony depends on both travel time and time to capture.…”

“…35 For a ¼ 0, the model simplifies to the one studied by Wall et al 32 For a ¼ 0 and s ¼ 0, it is essentially the model studied by Goldwyn and Hastings. 13 In our simulations, we will fix the scaling parameter g ¼ 1.…”

“…13,14 We model dispersal between patches as a density-dependent process that captures the behavioral response of the prey species to perceived predation risk. 35 We limit the density-dependent response of prey to predation risk rather than to their total fitness. 3 Specifically, densitydependent dispersal is proportional to the per capita (of prey) predation rate.…”

“…32 A stability analysis of our model showed that travel-time delay and density-dependent dispersal, while individually stabilizing, may synergistically act to destabilize the coexistence state of the populations. 35 Here, we focus on the effects of the two mechanisms and their interaction on synchrony. We present the model, a brief summary of its stability requirements and the transition to phase equations in Sec.…”

Stability Analysis of a Two-Patch Competition Model with Dispersal Delays

“…As a result, dispersal delays do exist and should be incorporated into modeling the dispersal process. With this in mind, recently, Zhang et al considered a two-patch predator-prey model with delayed dispersal of prey only and showed that such dispersal delay exhibits a stabilizing role on the stability of the coexistence equilibrium [17]. Later, Mai et al generalized the model considered in [17] into the case with an arbitrary number of patches and showed that the dispersal delay can indeed induce stability switches [18].…”