Taxis-driven pattern formation in a predator-prey model with group defense

Abstract

We consider a reaction-diffusion(-taxis) predator-prey system with group defense in the prey. Taxis-driven instability can occur if the group defense influences the taxis rate (Wang et al., 2017). We elaborate that this mechanism is indeed possible but biologically unlikely to be responsible for pattern formation in such a system. Conversely, we show that patterns in excitable media such as spatiotemporal Sierpinski gasket patterns occur in the reactiondiffusion model as well as in the reaction-diffusion-taxis model. If group defense leads to a dome-shaped functional response, these patterns can have a rescue effect on the predator population in an invasion scenario. Preytaxis with prey repulsion at high prey densities can intensify this mechanism leading to taxis-induced persistence. In particular, taxis can increase parameter regimes of successful invasions and decrease minimum introduction areas necessary for a successful invasion. Last, we consider the mean period of the irregular oscillations. As a result of the underlying mechanism of the patterns, this period is two orders of magnitude smaller than the period in the nonspatial system. Counter-intuitively, faster-moving predators lead to lower oscillation periods and eventually to extinction of the predator population. The study does not only provide valuable insights on theoretical spatially explicit predator-prey models with group defense but also comparisons of ecological data with model simulations.

A predator-prey model with cooperative hunting in the predator and group defense in the prey

“…To explore the defense strategy, Ajraldi et al [1,2] considered a square root functional response λ √ u (u is the density of the prey and λ is the rate of predation). After that, many diffusive predator-prey models with square root functional responses were widely discussed [21,32,39,42,43], and pattern formation, Turing instability, Turing-Hopf bifurcation were investigated [33]. Venturino and Petrovskii [36] proposed a more general functional response λu α in terms of the α power of the prey, where α ∈ (0, 1) describing the efficiency of aggregation for prey population.…”

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

“…Firstly, group defense [21][22][23][24] is a term used to describe the phenomenon whereby predation is decreased or even prevented altogether because of the enlarged ability of the prey to maintain its own survival via better defending or disguising itself when a sufficiently large number of prey appear. The explorations for predator-prey models with group defense were considered by many researchers such as in [24][25][26][27]. Particularly, Freedman and Wolkowicz introduced a general model of predatorprey interactions in which the prey behaves a group defense and there is no mutual interference among predators.…”