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

Modern models of trophic meta-communities

Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

The joint impacts of dispersal delay and dispersal patterns on the stability of predator-prey metacommunities

A predator-prey metapopulation model over arbitrary number of patches is considered in this paper. The model assumes that only prey move (with a dispersal delay) between all connected patches. Two cases of dispersal patterns are considered. For the case the dispersal of prey is due to random effect only (independent of predator density), we show that either the dispersal delay is harmless in the sense that it does not affect the stability of the metacommunity, or the dispersal delay can induce stability switches with finite number of stability intervals. For the case the dispersal of prey is due to predator-avoidance (dependent on predator density), we show that the interplay of density-dependent dispersal and dispersal delay may also induce finite number of stability switches. This indicates that the combination of the density-dependent dispersal and dispersal delay can exhibit both stabilizing and destabilizing effects on the stability of the coexistence equilibrium. Our results show that the delay and the patterns of prey dispersal jointly affect the stability of predator-prey metacommunities and can induce multiple stability switches.

Impacts of the Dispersal Delay on the Stability of the Coexistence Equilibrium of a Two-Patch Predator-Prey Model with Random Predator Dispersal

In this paper, we study a predator-prey system with random predator dispersal over two habitat patches. We show that in most cases the dispersal delay does not affect the stability and instability of the coexistence equilibrium. However, if the mean time that the predator spent in one patch is much shorter than the timescale of reproduction of the prey and is larger than the double mean time of capture of prey, the dispersal delay can induce stability switches such that an otherwise unstable coexistence equilibrium can be stabilized over a finite number of stability intervals.

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on the stability and behaviour of the predator-prey-subsidy system is investigated, with a primary focus on how incorporating travel time changes the dynamics. The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions. The model is motivated by the Arctic ecosystem, where the Arctic fox consumes both hunted lemming and scavenged seal carcass. The fox travels out on sea ice, in addition to quadrennially migrating over substantial distances. We model the spatial predator-prey-subsidy dynamics through a "stepping-stone" approach. We find that a temporal delay alone does not push species into extinction, but rather may stabilize or destabilize coexistence equilibria. We are able to show that delay can stabilize quasi-periodic or chaotic dynamics, and conclude that the incorporation of dispersal delay has a regularizing effect on dynamics, suggesting that dispersal delay can be proposed as a solution to the paradox of enrichment.