Effect of predator density dependent dispersal of prey on stability of a predator–prey system

Mchich, Rachid; Auger, Pierre; Poggiale, Jean-Christophe

doi:10.1016/j.mbs.2005.11.005

Cited by 57 publications

(43 citation statements)

References 11 publications

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“…Off-phase dynamics of local and inherently unstable predator-prey systems coupled by dispersal were shown to stabilize predator-prey dynamics at the metapopulation level, as exemplified by the seminal experiment carried out by Huffaker (1958) or by many modeling studies (e.g. Crowley, 1981;de Roos et al, 1991;Wilson et al, 1993;Mchich et al, 2007); see also Briggs and Hoopes (2004) for a nice review. Even strongly oscillating systems with foraging facilitation that we observed in some numerical simulations of system dynamics, prone to extinction due, e.g.…”

Section: Discussionmentioning

confidence: 99%

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

Berec

2009

Bull. Math. Biol.

135

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Whereas impacts of predator interference on predator-prey dynamics have received considerable attention, the "inverse" process-foraging facilitation among predators-have not been explored yet. Here we show, via mathematical models, that impacts of foraging facilitation on predator-prey dynamics depend on the way this process is modeled. In particular, foraging facilitation destabilizes predator-prey dynamics when it affects the encounter rate between predators and prey. By contrast, it might have a stabilizing effect if the predator handling time of prey is affected. Foraging facilitation is an Allee effect mechanism among predators and we show that for many parameters, it gives rise to a demographic Allee effect or a critical predator density in need to be crossed for predators to persist. We explore also the effects of predator interference, to make the picture "symmetric" and complete. Predator interference is shown to stabilize predator-prey dynamics once its strength is not too high, and thus corroborates results of others. On the other hand, there is a wide range of model parameters for which predator interference gives rise to three co-occurring co-existence equilibria. Such a multi-equilibrial regime is rather robust as we observe it for all the functional response types we explore. This is a previously unreported phenomenon which we show cannot occur for the Beddington-DeAngelis functional response. An interesting topic for future research thus might be to seek for general conditions on predator functional responses that would produce multiple co-existence equilibria in a predator-prey model.

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Section: Discussionmentioning

confidence: 99%

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

Berec

2009

Bull. Math. Biol.

135

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“…Specifically, the dispersal rate of the predator should decrease as a function of prey density. Some work in this direction was already started, when the prey movement rate depends on predator density alone (Abdllaoui et al 2007;Mchich et al 2005Mchich et al , 2007. Despite its limitations, our study contributes to the integration of complex effects of landscapes and behavior on movement, to a general theory of metacommunity stability.…”

Section: Density-dependent Dispersal and Timescales Of Movementmentioning

confidence: 99%

“…Alternatively, when movement is triggered by mechanisms operating over a much shorter timescale such as behavior, movement time can be scaled to that of behavioral responses. For example, the role of predator avoidance resulting in a non-consumptive response of prey to predator density can be formulated as density-dependent movement and has been well studied using models and experiments (Abdllaoui et al 2007;Mchich et al 2005;Mchich et al 2007). It has been generalized to behavioral response of prey to total expected fitness and to evolutionary dynamics of the traits mediating the response (Abrams 2007).…”

Section: Introductionmentioning

confidence: 99%

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

2015

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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.

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“…Studies of the effects of space races on large scale population dynamics have focused on the Lotka-Volterra predatorprey model and the Nicholson-Bailey host-parasitoid model. The effects on stability are variable, although stabilizing effects seem to predominate (van Baalen and Sabelis 1993;Krivan 1997Krivan , 1998van Baalen and Sabelis 1999;Cressman et al 2004;Mchich et al 2007). An interesting exception is the tri-trophic model of Abrams (2007), which differs from other models in that it assumes that the timescales of the studied movements are similar to those for the rates of birth and death.…”

Section: Introductionmentioning

confidence: 99%

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

Sjödin

Brännström

Söderquist

et al. 2014

Journal of Theoretical Biology

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In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighboring patches and when all patches are reached with equal probability.

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Effect of predator density dependent dispersal of prey on stability of a predator–prey system

Cited by 57 publications

References 11 publications

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics

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

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

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