Impact of dispersal on the stability of metapopulations

Tromeur, Eric; Rudolf, Lars; Groß, Thilo

doi:10.1016/j.jtbi.2015.11.029

Cited by 23 publications

(18 citation statements)

References 69 publications

(126 reference statements)

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“…Finally, superlinear mortality rates, such as quadratic mortality, have a stabilizing effect that can be much stronger than the effect of dispersal, thus that dispersal does not generally lead to a destabilization of such systems. These findings are consistent with Tromeur et al (2013), who studied the dynamics of a single population in a system with many patches. In contrast to this previous study we found that dispersal can in certain cases be stabilizing in the two-species system.…”

Section: Discussionsupporting

confidence: 91%

“…In ecology both the exploration of dynamical models of food webs (Pascual and Dunne, 2005;Thompson et al, 2012;Rooney and McCann, 2012) and the study of spatial metapopulations (Holland and Hastings, 2008;Hanski and Gaggiotti, 2004;Tromeur et al, 2013) are well established lines of research. The two modelling approaches emphasize different aspects of ecological dynamics that are both relevant for most species: the dispersal between different habitat patches and tropic interactions with other species.…”

Section: Introductionmentioning

confidence: 99%

“…Other authors find that increased dispersal can decrease synchrony in population dynamics depending on the interactions between migrating species (Koelle and Vandermeer, 2005). An general investigation of metapopulations based on a linear stability analysis (Tromeur et al, 2013) found that costly dispersal and social fencing are stabilizing, while positive density dependence and settlement facilitation reduce stability. Other papers have shown that costly dispersal might be destabilizing to a metapopulation with homogeneous patches (Kisdi, 2010) so the specific mechanisms appear to be of importance.…”

Section: Introductionmentioning

confidence: 99%

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The influence of dispersal on a predator–prey system with two habitats

Gramlich

Plitzko

Rudolf

et al. 2016

Journal of Theoretical Biology

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Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with dispersal rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.

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Section: Discussionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The influence of dispersal on a predator–prey system with two habitats

Gramlich

Plitzko

Rudolf

et al. 2016

Journal of Theoretical Biology

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“…This phenomenon can occur when selection forces are tied to such sudden environmental effects as algal blooms or flooding [1], or it can arise from more subtle, population-level effects such as overcrowding or resource depletion [2]. Analysis of such interactions within a unified theory of “eco-evolutionary dynamics” has been applied to a wide range of systems—from bacteria-phage interactions to bighorn sheep [3]—by describing population fluctuations in terms of the feedback between demographic change and natural selection [4].…”

Section: Introductionmentioning

confidence: 99%

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

Gilpin

Feldman

2017

PLoS Comput Biol

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In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

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“…The second avenue of investigation asks how spatial distribution affects the persistence of species. Early models considered only a single species in space, a socalled meta-populations [29][30][31]. These models were subsequently extended to meta-communities, systems of competing similar species, e.g.…”

Section: Introductionmentioning

confidence: 99%

Master stability functions reveal diffusion-driven pattern formation in networks

et al. 2018

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We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

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Impact of dispersal on the stability of metapopulations

Cited by 23 publications

References 69 publications

The influence of dispersal on a predator–prey system with two habitats

The influence of dispersal on a predator–prey system with two habitats

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

Master stability functions reveal diffusion-driven pattern formation in networks

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