Does migration stabilize local population dynamics? analysis of a discrete metapopulation model

Gyllenberg, Mats; Söderbacka, Gunnar; Ericsson, Stefan

doi:10.1016/0025-5564(93)90032-6

Cited by 140 publications

(122 citation statements)

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“…Yamada and Fujisaka (1983) and Lloyd (1995) describe the stability criterion for the strictly in-phase orbits, and Gyllenberg et al (1993) and Hastings (1993) give the positions and stability of the various equilibria and period-2 orbits. Lloyd (1995) gave qualitative descriptions of the various complex attractors.…”

Section: Model Formulationmentioning

confidence: 99%

“…This model can be used to look at spatial population structure and spatial environmental heterogeneity, both separately and together. This model has been studied previously (Gyllenberg et al, 1993;Hastings, 1993;Lloyd, 1995); we combine those results (mostly pertaining to spatial structure) with many new ones to develop a broad synthesis of the model. This mathematical synthesis is our primary objective in this paper, but we also point out some biologically interesting insights gained along the way.…”

Section: Introductionmentioning

confidence: 99%

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Spatial Structure, Environmental Heterogeneity, and Population Dynamics: Analysis of the Coupled Logistic Map

Kendall

Fox

1998

Theoretical Population Biology

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Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial Structure, Environmental Heterogeneity, and Population Dynamics: Analysis of the Coupled Logistic Map

Kendall

Fox

1998

Theoretical Population Biology

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“…Asynchronous local dynamics have also been demonstrated in many simulation studies (e.g., Hassell et al, 1991;Comins et al, 1992, Rohani et al, 1997 and in simple analytic models for a single species metapopulation (Gyllenberg et al, 1993;Hastings, 1993). Despite this there is no complete understanding of how and when asynchronous local dynamics may appear.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

155

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I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

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“…These riches include cyclic and chaotic behaviour with complicated bifurcation patterns, multiple attractors with fractal basins of attraction, and spatial pattern formation of various kinds (e.g. Kaneko 1990Kaneko , 1998Hastings 1993;Gyllenberg et al 1993;Doebeli 1995;Lloyd 1995;Doebeli and Ruxton 1998;Utz et al 2007). Because of this inherently complex dynamics, much work on discrete-time metapopulations falls back on numerical analysis and simulations, and hence is forced to commit to particular choices such as using the logistic map, or assuming nearest-neighbour dispersal or a Gaussian dispersal kernel.…”

Section: Introductionmentioning

confidence: 99%

Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

Kisdi¹

2010

Journal of Theoretical Biology

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A c c e p t e d m a n u s c r i p t 2 AbstractI investigate the stability of the homogeneous equilibrium of a discrete-time metapopulation assuming costly dispersal with arbitrary (but fixed) spatial pattern of connectivity between the local populations. First, I link the stability of the metapopulation to the stability of a single isolated population by proving that the homogeneous metapopulation equilibrium, provided that it exists, is stable if and only if a single population, which is subject to extra mortality matching the average dispersal-induced mortality of the metapopulation, has a stable fixed point. Second, I demonstrate that extra mortality may destabilize the fixed point of a single population.Taken together, the two results imply that costly dispersal can destabilize the homogeneous equilibrium of a metapopulation. I illustrate this by simulations and discuss why earlier work, arriving at the opposite conclusion, was flawed.A c c e p t e d m a n u s c r i p t 3

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Does migration stabilize local population dynamics? analysis of a discrete metapopulation model

Cited by 140 publications

References 14 publications

Spatial Structure, Environmental Heterogeneity, and Population Dynamics: Analysis of the Coupled Logistic Map

Spatial Structure, Environmental Heterogeneity, and Population Dynamics: Analysis of the Coupled Logistic Map

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

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