Stability in an age-structured metapopulation model

Castro, Manuela Longoni de; Silva, Jacques A. L.; Justo, Dagoberto Adriano Rizzotto

doi:10.1007/s00285-005-0352-4

Cited by 12 publications

(12 citation statements)

References 20 publications

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“…Furthermore, we describe local dynamics as scalars, while local populations might have a more detailed structure, especially in age. The interaction between age structure and spatial structure has been shown to influence metapopulation stability, as dispersal rates may vary among age classes (Hastings, 1992;de Castro et al, 2006). As de Castro et al (2006) pointed out, this effect is however dependent on conditions outside which our conclusions remain valid.…”

Section: Heterogeneous Metapopulation Density-independencementioning

confidence: 68%

Impact of dispersal on the stability of metapopulations

Tromeur

Rudolf

Groß

2016

Journal of Theoretical Biology

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Dispersal is a key ecological process that enables local populations to form spatially extended systems called metapopulations. In the present study, we investigate how dispersal affects the linear stability of a general single-species metapopulation model. We discuss both the influence of local within-patch dynamics and the effects of various dispersal behaviours on stability. We find that positive density-dependent dispersal and positive density-dependent settlement are destabilizing dispersal behaviours while negative density-dependent dispersal and negative density-dependent settlement are stabilizing. It is also shown that dispersal has a stabilizing impact on heterogeneous metapopulations that correlates positively with the number of patches and the connectance of metapopulation networks.

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Section: Heterogeneous Metapopulation Density-independencementioning

confidence: 68%

Impact of dispersal on the stability of metapopulations

Tromeur

Rudolf

Groß

2016

Journal of Theoretical Biology

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“…Of course, if migration is density-independent (µ(x) = µ, 0 < µ < 1) we have ϕ (x) = µ, for all x, and thus the hypothesis ϕ (x) < 1 is automatically satisfied showing that density-independent dispersal in single species metapopulation models do not present dispersal driven instabilities (see Rohani et al, 1996;Jansen and Lloyd, 2000). However this is not true in multi-species metapopulation (Rohani and Ruxton, 1999) or in age-structured single species models (De Castro et al, 2005). The same ideas apply in the case of a synchronous periodic orbit of period k, let us say p 1 , p 2 , .…”

Section: The Basic Theorymentioning

confidence: 88%

Density-dependent migration and synchronism in metapopulations

Silva

Giordani

2006

Bull. Math. Biol.

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A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.

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“…by age or because there are several interacting species (such as predator-prey or host-parasitoid), provided that different age/stage classes or different species differ in dispersal (Hastings 1992;Rohani and Ruxton 1999a,b;Jansen and Lloyd 2000;White and White, 2005;de Castro et al 2006). Concerning the reverse case, cost-free dispersal cannot stabilize the homogeneous equilibrium if it is unstable in absence of dispersal: this holds for density-dependent dispersal (Silva et al 2001) and for multi-species systems (Jansen and Lloyd 2000) as well.…”

Section: Discussionmentioning

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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Stability in an age-structured metapopulation model

Cited by 12 publications

References 20 publications

Impact of dispersal on the stability of metapopulations

Impact of dispersal on the stability of metapopulations

Density-dependent migration and synchronism in metapopulations

Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

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