Interplay between Local Dynamics and Dispersal in Discrete-time Metapopulation Models

Yakubu, Abdul Aziz; Castillo‐Chavez, Carlos

doi:10.1006/jtbi.2002.3075

Cited by 41 publications

(65 citation statements)

References 49 publications

(122 reference statements)

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“…Autonomous and nonautonomous unidirectional dispersal linked metapopulation models are capable of supporting multiple attractors, where local populations are governed by equations like the classic Ricker model that supports single attractors [16,40,41]. Also, single species nonautonomous models support multiple attractors where the corresponding autonomous models support single attractors [16].…”

Section: Resultsmentioning

confidence: 99%

“…These results may support the need to maintain dispersal corridors in periodically fluctuating environments. The use of dispersal corridors as a mechanism to increase the number of attractors may increase the likelihood of species survival in periodically varying environments [2,41].…”

Section: Resultsmentioning

confidence: 99%

“…The overall fate of a metapopulation becomes less predictable as the complexity of the local dynamics increases. That is, the complex structure of the basins of attraction and their basin boundaries increases as the complexity of the local dynamics increases to the point that it may be impossible to determine, with any degree of certainty, the fate of such metapopulations [19,27,41]. …”

Section: Resultsmentioning

confidence: 99%

“…System (2), like the classic Ricker model, is capable of supporting period-doubling bifurcations route to chaos. However, unlike the classic Ricker model, System (2) is capable of generating multiple cyclic attractors [16,39,41].…”

Section: Single Patch Nonautonomous Population Modelsmentioning

confidence: 99%

“…Hastings [27], Gyllenburg et al [20], Doebeli [8,9], Yakubu [40], Yakubu and CastilloChavez [41] have studied discrete-time, autonomous, single-species metapopulation models that implicitly assume that dispersal is either bidirectional or unidirectional. A two-patch version of these metapopulation models is given by the following system of coupled nonlinear autonomous difference equations: To account for a periodic fluctuating environment, the dynamics at generation t of a singlespecies metapopulation under unidirectional dispersal are modeled with equations of the general form …”

Section: Two Patch Periodically Forced Unidirectional Dispersal Modelsmentioning

confidence: 99%

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Periodic dynamical systems in unidirectional metapopulation models

Franke

Yakubu

2005

Journal of Difference Equations and Applications

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In periodically varying environments, population models generate periodic dynamical systems. To understand the effects of unidirectional dispersal on local patch dynamics in fluctuating environments, dynamical systems theory is used to study the resulting periodic dynamical systems. In particular, a unidirectional dispersal linked two patch nonautonomous metapopulation model is constructed and used to explain the qualitative dynamics of linked versus unlinked independent patches. As in singlepatch, single-species population models, unidirectional nonautonomous models support multiple attractors where local population models support single attractors.

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