Geodesic
Impact of Dispersal on the Total Population Size, Constancy and Persistence of Two-patch Spatially-separated Populations
P. Carmona1 ; D. Franco1
1 Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, 28040, Madrid, Spain
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 45-55.

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This paper explores by means of extensive numerical simulation how unidirectional and bidirectional symmetric dispersal can affect the mean total population size and the fluctuation range in a two-patch population model described by coupled difference equations. The obtained results show that the response to dispersal varies not only with the type of connection between subpopulations, but also with the intrinsic dynamics in each subpopulation. We find that the mean total population size increases monotonically with unidirectional dispersal from a region with local complicated dynamics to a region with an attracting equilibrium, whereas in the other studied scenarios the response is generically unimodal. Constancy and persistence are considered by relating them to the fluctuation range. Our results show that dispersal is capable of enhancing constancy and persistence only in certain situations. Additionally, we show that multistability affects the behaviour of the mean total population size and its fluctuation range. Hence it can be concluded that, in contrast to other control strategies, only if there is a good knowledge of the local population dynamics, then a modification of the natural dispersal rate between regions might be used as a way to control the size and stability of the population.
DOI : 10.1051/mmnp/201510204

P. Carmona 1 ; D. Franco 1

1 Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, 28040, Madrid, Spain 
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     title = {Impact of {Dispersal} on the {Total} {Population} {Size,} {Constancy} and {Persistence} of {Two-patch} {Spatially-separated} {Populations}},
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P. Carmona; D. Franco. Impact of Dispersal on the Total Population Size, Constancy and Persistence of Two-patch Spatially-separated Populations. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 45-55. doi : 10.1051/mmnp/201510204. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510204/

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