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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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

[1] P. A. Abrams Ecol. Lett. 2009 462 474

[2] Y. Ben-Zion, G. Yaari, N. M. Shnerb PLoS Comput. Biol. 2010 e1000643

[3] R. Capeáns, J. Sabuco, M. A. Sanjuán Ecol. Complexity 2014 1 8

[4] S. Dey, B. Goswami, A. Joshi J. Theoret. Biol. 2014 52 60

[5] S. Dey, B. Goswami, A. Joshi J. Theoret. Biol. 2015 100 110

[6] S. Dey, A. Joshi Science 2006 434 436

[7] M. Doebeli Theoret. Popul. Biol. 1995 82 106

[8] D. J. Earn, S. A. Levin, P. Rohani Science 2000 1360 1364

[9] D. Franco, F. M. Hilker J. Theoret. Biol. 2013 161 173

[10] D. Franco, F. M. Hilker SIAM J. Appl. Dyn. Syst. 2014 447 465

[11] D. Franco, A. Ruiz-Herrera J. Theoret. Biol. 2015 72 80

[12] E. E. Goldberg, R. Lande Am. Nat. 2007 297 304

[13] A. Gonzalez, J. Lawton, F. Gilbert, T. Blackburn, I. Evans-Freke Science 1998 2045 2047

[14] N. J. Gotelli Am. Nat. 1991 768 776

[15] V. Grimm, C. Wissel Oecologia 1997 323 334

[16] M. Gyllenberg, I. Hanski, T. Lindström Math. Biosci. 1996 119 152

[17] M. Gyllenberg, G. Söderbacka, S. Ericsson Math. Biosci. 1993 25 49

[18] A. Hastings Ecology 1993 1362 1372

[19] A. Hastings, L. W. Botsford Proc. Natl. Acad. Sci. USA 2006 6067 6072

[20] F. M. Hilker, E. Liz Ecol. Complexity 2013 95 107

[21] A. R. Ives, S. T. Woody, E. V. Nordheim, C. Nelson, J. H. Andrews Am. Nat. 2004 375 387

[22] D. Juher, V. Mañosa Math. Model. Nat. Phenom. 2014 108 120

[23] B. E. Kendall, G. A. Fox Theoret. Popul. Biol. 1998 11 37

[24] A. L. Lloyd J. Theoret. Biol. 1995 217 230

[25] R. Nathan Trends Ecol. Evol. 2001 481 483

[26] K. Parvinen Math. Model. Nat. Phenom. 2014 124 137

[27] W. E. Ricker J. Fish. Board Can. 1954 559 623

[28] P. Sah, P. J. Salve, S. Dey J. Theoret. Biol. 2013 113 123

[29] J. Saldaña Math. Model. Nat. Phenom. 2010 22 37

[30] R. V. Solé, J. G. Gamarra, M. Ginovart, D. López Bull. Math. Biol. 1999 1187 1207

[31] H. Thunberg SIAM Review 2001 3 30

[32] J. E. Tillmann GAIA-Ecological Perspectives for Science and Society 2005 119 123

[33] J. M. J. Travis, C. Dytham Proc. R. Soc. B 1999 723 728

[34] S. Tung, A. Mishra, S. Dey J. Theoret. Biol. 2014 163 173

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