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Environmentally induced dispersal under heterogeneous logistic growth. (English) Zbl 1086.92054
Summary: We consider a single-species model which is composed of several habitats connected by linear migration rates and having logistic growth. A spatially varying, temporally constant environment is introduced by the non-homogeneity of its carrying capacity. Under this condition any type of purely diffusive behavior, characterized in our model by symmetric migration rates, produces an unbalanced population distribution, i.e., some locations receive more individuals than can be supported by the environmental carrying capacity, while others receive less. Using an evolutionarily stable strategy (ESS) approach we show that an asymmetric migration mechanism, induced by the heterogeneous carrying capacity of the environment, will be selected. This strategy balances the inflow and outflow of individuals in each habitat (balanced dispersal), as well as `balancing’ the spatial distribution relative to variation in carrying capacity (the Ideal Free Distribution from habitat selection theory). We show that several quantities are maximized or minimized by the evolutionarily stable dispersal strategy.

MSC:
92D40Ecology
91A40Game-theoretic models
34A34Nonlinear ODE and systems, general
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References:
[1] Johnson, M. L.; Gaines, M. S.: Evolution of dispersal: theoretical models and empirical tests using birds and mammals. Ann. rev. Ecol. syst. 21, 449 (1990)
[2] Dieckmann, U.; O’hara, B.; Weisser, W.: The evolutionary ecology of dispersal. Trends ecol. Evol. 14, 88 (1999)
[3] Holt, R. D.: Spatial heterogeneity, indirect interactions and the coexistence of prey species. Am. nat. 124, 377 (1984)
[4] Holt, R. D.: Population dynamics in two-patch environments: some anomalous consequences of optimal habitat distribution. Theor. pop. Biol. 28, 181 (1985) · Zbl 0584.92022
[5] Pulliam, R. H.: Sources, sinks and population regulation. Am. nat. 132, 652 (1998)
[6] Pulliam, R. H.; Danielson, B. J.: Sources, sinks and habitat selection: a landscape perspective on population dynamics. Am. nat. 137, 850 (1991)
[7] Mcpeek, M. A.; Holt, R. D.: The evolution of dispersal in spatially and temporally varying environments. Am. nat. 140, 1010 (1992)
[8] Doncaster, C. P.; Clobert, J.; Doligez, B.; Gusftafsson, L.; Danchin, E.: Balanced dispersal between spatially varying local populations: an alternative to the source-sink model. Am. nat. 150, 425 (1997)
[9] Lemel, J.; Belichon, S.; Clobert, J.; Hochberg, M. E.: The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents. Evol. ecol. 11, 613 (1997)
[10] Lebreton, J. D.; Khaladi, M.; Grosbois, V.: An explicit approach to evolutionarily stable strategies: no cost of dispersal. Math. biosci. 165, 163 (2000) · Zbl 0948.92017
[11] Holt, R. D.; Barfield, M.: On the relationship between the ideal free distribution and the evolution of dispersal. Dispersal, 83 (2001)
[12] Morris, D. W.; Diffendorfer, J. E.; Lundberg, P.: Dispersal among habitats varying in fitness: reciprocating migration through ideal habitat selection. Oikos 107, 559 (2004)
[13] Doebeli, M.: Dispersal and dynamics. Theor. pop. Biol. 47, 82 (1995) · Zbl 0814.92015
[14] Hastings, A.: Can spatial variation alone lead to selection for dispersal?. Theor. pop. Biol. 24, 244 (1983) · Zbl 0526.92025
[15] Fretwell, S. D.; Lucas, H. L.: On territorial behaviour and other factors influencing habitat distributions on birds. Acta biotheoretica 19, 16 (1970)
[16] Verhulst, P. F.: Notice sur la loi que la population suit dans son accroissement. Corr. math. Phys. 10, 113 (1838)
[17] Padrón, V.; Trevisan, M. C.: Effect of aggregating behaviour on population recovery on a set of habitat islands. Math. biosci. 165, 63 (2000) · Zbl 0964.92043
[18] H. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, American Mathematical Society, SURV/41, 1995. · Zbl 0821.34003
[19] Cantrell, R. S.; Cosner, C.: Spatial ecology via reaction-diffusion equations. (2003) · Zbl 1059.92051
[20] Jr., W. Z. Lidicker: Emigration as a possible mechanism permitting the regulation of population density below the carrying capacity. Am. nat. 96, 23 (1962)
[21] łomnicki, A.: Population ecology of individuals. (1988)
[22] Holt, R. D.: Adaptive evolution in source-sink environments: direct and indirect effects of density-dependence on niche evolution. Oikos 75, 182 (1996)
[23] Wares, J. P.; Gaines, S. D.; Cunningham, C. W.: A comparative study of symmetric migration events across a marine biogeographic boundary. Evolution 55, 295 (2001)
[24] Keddy, P. A.: Experimental demography of the sand dune annual, calike edentula, growing along an environmental gradient in nova scotia. J. ecol. 69, 615 (1981)
[25] Keddy, P. A.: Population ecology on an environmental gradient: calike edentula on a sand dune. Oecologia (Berlin) 52, 345 (1982)
[26] Watkinson, A. R.: On the abundance of plants along an environmental gradient. J. ecol. 73, 569 (1985) · Zbl 0587.05027
[27] Khaladi, M.; Grosbois, V.; Lebreton, J. D.: An explicit approach to evolutionarily stable dispersal strategies with a cost of dispersal. J. nonlinear anal. Ser. B 1, No. 1, 137 (2000) · Zbl 0984.92021
[28] Morris, D. W.: Habitat matching: alternatives and implications to populations and communities. Evol. ecol. 8, 387 (1994)
[29] Houston, A. I.; Mcnamara, J. M.; Milinski, M.: The distribution of animals between resources: a compromise between equal numbers and equal intake rates. Anim. behav. 49, 248 (1995)
[30] Kawecki, T. J.; Holt, R. D.: Evolutionary consequences of asymmetric dispersal rates. Am. nat. 160, No. 3, 333 (2002)
[31] Parker, G. A.: Searching for mates. Behavioural ecology: an evolutionary approach, 214 (1978)
[32] Sutherland, W. J.: From individual behaviour to population ecology. (1996)
[33] Okubo, A.: Dynamical aspects of animal; grouping: swarms, schools, flocks and herds. Adv. biophys. 22, 1 (1986)
[34] Smith, J. Maynard: Evolution and the theory of games. Amer. sci. 64, 41 (1976) · Zbl 0526.90102
[35] Calsina, A.; Cuadrado, S.: Small mutation rate and evolutionary stable strategies in infinite dimensional adaptive dynamics. J. math. Biol. 48, 135 (2004) · Zbl 1078.92051
[36] Haldane, J. B. S.: The effect of variation on fitness. Am. nat. 71, 337 (1937) · Zbl 0016.41203
[37] Dockery, J.; Hutson, V.; Mischaikow, K.; Pernarowski, M.: The evolution of slow dispersal rates: a reaction diffusion model. J. math. Biol. 37, 61 (1998) · Zbl 0921.92021
[38] Hutson, V.; Martinez, S.; Mischaikow, K.; Vickers, G. T.: The evolution of dispersal. J. math. Biol. 47, 483 (2003) · Zbl 1052.92042
[39] S. Kirkland, C.-K. Li, S.J. Schreiber, On the evolution of dispersal in patchy landscapes, preprint. · Zbl 1100.39011
[40] Hutson, V.; Mischaikow, K.; Poláčik, P.: The evolution of dispersal rates in a heterogeneous time-periodic environment. J. math. Biol. 43, 501 (2001) · Zbl 0996.92035