Abstract
In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.
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References
Caswell H (2001) Matrix population models, 2nd edn. Sinauer Associates, Sunderland
Charnov EL (1993) Life history invariants: some explorations of symmetry in evolutionary ecology. Oxford series in ecology and evolution. Oxford University Press, Oxford
Diekmann O (1997) The many facets of evolutionarily dynamics. J Biol Syst 5:325–339
Doebeli M (1995) Dispersal and dynamics. Theor Pop Biol 14:82–106
Furstenberg H, Kesten H (1960) Products of random matrices. Ann Math Stat 104:457–469
Hines WGS (1987) Evolutionary stable strategies: a review of basic theory. Theor Pop Biol 31:195–272
Huston V, Martnez S, Mischaikow K, Vikers GT (2003) The evolution of dispersal. J Math Biol 47:483–517
Johnson ML, Gaines MS (1990) Evolution of dispersal: theoretical models and empirical tests using birds and mammals. Annu Rev Ecol Syst 21:449–490
Khaladi M, Grosbois V, Lebreton JD (2000) An explicit approach to evolutionarily stable strategies with a cost of dispersal. Nonlinear Anal Real World Appl 1:137–144
Lebreton JD, Khaladi M, Grosbois V (2000) An explicit approach to evolutionarily stable strategies no cost of dispersal. Math Biosci 165:163–176
Levin SA, Cohen D, Hastings A (1984) Dipersal strategies in patchy environments. Theor Popul Biol 26:165–191
McPeek MA, Holtz RD (1992) The evolution of dispersal in spatially and temporally varying environments. Am Nat 140:1010–1027
Mylius SD, Diekmann O (1995) On evolutionarily stable strategies, optimization and the need to be specific about density dependence. Oikos 74:218–224
Orzack SH, Tuljapurkar S (1989) Population dynamics in variable environments VII. The demography and evolution of iteroparity. Am Nat 133:901–923
Parker GA, Maynard Smith J (1990) Optimality theory in evolutionary biology. Nat Biotechnol 348:27–43
Stearns SC, Koella J (1986) The evolution of phenotypic plasticity in life-history traits: predictions for norms of reaction for age and size at maturity. Evol Appl 40:893–913
Stearns SC (1992) The evolution of life histories. Oxford University Press, Oxford
Tuljapurkar S, Orzack SH (1980) Population dynamics in variable environments, I. Long-run growth rates and extinction. Theor Popul Biol 18:314–342
Tuljapurkar S (1990) Population dynamics in variable environments. Springer, New York
Tuljapurkar S, Horvitz CC, Pascrarella JB (2003) The many growth rates and elasticities of populations in random environments. Am Nat 162:489–502
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Khaladi, M., Lebreton, JD. & Khermjioui, A. The Evolution of Dispersal in Random Environment. Acta Biotheor 60, 155–165 (2012). https://doi.org/10.1007/s10441-011-9142-0
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DOI: https://doi.org/10.1007/s10441-011-9142-0