Vincent Jansen and Renaud Vitalis (2007) The evolution of dispersal in a Levins’ type metapopulation model. Evolution, 61 (10). pp. 2386 - 2397. ISSN 0014-3820
Full text access: Open
We study the evolution of the dispersal rate in a metapopulation model with extinction and colonisation dynamics, akin to the model as originally described by Levins. To do so we extend the metapopulation model with a description of the within patch dynamics. By means of a separation of time scales we analytically derive a fitness expression from first principles for this model. The fitness function can be written as an inclusive fitness equation (Hamilton’s rule). By recasting this equation in a form that emphasizes the effects of competition we show the effect of the local competition and on the local population size on the evolution of dispersal. We find that the evolution of dispersal cannot be easily interpreted in terms of avoidance of kin competition, but rather that increased dispersal reduces the competitive ability. Our model also yields a testable prediction in term of relatedness and life history parameters.
This is a Draft version This version's date is: 14/06/2007 This item is peer reviewed
https://repository.royalholloway.ac.uk/items/2da988c5-2a90-b26f-9fb5-a271f868ff21/1/
Deposited by () on 31-Mar-2010 in Royal Holloway Research Online.Last modified on 22-Dec-2010
(C) 2007 Wiley-Blackwell, whose permission to mount this version for private study and research is acknowledged. The repository version is the author's final draft.
Ajar, E. (2003) Analysis of disruptive selection in subdivided populations BMC Evol. Biol. 3: 22-34.
Barbour, A.D. and Pugliese, A. (2004). Convergence of a structured metapopulation model to Levins model. J. Math. Biol. 49: 468-500.
Bowler. D. and Benton T.G. (2005) Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics. Biol. Rev. 80: 205-225.
Cadet C., Ferriere R., Metz J.A.J. and Van Baalen, M. (2003) The evolution of dispersal underdemographic stochasticity Am. Nat. 162: 427-441.
Clobert, J., Danchin, E., Dhontdt, A.A. and Nichols, J. Dispersal Oxford University Press, Oxford.
Comins, H.N., Hamilton, W.D. and May, R.M. (1980). Evolutionarily stable dispersal strategies. J. theor. Biol., 82: 205-230.
Day, T. and Taylor, P.D. (1998). Unifiying genetic and game theory models of kin selection for continuous traits. J. theor. Biol., 194: 391-407.
Ferriere, R. and Le Galliard, J-F, (2001) Invasion fitness and adaptive dynamics in spatial population models. In: Dispersal (eds. Clobert, J., Danchin, E., Dhontdt, A.A. and Nichols, J.) Oxford University Press, Oxford, p. 57–82.
Frank S.A. (1986) Dispersal polymorphisms in subdivided habitats. J. Theor. Biol. 122: 303-309.
Gandon, S. (1999). Kin-competition, the cost of inbreeding and the evolution of dispersal. J. theor.Biol., 200: 345-364.
Gandon, S. and Michalakis, Y. (1999) Evolutionarily stable dispersal rate in a metapopulation with extinctions and kin competition. J. theor. Biol. 199: 275-290.
Gandon, S. and Rousset F. (1999) Evolution of stepping-stone dispersal rates. Proc. Roy. Soc. B 266: 2507-2513.
Gerlach, G. and Hoeck, H.N. (2001) Islands on the plains: metapopulation dynamics and female biased dispersal in hyraxes (Hyracoidea) in the Serengeti National Park. Mol. Ecol. 10: 2307-2317.
Goel, N.S and Richter-Dyn, N (1974) Stochastic Models in Biology. Academic Press, New York.
Gyllenberg, M, and Metz, J.A.J. (2001) On fitness in structured metapopulations J. Math. Biol. 43:545-560.
Gyllenberg M., Parvinen K., Dieckmann U. (2002) Evolutionary suicide and evolution of dispersal in structured metapopulations. J. Math. Biol. 45: 79-105.
Gyllenberg M. and Hanski, I. (1992) Single-species metapopulation dynamics - a structured model.Theor. Pop. Biol. 42: 35-61.
Hamilton W.D. (1964) The genetic evolution of social behaviour, II. J. theor. Biol. 7, 17-52.
Hamilton W.D. and May, R.M. (1977) Dispersal in stable habitats. Nature 269: 578-581.
Hanski, I. (1999) Metapopulation Ecology Oxford University Press, 313 p.
Hastings A. (1983) Can spatial variation alone lead to selection for dispersal. Theor. Pop. Biol. 24:244-251.
Hastings, A., and Harrison, S. (1994) Metapopulation dynamics and genetics. Ann. Rev. Evol. Syst. 25: 167-188.
Heino M. and Hanski I. (2001) Evolution of migration rate in a spatially realistic metapopulation model. Am. Nat. 157: 495-511.
Ingvarsson P.K. (1998) Kin-structured colonization in Phalacrus substriatus. Heredity 80: 456-463.
Jansen, V.A.A. and Mulder, G.S.E.E. (1999) Evolving biodiversity. Ecol. Lett. 2: 379–386.
Jansen, V.A.A. and Yoshimura J. (1998) Populations can persist in an environment consisting of sink habitats only. Proc. Natl. Acad. Sci. USA, 95: 3696-3698.
Kisdi, E. (2004) Conditional dispersal under kin competition: extension of the HamiltonMay model to brood size-dependent dispersal. Theor. Pop. Biol. 66, 369-380.
Kuno, E. (1981) Dispersal and the persistence of populations in unstable habitats – a theoretical note. Oecologia 49: 123-126.
Levins, R. (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. B. Entomol. Soc. Am. 15: 237-240.
Metz, J.A.J., and Gyllenberg, M. (2001) How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies. Proc. Roy. Soc. B. 268: 499-508.
Metz, J.A.J, Nisbet, R.M. and Geritz, J.A.J. (1992) How should we define fitness for general ecological scenarios. Trends Ecol. Evol. 7: 198-202.
Morgan, M.T. (2002) Genome-wide deleterious mutation favors dispersal and species integrity Heredity 89: 253-257.
Pamilo P. (1984) Genetic correlation and regression in social groups - multiple alleles, multiple loci and subdivided populations. Genetics 107: 307-320.
Parvinen K. (1999) Evolution of migration in a metapopulation Bull. Math. Biol. 61: 531-550.
Parvinen K., Dieckmann U., Gyllenberg M. and Metz, J.A.J. (2003) Evolution of dispersal in metapopulationswith local density dependence and demographic stochasticity J. Evol. Biol. 16: 143-153.
Parvinen K. (2006) Evolution of dispersal in a structured metapopulation model in discrete time Bull. Math. Biol., 68; 655–678.
Queller D.C. and Goodnight K.F. (1989) Estimating relatedness using genetic markers. Evolution 43:258-275.
Perrin, N. and Mazalov, V. (1999). Local competition, inbreeding, and the evolution of sex-baised dispersal. Am. Nat., 155: 116-127.
Ronce, O., Olivieri, I., Clobert, J. and Danchin, E. (2001) Perspectives on the study of dispersal evolution. In: Dispersal (eds. Clobert, J., Danchin, E., Dhontdt, A.A. and Nichols, J.) Oxford University Press, Oxford, p. 341-357.
Ronce, O., Perret, F. and Olivieri, I. (2000) Evolutionary stable dispersal rates do not always increase with local extinction rates. Am. Nat. 155: 485-496.
Rousset, F. (2004) Genetic Structure and Selection in Subdivided Populations. Princeton University Press, Princeton.
Rousset, F. and Billiard, S. (2000) A theoretical basis for measures of kin selection in sub-divided populations: finite populations and localized dispersal. J. Evol. Bio. 13 : 814-825.
Rousset, F. and Ronce, O. (2004) Inclusive fitness for traits affecting metapopulation demography. Theor. Pop. Biol. 65: 127-141.
Roze D. and Rousset, F. (2005) Inbreeding depression and the evolution of dispersal rates: A multilocus model Am. Nat. 166: 708-721.
Stow A.J., Sunnucks P., Briscoe D.A. and Gardner M.G. (2001) The impact of habitat fragmentation on dispersal of Cunningham’s skink (Egernia cunninghami): evidence from allelic and genotypic analyses of microsatellites. Mol. Ecol. 10: 867-878.
Taylor, P.D. (1988) An inclusive fitness model for the dispersal of offspring. J. Theor. Biol. 130:363-378.
Taylor, P.D. and Frank S.A. (1996) How to make a kin selection model J. Theor. Biol. 180: 27-37.
Van Baalen, M. and Jansen V.A.A. (2001) Dangerous liaisons: the ecology of private interest and common good Oikos 95: 211-224.
Van Baalen, M. and Rand, D. (1998) The unit of selection in viscous populations and the evolution of altruism J. theor. Biol. 193: 631-648.
Van Baalen, M. and Sabelis, M.W. (1995a) The dynamics of multiple infection and the evolution of virulence Am. Nat. 146: 881-910.
Van Baalen, M. and Sabelis, M.W. (1995b) The milker-killer dilemma in spatially structured predatorprey interactions Oikos 74: 391-400.
Venable, D.L. and Brown J.S. (1988) The selective interactions of dispersal, dormancy, and seed size as adaptations for reducing risk in variable environments. Am. Nat. 131: 360-384.
Verdade L.M., Zucoloto R.B., Coutinho L.L. (2002) Microgeographic variation in Caiman latirostris.J. Exp. Zool. 294: 387-396.
West, S.A., Pen, I. and Griffin A. S. (2002) Cooperation and competition between relatives. Science 296: 72-75.
Zeineddine, M. and Jansen, V.A.A. (2005) The evolution of stability in a competitive system J. theor.Biol. 236: 208-215.