Dispersal, kin competition, and the ideal free distribution in a spatially heterogeneous population.

In this paper, we reanalyze simple models of the evolution of dispersal in a heterogeneous landscape. Previous analyses concluded that without temporal variability, dispersal can evolve only if it is not costly and if it is conditional on the habitat. If both conditions hold, these models predict that selection on dispersal should lead to balanced dispersal between habitats (the number of immigrants equals the number of emigrants in each habitat). To evaluate the generality of these conclusions, we extended the analysis of these models to finite populations. This requires us to establish fitness measures for finite class-structured populations. These fitness measures allow us to take kin competition into account. Our analysis shows that even without temporal variability, conditional dispersal and the absence of a dispersal cost are not necessary conditions for dispersal to evolve. In the absence of a dispersal cost, we predict that selection on conditional dispersal will always lead to panmixia and not simply to balanced dispersal. When dispersal is costly, we show that the ideal free distribution (IFD) and balanced dispersal do not occur. Our results show that the deviations from IFD are of the order of the dispersal cost. We propose an approach to test our predictions.

[1]  I. Eshel,et al.  Continuous stability and evolutionary convergence. , 1997, Journal of theoretical biology.

[2]  P. Taylor.  An inclusive fitness model for dispersal of offspring , 1988 .

[3]  L. V. Valen.  GROUP SELECTION AND THE EVOLUTION OF DISPERSAL. , 1971 .

[4]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[5]  F. Rousset,et al.  Inbreeding and relatedness coefficients: what do they measure? , 2002, Heredity.

[6]  P. Taylor,et al.  Dispersal Rates Under Variable Patch Density , 1990, The American Naturalist.

[7]  W. Hamilton,et al.  Selfish and Spiteful Behaviour in an Evolutionary Model , 1970, Nature.

[8]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[9]  J. Clobert,et al.  The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents , 1997, Evolutionary Ecology.

[10]  S. Fretwell,et al.  On territorial behavior and other factors influencing habitat distribution in birds , 1969 .

[11]  M. McPeek,et al.  The Evolution of Dispersal in Spatially and Temporally Varying Environments , 1992, The American Naturalist.

[12]  J. Diffendorfer.  Testing models of source-sink dynamics and balanced dispersal , 1998 .

[13]  C. Patrick Doncaster,et al.  Balanced Dispersal Between Spatially Varying Local Populations: An Alternative To The Source‐Sink Model , 1997, The American Naturalist.

[14]  S. Frank,et al.  Dispersal polymorphisms in subdivided populations. , 1986, Journal of theoretical biology.

[15]  Robert M. May,et al.  Dispersal in stable habitats , 1977, Nature.

[16]  Pierre-Henri Gouyon,et al.  Metapopulation Genetics and the Evolution of Dispersal , 1995, The American Naturalist.

[17]  I. Eshel.  On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution , 1996, Journal of mathematical biology.

[18]  P. Taylor,et al.  How to make a kin selection model. , 1996, Journal of theoretical biology.

[19]  François Rousset,et al.  Evolution of the distribution of dispersal distance under distance‐dependent cost of dispersal , 2002 .

[20]  F. Rousset,et al.  Kin selection and natal dispersal in an age-structured population. , 2000, Theoretical population biology.

[21]  Michael L. Johnson,et al.  Evolution of Dispersal: Theoretical Models and Empirical Tests Using Birds and Mammals , 1990 .

[22]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[23]  Rousset,et al.  A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal , 2000 .

[24]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[25]  U. Motro.  Optimal rates of dispersal II. Diploid populations , 1982 .

[26]  M. Gadgil.  Dispersal: Population Consequences and Evolution , 1971 .

[27]  F. Rousset,et al.  Evolution of stepping-stone dispersal rates , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  R. Holt.  Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution , 1985 .

[29]  Alan Hastings,et al.  Can spatial variation alone lead to selection for dispersal , 1983 .

[30]  Jean Clobert,et al.  Density Dependence in the Common Lizard: Demographic Consequences of a Density Manipulation , 1992 .

[31]  F. Rousset.  Reproductive value vs sources and sinks , 1999 .

[32]  Peter D. Taylor,et al.  Allele-Frequency Change in a Class-Structured Population , 1990, The American Naturalist.

[33]  F. Rousset.  Genetic differentiation within and between two habitats. , 1999, Genetics.

[34]  W. Hamilton.  The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[35]  W. Hamilton.  The moulding of senescence by natural selection. , 1966, Journal of theoretical biology.

[36]  J. Lebreton,et al.  An explicit approach to evolutionarily stable dispersal strategies with a cost of dispersal , 2000 .

[37]  Alan Hastings,et al.  Dispersal strategies in patchy environments , 1984 .