Selection
Volume/Issue:
Volume 1: Issue 1-3
Inclusive Fitness in Finite Deme-structured and Stepping-stone Populations
Authors: P. D. Taylor 1 , A. J. Irwin, and T. Day
View More View Less
  • 1 Department of Mathematics and Statistics, Queen's University Kingston ON K7L 3N6, Canada
DOI:
https://doi.org/10.1556/select.1.2000.1-3.15
Page Count:
153–164
Publication Date:
01 Jan 2001
Online Publication Date:
22 Jul 2005
Article Category:
Research Article
Restricted access

Very little attention has been given in the literature to the interesting question of how to handle relatedness in finite populations. The main problem is that a finite population is never really ieat equilibriuml. in that it represents just one realization of an infinite assemblage of possible allelic distributions. A recent paper of Rousset and Billiard (manu- script) provides coefficients which, if used in inclusive fitness models under conditions of weak selection, give us a measure of average allele frequency change where the average is taken over all such realizations. Their coefficients are expressed in terms of identity in state, and an alternative formulation (Taylor and Day, manuscript) in terms of coefficients of consanguinity permits the calculation of relatedness in simple cases from pedigree analysis. Here we implement these calculations in a finite asexual haploid population with either a deme structure or a one-dimensional stepping-stone structure and verify our results with numerical simulations in small populations. Our simulations al- low us to investigate the dependence of relatedness on allele frequency, and our results here agree qualitatively with those obtained by Rousset and Billiard. Finally, we examine a model of altruism in a deme-structured population to verify numerically that our relatedness coefficients provide a correct measure of allele frequency change.

  • Wright, S. (1943): Isolation by distance. Genetics 28: 114-138.

    'Isolation by distance ' () 28 Genetics : 114 -138.

  • Taylor, P. D. and Day, T.: IBD measures of relatedness in finite populations (submitted).

  • Kelly, J. K. (1997): Fitness variation across a subdivided population of the annual plant impatiens capensis. Evolution 51: 1100-1111.

    'Fitness variation across a subdivided population of the annual plant impatiens capensis ' () 51 Evolution : 1100 -1111.

    • Search Google Scholar

  • Kimura, M. and Weiss, G. H. (1964): The stepping-stone model of population structure and the decrease of genetic correlation with distance. Genetics 49:561-576.

    'The stepping-stone model of population structure and the decrease of genetic correlation with distance ' () 49 Genetics : 561 -576.

    • Search Google Scholar

  • Latter, B. D. H. (1973): The island model of population differentiation: A general solution. Genetics 73:147-157.

    'The island model of population differentiation: A general solution ' () 73 Genetics : 147 -157.

    • Search Google Scholar

  • Malécot, G. (1975): Heterozygosity and relationship in regularly subdivided populations. Theor. Popul. Biol. 8: 212-241.

    'Heterozygosity and relationship in regularly subdivided populations ' () 8 Theor. Popul. Biol : 212 -241.

    • Search Google Scholar

  • Michod, R. E. and Hamilton, W. D. (1980): Coefficients of relatedness in sociobiology. Nature 288: 694-697.

    'Coefficients of relatedness in sociobiology ' () 288 Nature : 694 -697.

  • Price, G. R. (1970): Selection and covariance. Nature 227: 520-521.

    'Selection and covariance ' () 227 Nature : 520 -521.

  • Rousset, F. and Billiard, S.: A theoretical basis for measures of kin selection in subdivided populations: Finite populations and localized dispersal. Evol. Biol. (in press).

  • Seger, J. (1981): Kinship and covariance. J. Theor. Biol. 91: 191-213.

    'Kinship and covariance ' () 91 J. Theor. Biol. : 191 -213.

  • Taylor, P. D. (1992a): Altruism in viscous populations - an inclusive fitness model. Evolutionary Ecology 6: 352-356.

    'Altruism in viscous populations - an inclusive fitness model ' () 6 Evolutionary Ecology : 352 -356.

    • Search Google Scholar

  • Taylor, P. D. (1992b): Inclusive fitness in a homogeneous environment. Proc. R. Soc. Lond. B 249: 299-302.

    'Inclusive fitness in a homogeneous environment ' () 249 Proc. R. Soc. Lond. B : 299 -02.

  • Taylor, P. D. (1996): Inclusive fitness arguments in genetic models of behaviour. J. Math. Biol. 34: 654-674.

    'Inclusive fitness arguments in genetic models of behaviour ' () 34 J. Math. Biol. : 654 -674.

    • Search Google Scholar

  • Wilson, D. S., Pollock, G. B. and Dugatkin, L. A. (1992): Can altruism evolve in purely viscous populations? Evolutionary Ecology 6: 331-341.

    'Can altruism evolve in purely viscous populations? ' () 6 Evolutionary Ecology : 331 -341.

    • Search Google Scholar

  • Crow, J. F. and Kimura, M. (1970): An Introduction to Population Genetics Theory. Harper and Row, New York.

    An Introduction to Population Genetics Theory , ().

  • Grafen, A. (1985): A geometric view of relatedness. Oxford Surveys in Evolutionary Biology 2: 28-89.

    'A geometric view of relatedness ' () 2 Oxford Surveys in Evolutionary Biology : 28 -89.

  • Hamilton, W. D. (1964): The genetical evolution of social behaviour, I and II. J. Theor. Biol. 7: 1-52.

    'The genetical evolution of social behaviour, I and II ' () 7 J. Theor. Biol. : 1 -52.
Cover Selection
Selection
Print ISSN:
1585-1931
Online ISSN:
1588-287X

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Aug 2020 6 0 0
Sep 2020 6 0 0
Oct 2020 0 0 0
Nov 2020 1 14 5
Dec 2020 3 0 0
Jan 2021 2 0 0
Feb 2021 0 0 0