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Multilocus models in the infinite island model of population structure

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  • Roze, Denis
  • Rousset, François

Abstract

Different methods have been developed to consider the effects of statistical associations among genes that arise in population genetics models: kin selection models deal with associations among genes present in different interacting individuals, while multilocus models deal with associations among genes at different loci. It was pointed out recently that these two types of models are very similar in essence. In this paper, we present a method to construct multilocus models in the infinite island model of population structure (where deme size may be arbitrarily small). This method allows one to compute recursions on allele frequencies, and different types of genetic associations (including associations between different individuals from the same deme), and incorporates selection. Recursions can be simplified using quasi-equilibrium approximations; however, we show that quasi-equilibrium calculations for associations that are different from zero under neutrality must include a term that has not been previously considered. The method is illustrated using simple examples.

Suggested Citation

  • Roze, Denis & Rousset, François, 2008. "Multilocus models in the infinite island model of population structure," Theoretical Population Biology, Elsevier, vol. 73(4), pages 529-542.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:4:p:529-542
    DOI: 10.1016/j.tpb.2008.03.002
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    Cited by:

    1. Thomas W. Scott & Alan Grafen & Stuart A. West, 2022. "Multiple social encounters can eliminate Crozier’s paradox and stabilise genetic kin recognition," Nature Communications, Nature, vol. 13(1), pages 1-19, December.
    2. Bürger, Reinhard, 2010. "Evolution and polymorphism in the multilocus Levene model with no or weak epistasis," Theoretical Population Biology, Elsevier, vol. 78(2), pages 123-138.
    3. Steiner, Ulrich K. & Tuljapurkar, Shripad, 2020. "Drivers of diversity in individual life courses: Sensitivity of the population entropy of a Markov chain," Theoretical Population Biology, Elsevier, vol. 133(C), pages 159-167.
    4. Van Cleve, Jeremy, 2015. "Social evolution and genetic interactions in the short and long term," Theoretical Population Biology, Elsevier, vol. 103(C), pages 2-26.
    5. Lehmann, Laurent & Rousset, François, 2009. "Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill–Robertson effect and to the joint evolution of helping and punishment," Theoretical Population Biology, Elsevier, vol. 76(1), pages 35-51.
    6. Rousset, François & Kirkpatrick, Mark & Guerrero, Rafael F., 2014. "Matrix inversions for chromosomal inversions: A method to construct summary statistics in complex coalescent models," Theoretical Population Biology, Elsevier, vol. 97(C), pages 1-10.

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