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The coalescent in finite populations with arbitrary, fixed structure

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  • Allen, Benjamin
  • McAvoy, Alex

Abstract

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary – but fixed – spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings C=Ctt=0∞ from a finite set G to itself. The set G represents the “sites†(in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, Ct:G→G, maps each site g∈G to the site containing g’s ancestor, t time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio r, we find that measures of genetic dissimilarity, among any set of sites, are scaled by 4r(1−r) relative to the even sex ratio case.

Suggested Citation

  • Allen, Benjamin & McAvoy, Alex, 2024. "The coalescent in finite populations with arbitrary, fixed structure," Theoretical Population Biology, Elsevier, vol. 158(C), pages 150-169.
    • Handle: RePEc:eee:thpobi:v:158:y:2024:i:c:p:150-169
    DOI: 10.1016/j.tpb.2024.06.004
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    References listed on IDEAS

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