The coalescent in finite populations with arbitrary, fixed structure

Benjamin Allen and Alex McAvoy

Theoretical Population Biology, 2024, vol. 158, issue C, 150-169

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.

Keywords: Coalescent theory; Identity-by-descent; Genetic drift; Random mapping (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:158:y:2024:i:c:p:150-169

DOI: 10.1016/j.tpb.2024.06.004

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