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.

Benjamin Allen

Alex McAvoy

Theoretical Population Biology

跨学科期刊《理论种群生物学》发表了关于种群生物学理论方面的文章，特别是在人口学、生态学、流行病学、进化和遗传学领域。重点是发展数学理论和模型，以增强对生物现象的理解。文章强调了这项工作对于推进生物学进步的动机和意义，依靠大量的数学努力来获得生物学洞察力。该杂志还介绍了直接影响人口生物学理论问题的经验结果以及计算和统计方法。

Theoretical Population Biology is an interdisciplinary journal that publishes articles on the theory of population biology, particularly in the fields of demography, ecology, epidemiology, evolution, and genetics. The focus is on developing mathematical theories and models to enhance the understanding of biological phenomena. The articles emphasize the motivation and significance of this work in advancing biological knowledge, relying on substantial mathematical efforts to gain biological insights. The journal also presents empirical results that directly impact theoretical issues in population biology, along with computational and statistical methods.

《理论种群生物学》是一本跨学科的期刊，专注于种群生物学理论的研究，尤其在人口学、生态学、流行病学、进化和遗传学等领域。期刊强调发展数学理论和模型，以加深对生物现象的理解。文章不仅探讨了推动生物学进步的动机和意义，还依赖大量的数学工作来获得生物学的洞察。此外，期刊还介绍了直接影响种群生物学理论问题的实证结果以及相关的计算和统计方法。

Category	Quartile
生物学	4
生物学, 生态学	4
生物学, 进化生物学	4
生物学, 遗传学	4
生物学, 数学与计算生物学	4

The coalescent in finite populations with arbitrary, fixed structure

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Journal Info

Category	Quartile
MATHEMATICAL & COMPUTATIONAL BIOLOGY	4