论文标题
具有任意，固定结构的有限种群的合并
The coalescent in finite populations with arbitrary, fixed structure
论文作者
论文摘要
结合是一个随机过程，代表经历中性遗传漂移的人群中的祖先谱系。这种合并最初定义为混合良好的人口，以各种方式适应了空间，年龄和阶级结构，以及现实世界中的其他特征。为了进一步扩展合并理论应用的种群结构范围，我们为具有任意（但固定的）空间，年龄，性别和阶级结构，单倍体或二倍体遗传学以及任何固定配合模式的广泛的中性漂移模型制定了一个合并过程。在这里，合并表示为映射的随机序列$ \ MATHCAL {c} = \ left（C_T \ right）_ {t = 0}^\ infty $从有限的集合$ g $到本身。集合$ g $表示这些等位基因可以居住的``站点''（在个人，尤其是位置和/或类中）。合并状态，$ c_t：g \ to g $，将每个站点$ g \ in g $映射到包含$ g $祖先的网站，$ t $ t $ time stort to to to to to to to to the过去。使用此表示，我们定义和分析聚结时间，聚结的长度，合并之前的突变以及逐个状态和身份的固定概率。对于低突变，我们提供了通过合并来计算逐个状态和逐个状态概率的配方。将我们的结果应用于任意性别比率$ r $的二倍体人群，我们发现，在任何一组站点中，遗传差异的衡量标准相对于均匀的性别比案例，均按$ 4R（1-R）$缩放。
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 $\mathcal{C} = \left(C_t\right)_{t=0}^\infty$ 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, $C_t:G \to G$, maps each site $g \in G$ 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.
