Crop Plant Biodiversity and Breeding Informatics Group (350b), Institute of Plant Breeding, Seed Science and Population Genetics, University of Hohenheim, Fruwirthstrasse 21, 70599, Stuttgart, Germany.
J Math Biol. 2020 Apr;80(5):1497-1521. doi: 10.1007/s00285-020-01470-5. Epub 2020 Feb 1.
Multiple-merger coalescents, e.g. [Formula: see text]-n-coalescents, have been proposed as models of the genealogy of n sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's n-coalescent. [Formula: see text]-n-coalescents can be seen as the limit process of the discrete genealogies of Cannings models with fixed population size, when time is rescaled and population size [Formula: see text]. As established for Kingman's n-coalescent, moderate population size fluctuations in the discrete population model should be reflected by a time-change of the limit coalescent. For [Formula: see text]-n-coalescents, this has been explicitly shown for only a limited subclass of [Formula: see text]-n-coalescents and exponentially growing populations. This article gives a more general construction of time-changed [Formula: see text]-n-coalescents as limits of specific Cannings models with rather arbitrary time changes.
多合并 coalescents，例如 [公式：见文本]-n-coalescents，已被提议作为 n 个抽样个体的系谱模型，用于一系列群体，其系谱结构不能很好地被 Kingman 的 n-coalescent 所捕捉。[公式：见文本]-n-coalescents 可以被看作是 Cannings 模型的离散系谱，当时间被重标度并且种群大小 [公式：见文本]时的极限过程。正如 Kingman 的 n-coalescent 所确立的那样，离散种群模型中的适度种群大小波动应该反映在极限合并中的时间变化。对于 [公式：见文本]-n-coalescents，这仅在有限的 [公式：见文本]-n-coalescents 和指数增长种群的子类中被明确显示。本文给出了一种更一般的时间变化 [公式：见文本]-n-coalescents 的构造，作为具有相当任意时间变化的特定 Cannings 模型的极限。
