Möhle Martin, Sagitov Serik
Eberhard Karls University of Tübingen, Mathematics Institute, 72076 Tübingen, Germany.
J Math Biol. 2003 Oct;47(4):337-52. doi: 10.1007/s00285-003-0218-6. Epub 2003 May 15.
A class of two-sex population models is considered with N females and equal number N of males constituting each generation. Reproduction is assumed to undergo three stages: 1) random mating, 2) exchangeable reproduction, 3) random sex assignment. Treating individuals as pairs of genes at a certain locus we introduce the diploid ancestral process (the past genealogical tree) for n such genes sampled in the current generation. Neither mutation nor selection are assumed. A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged. Conditions are specified when the limiting process (coalescent) is the Kingman coalescent and situations are discussed when the coalescent allows for multiple mergers of ancestral lines.
考虑一类两性种群模型，其中每一代由(N)名雌性和数量相等的(N)名雄性组成。假设繁殖经历三个阶段：1）随机交配，2）可交换繁殖，3）随机性别分配。将个体视为某一位点上的基因对，我们引入了当前一代中抽取的(n)个此类基因的二倍体祖先过程（过去的系谱树）。假设既没有突变也没有选择。证明了随着(N)趋于无穷而(n)保持不变时二倍体祖先过程的收敛准则。指定了极限过程（合并过程）为金曼合并过程的条件，并讨论了合并过程允许祖先线多重合并的情况。
