Rosenberg Noah A, Degnan James H
Department of Human Genetics, University of Michigan, Ann Arbor, MI 48109, United States.
Theor Popul Biol. 2010 May;77(3):145-51. doi: 10.1016/j.tpb.2009.12.004. Epub 2010 Jan 11.
Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n>or=7, there exist a species tree topology S and a gene tree topology G not equalS, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees.
给定一个基因树和一个物种树，一个溯祖历史是物种树的分支列表，基因树中的合并事件发生在这些分支上。由一个基因树拓扑结构和一个物种树拓扑结构组成的每一对都有一定数量的可能的溯祖历史。在这里我们表明，对于每个(n\geq7)，存在一个具有(n)个叶子的物种树拓扑结构(S)和一个与(S)不同的基因树拓扑结构(G)，当物种树拓扑结构是(S)且基因树拓扑结构也是(S)时，对于这两者，溯祖历史的数量超过了相应的溯祖历史数量。这个结果可以解释为，与物种树拓扑结构(S)不一致的基因树拓扑结构(G)，比与物种树拓扑结构匹配的基因树拓扑结构，能够通过进化过程以更多方式产生，这进一步深入了解了基因树与物种树联合考虑时出现的令人惊讶的组合特性。
