THE DISTRIBUTIONS UNDER TWO SPECIES-TREE MODELS OF THE NUMBER OF ROOT ANCESTRAL CONFIGURATIONS FOR MATCHING GENE TREES AND SPECIES TREES
成果类型：
Article
署名作者：
Disanto, Filippo; Fuchs, Michael; Paningbatan, Ariel R.; Rosenberg, Noah A.
署名单位：
University of Pisa; National Chengchi University; University of the Philippines System; University of the Philippines Diliman; Stanford University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/22-AAP1791
发表日期：
2022
页码：
4426-4458
关键词：
binary search-trees
coalescent histories
probability
enumeration
parameters
inference
variance
cherries
摘要：
For a pair consisting of a gene tree and a species tree, the ancestral con-figurations at a species-tree internal node are the distinct sets of gene lin-eages that can be present at that node. The enumeration of root ancestral configurations-ancestral configurations at the species-tree root-assists in describing the complexity of gene-tree probability calculations in evolution-ary biology. Assuming that the gene tree and species tree match in topology, we study the distribution of the number of root ancestral configurations of a random labeled tree topology under the uniform and Yule-Harding models. We employ analytic combinatorics, considering ancestral configurations in the context of additive tree parameters and using singularity analysis to eval-uate asymptotic growth of the coefficients of generating functions. For both models, we obtain asymptotic lognormal distributions for the number of root ancestral configurations. For Yule-Harding random trees, we also obtain the asymptotic mean (-1.425n) and variance (-2.045n) of the number of root ancestral configurations, paralleling previous results for the uniform model (mean (4/3)n, variance -1.822n). A methodological innovation is that to ob-tain the Yule-Harding asymptotic variance, singularity analysis is conducted from the Riccati differential equation that the generating function satisfies- without possessing the generating function itself.