On joint subtree distributions under two evolutionary models

详细信息    查看全文

• 作者：Taoyang Wu^a ; ^{taoyang.wu@uea.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; ^{taoyang.wu@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Kwok Pui Choi^b ; ^c ; ^{stackp@nus.edu.sg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Phylogenetic tree ; Subtree distribution ; Yule&ndash ; Harding&ndash ; Kingman model ; PDA model ; Tree indices ; Joint distribution
• 刊名：Theoretical Population Biology
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：108
• 期：Complete
• 页码：13-23
• 全文大小：676 K

文摘

In population and evolutionary biology, hypotheses about micro-evolutionary and macro-evolutionary processes are commonly tested by comparing the shape indices of empirical evolutionary trees with those predicted by neutral models. A key ingredient in this approach is the ability to compute and quantify distributions of various tree shape indices under random models of interest. As a step to meet this challenge, in this paper we investigate the joint distribution of cherries and pitchforks (that is, subtrees with two and three leaves) under two widely used null models: the Yule–Harding–Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model. Based on two novel recursive formulae, we propose a dynamic approach to numerically compute the exact joint distribution (and hence the marginal distributions) for trees of any size. We also obtained insights into the statistical properties of trees generated under these two models, including a constant correlation between the cherry and the pitchfork distributions under the YHK model, and the log-concavity and unimodality of the cherry distributions under both models. In addition, we show that there exists a unique change point for the cherry distributions between these two models.