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On the distribution of interspecies correlation for Markov models of character evolution on Yule trees

Authors
Journal
Journal of Theoretical Biology
0022-5193
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/j.jtbi.2014.09.016
Keywords
  • Infinite Sites
  • Mutation Model
  • Phylogenetics
  • Phylogenetic Informativeness
  • Yule Process
Disciplines
  • Design
  • Engineering
  • Logic
  • Mathematics

Abstract

Abstract Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule process, in which new species are “born” from existing lineages at a constant rate. Recent work has illuminated some of the structural properties of Yule trees, but it remains mostly unknown how these properties affect sequence and trait patterns observed at the tips of the phylogenetic tree. Understanding the interplay between speciation and mutation under simple models of evolution is essential for deriving valid phylogenetic inference methods and gives insight into the optimal design of phylogenetic studies. In this work, we derive the probability distribution of interspecies covariance under Brownian motion and Ornstein–Uhlenbeck models of phenotypic change on a Yule tree. We compute the probability distribution of the number of mutations shared between two randomly chosen taxa in a Yule tree under discrete Markov mutation models. Our results suggest summary measures of phylogenetic information content, illuminate the correlation between site patterns in sequences or traits of related organisms, and provide heuristics for experimental design and reconstruction of phylogenetic trees.

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