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Efforts to reconstruct phylogenetic trees and understand evolutionaryprocesses depend fundamentally on stochastic models of speciation and mutation.The simplest continuous-time model for speciation in phylogenetic trees is theYule process, in which new species are "born" from existing lineages at aconstant rate. Recent work has illuminated some of the structural properties ofYule trees, but it remains mostly unknown how these properties affect sequenceand trait patterns observed at the tips of the phylogenetic tree. Understandingthe interplay between speciation and mutation under simple models of evolutionis essential for deriving valid phylogenetic inference methods and givesinsight into the optimal design of phylogenetic studies. In this work, wederive the probability distribution of interspecies covariance under Brownianmotion and Ornstein-Uhlenbeck models of phenotypic change on a Yule tree. Wecompute the probability distribution of the number of mutations shared betweentwo 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 ofrelated organisms, and provide heuristics for experimental design andreconstruction of phylogenetic trees.

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