Interspecies correlation for neutrally evolving traits

TL;DR

This paper derives formulas for interspecies trait correlations and statistical measures of trait data under a model of neutral evolution, incorporating phylogenetic uncertainty via conditioned branching processes.

Contribution

It introduces a novel approach to quantify interspecies trait correlations considering phylogenetic uncertainty with explicit formulas.

Findings

Derived formulas for variance of sample mean and mean of sample variance.

Quantified interspecies correlation coefficient accounting for phylogenetic uncertainty.

Modeled phylogenetic tree uncertainty using conditioned branching processes.

Abstract

A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned on the number, n, of extant species) we study the random vector (X_1,...,X_n) of the observed trait values. In this paper we derive compact formulae for the variance of the sample mean and the mean of the sample variance for the vector (X_1,...,X_n). The key ingredient of these formulae is the correlation coefficient between two trait values randomly chosen from (X_1,...,X_n). This interspecies correlation coefficient takes into account not only variation due to the random sampling of two species out of n and the stochastic nature of Brownian motion but also the uncertainty in the phylogenetic tree. The latter is modeled by a (supercritical or critical) conditioned branching process. In the critical case we modify the Aldous-Popovic model by assuming a proper prior for the time of origin.