Interspecies correlation for neutrally evolving traits

Details Interspecies correlation for neutrally evolving traits Interspecies correlation for neutrally evolving traits

2012-01-25

arxiv.org/abs/1201.5364v2

Biology

Quantitative Biology

Populations and Evolution

19 pages, 5 figures

Scientific paper

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.

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