Robustness of the Phylogenetic Comparative Method

Eric Stone, NCSU Statistics and Bioinformatics

Comparative studies of contemporary species shed light on the adaptive
significance of phenotypic and genotypic variation through evidence that
two or more quantitative traits have coevolved.  The phylogenetic
comparative method seeks this evidence in the slope of a linear
regression, with the tree relating the species incorporated into the
covariance matrix of the error term.  In this work I resolve the
longstanding issue of how inaccuracies in the phylogenetic tree influence
subsequent regression estimates.  Motivated by the generalized
least-squares problem, I introduce a square root of the inverse covariance
matrix that is readily interpretable in terms of the phylogenetic tree.
Using this result, I show that small inaccuracies in the phylogeny
translate into scale factors on exactly one linear contrast of the data;
consequently, the impact of any such inaccuracy can be understood as an
instance of weighted least squares.  I will discuss the implications of
this work on future comparative studies, including the development of
robust statistical procedures.