Richard A. Neher
bioRxiv -- won't submit, vol. , 408005, 2018
Shared ancestry among individuals results in correlated traits and these dependencies need to be accounted for in probabilistic inference. In strictly asexual populations, the covariances have a particularly simple block-like structure imposed by the phylogenetic tree. Ho and Ane showed how this block-like structure can be exploited to efficiently invert covariance matrices and fit linear models on trees in linear time. In this short note, I use these methods to estimate evolutionary rates and to find the root of the tree that optimizes the time-divergence relationship. The algorithm is implemented in TreeTime and can be used to estimate evolutionary rates and their confidence intervals with computational cost scaling linearly in the number of tips.