Theoretical foundation of the RelTime method for estimating divergence times from variable evolutionary rates

RelTime estimates divergence times by relaxing the assumption of a strict molecular clock in a phylogeny. It showed excellent performance in estimating divergence times for both simulated and empirical molecular sequence datasets in which evolutionary rates varied extensively throughout the tree. RelTime is computationally efficient and scales well with increasing size of datasets. Until now, however, RelTime has not had a formal mathematical foundation. Here, we show that the basis of the RelTime approach is a relative rate framework (RRF) that combines comparisons of evolutionary rates in sister lineages with the principle of minimum rate change between an evolutionary lineage and its descendants. We present analytical solutions for estimating relative lineage rates and divergence times under RRF. We also discuss the relationship of RRF with other approaches, including the Bayesian framework. We conclude that RelTime will be also useful for phylogenies with branch lengths derived not only from molecular data, but also morphological and biochemical traits.