The inference of stepwise changes in substitution rates using serial sequence samples

It is frequently true that molecular sequences do not evolve in a strictly clocklike manner. Instead, substitution rate may vary for a number of reasons, including changes in selection pressure and effective population size, as well as changes in mean generation time. Here we present two new methods for estimating stepwise changes in substitution rates when serially sampled molecular sequences are available. These methods are based on multiple rates with dated tips (MRDT) models and allow different rates to be estimated for different intervals of time. These intervals may correspond to the sampling intervals or to a priori-defined intervals that are not coincident with the times the serial samples are obtained. Two methods for obtaining estimates of multiple rates are described. The first is an extension of the phylogeny-based maximum-likelihood estimation procedure introduced by Rambaut. The second is a new parameterization of the pairwise distance least-squares procedure used by Drummond and Rodrigo. The utility of these methods is demonstrated on a genealogy of HIV sequences obtained at five different sampling times from a single patient over a period of 34 months.