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The accuracy and precision of species divergence date estimation from molecular data strongly depend on the models describing the variation of substitution rates along a phylogeny. These models generally assume that rates randomly fluctuate along branches from one node to the next. However, for mathematical convenience, the stochasticity of such a process is ignored when translating these rate trajectories into branch lengths. This study addresses this shortcoming. A new approach is described that explicitly considers the average substitution rates along branches as random quantities, resulting in a more realistic description of the variations of evolutionary rates along lineages. The proposed method provides more precise estimates of the rate autocorrelation parameter as well as divergence times. Also, simulation results indicate that ignoring the stochastic variation of rates along edges can lead to significant overestimation of specific node ages. Altogether, the new approach introduced in this study is a step forward to designing biologically relevant models of rate evolution that are well suited to data sets with dense taxon sampling which are likely to present rate autocorrelation. The computer programme PhyTime, part of the PhyML package and implementing the new approach, is available from http://code.google.com/p/phyml (last accessed 1 August 2012).

From Trajectories to Averages: An Improved Description of the Heterogeneity of Substitution Rates Along Lineages