A heuristic rate smoothing procedure for maximum likelihood estimation of species divergence times

Estimation of species divergence times is well2known to be sensitive to violation of the molecular clock assump2 tion (rate constancy over time) . However , the molecular clock is almost always violated in comparisons of distantly related species , such as different orders of mammals. Thus it is important to take into account different rates among lineages when divergence times are estimated. The maximum likelihood method provides a framework for accommodating rate variation and can naturally accommodate heterogeneous datasets from multiple loci and fossil calibrations at multiple nodes. Previous implementations of the likelihood method require the researcher to assign branches to different rate classes. In this paper , I implement a heuristic rate2smoothing algorithm ( the AHRS algorithm) to automate the assignment of branches to rate groups. The method combines features of previous likelihood , Bayesian and rate2smoothing methods. The likelihood algorithm is also improved to accommodate missing sequences at some loci in the combined analysis. The new al2 gorithms are applied to estimate the divergence times of Malagasy mouse lemurs using a dataset of mammalian mitochon2 drial genes and compared with previous likelihood and Bayesian Markov chain Monte Carlo analyses [ Acta Zoologica S ini2 ca 50 (4) : 645 656 , 2004 ] .