A NONPARAMETRIC APPROACH TO ESTIMATING DIVERGENCE TIMES IN THE ABSENCE OF RATE CONSTANCY

A new method for estimating divergence times when evolutionary rates a re variable across lineages is proposed. The method, called nonparamet ric rate smoothing (NPRS), relies on minimization of ancestor-descenda nt local rate changes and is motivated by the likelihood that evolutio nary rates are autocorrelated in time. Fossil information pertaining t o minimum and/or maximum ages of nodes in a phylogeny is incorporated into the algorithms by constrained optimization techniques. The accura cy of NPRS was examined by comparison to a clock-based maximum-likelih ood method in computer simulations. NPRS provides more accurate estima tes of divergence times when (1) sequence lengths are sufficiently lon g, (2) rates are truly nonclocklike, and (3) rates are moderately to h ighly autocorrelated in time. The algorithms were applied to estimate divergence times in seed plants based on data from the chloroplast rbc L gene. Both constrained and unconstrained NPRS methods tended to prod uce divergence time estimates more consistent with paleobotanical evid ence than did clock-based estimates.