Estimating divergence times in the presence of an overdispersed molecular clock

Molecular loci that fail relative-rate tests are said to be "overdispersed. " Traditional molecular-clock approaches to estimating divergence times do not take this into account. In this study, a method was developed to estima te divergence times using loci that may be overdispersed. The approach was to replace the traditional Poisson process assumption with a more general s tationary process assumption. A probability model was developed, and an acc ompanying computer program was written to find maximum-likelihood estimates of divergence times under both the Poisson process and the stationary proc ess assumptions. In simulation, it was shown that confidence intervals unde r the traditional Poisson assumptions often vastly underestimate the true c onfidence limits for overdispersed loci. Both models were applied to two da ta sets: one from land plants, the other from the higher metazoans. In both cases, the traditional Poisson process model could be rejected with high c onfidence. Maximum-likelihood analysis of the metazoan data set under the m ore general stationary process suggested that their radiation occurred well over a billion years ago, but confidence intervals were extremely wide. It was also shown that a model consistent with a Cambrian (or nearly Cambrian ) origination of the animal phyla, although significantly less likely than a much older divergence, fined the data well. It is argued that without an a priori understanding of the variance in the time between substitutions, m olecular data sets may be incapable of ever establishing the age of the met azoan radiation.