Understanding the overdispersed molecular clock

Rates of molecular evolution at some protein-encoding loci are more irregul ar than expected under a simple neutral model of molecular evolution. This pattern of excessive irregularity in protein substitutions is often called the "overdispersed molecular clock" and is characterized by an index of dis persion, R(T) > 1. Assuming infinite sites, no recombination model of the g ene R(T) is given for a general stationary model of molecular evolution. R( T) is shown to be affected by only three things: fluctuations that occur on a very slow rime scale, advantageous or deleterious mutations, and interac tions between mutations. In the absence of interactions, advantageous mutat ions are shown to lower R(T); deleterious mutations are shown to raise it. Previously described models for the: overdispersed molecular clock are anal yzed in terms of this work as are a few very simple new models. A model of deleterious mutations is shown to be sufficient to explain the observed val ues of R(T). Our current brst estimates of R(T) suggest that either most mu tations are deleterious or some key population parameter changes on a very slow time scale. No other interpretations seem plausible. Finally, a commen t is made on how R(T) might be used to distinguish selective sweeps from ba ckground selection.