| Rates of molecular evolution at some protein encoding loci are more irregular 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 dispersion, R(T) > 1. Assuming an infinite sites, no recombination model of the gene, and a haploid, Moran population structure, R( T) is derived, in chapter two, for a general stationary model of molecular evolution. R(T) is shown to be affected by fluctuations in parameters only when they occur on a very slow time scale. In order for parameter fluctuations to cause R( T) to deviate significantly from one, the time between parameter changes must be roughly as large, or larger, than the time between substitutions.; Taking a broader look at the theoretical results of chapter two, and aided by computer simulations, chapter three argues that R( T) is affected by only three things: fluctuations that occur on a very slow time scale, advantageous or deleterious mutations, and interactions between mutations. In the absence of interactions, advantageous mutations are shown to lower R(T); deleterious mutations are shown to raise it. Previously described models for the overdispersed molecular clock are analyzed 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 values of R(T). Our current best estimates of R(T) suggest that either most mutations are deleterious, or some key population parameter changes on a very slow time scale. Chapter four examines one particular proposed explanation of the overdispersed clock, one which lacks both slow fluctuations and deleterious sites, and shows that this explanation is incapable of explaining the overdispersed clock.; Chapter five examines the consequences an overdispersed clock as on the ability to estimate divergence dates. In this chapter, a method is developed to estimate divergence times using loci that may be overdispersed. The approach is to replace the traditional Poisson process assumption with a more general stationary process assumption. A maximum likelihood model is developed, and a computer program is written to estimate divergence times. In simulation, it is shown that confidence intervals estimated under the traditional Poisson assumptions often vastly underestimate the true confidence limits for overdispersed loci. The method is applied to two data sets, one from land plants, the other from the higher metazoans. Maximum likelihood analysis of the metazoan data set suggests their radiation occurred well over a billion years ago, but confidence intervals are extremely wide. Moreover, it is 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, in absolute terms, fits the data well. It is argued that without an a priori understanding of the variance in the time between substitutions, molecular data sets may be incapable of ever establishing the age of the metazoan radiation. |
