The transformation of genomic data into functionally relevant information about the composition of biological systems hinges critically on the field of computational genome biology, at the core of which lies comparative genomics. The aim of comparative genomics is to extract meaningful functional information from the differences and similarities observed across genomes of different organisms. We develop and test a novel framework for applying complex models of nucleotide evolution to solve phylogenetic and comparative genomic problems, and demonstrate that these techniques are crucial for accurate comparative evolutionary inferences. Additionally, we conduct an exploratory study using vertebrate mitochondrial genomes as a model to identify the reciprocal influences that genome structure, nucleotide evolution, and multi-level molecular function may have on one another. Collectively this work represents a significant and novel contribution to accurately modeling and characterizing patterns of nucleotide evolution, a contribution that enables the enhanced detection of patterns of genealogical relationships, selection, and function in comparative genomic datasets. Our work with entire mitochondrial genomes highlights a coordinated evolutionary shift that simultaneously altered genome architecture, replication, nucleotide evolution and molecular function (of proteins, RNAs, and the genome itself). Current research in computational biology, including the advances included in this dissertation, continue to close the gap that impedes the transformation of genomic data into powerful tools for the analysis and understanding of biological systems function.

Central to the study of Life is knowledge both about the underlying relationships among living things and the processes that have molded them into their diverse forms. Phylogenetics provides a powerful toolkit for investigating both aspects. Bayesian phylogenetics has gained much popularity, due to its readily interpretable notion of probability. However, the posterior probability of a phylogeny, as well as any dependent biological inferences, is conditioned on the assumed model of evolution and its priors, necessitating care in model formulation. In Chapter 1, I outline the Bayesian perspective of phylogenetic inference and provide my view on its most outstanding questions. I then present results from three studies that aim to (i) improve the accuracy of Bayesian phylogenetic inference and (ii) assess when the model assumed in a Bayesian analysis is insufficient to produce an accurate phylogenetic estimate. As phylogenetic data sets increase in size, they must also accommodate a greater diversity of underlying evolutionary processes. Partitioned models represent one way of accounting for this heterogeneity. In Chapter 2, I describe a simulation study to investigate whether support for partitioning of empirical data sets represents a real signal of heterogeneity or whether it is merely a statistical artifact. The results suggest that empirical data are extremely heterogeneous. The incorporation of heterogeneity into inferential models is important for accurate phylogenetic inference. Bayesian phylogenetic estimates of branch lengths are often wildly unreasonable. However, branch lengths are important input for many other analyses. In Chapter 3, I study the occurrence of this phenomenon, identify the data sets most likely to be affected, demonstrate the causes of the bias, and suggest several solutions to avoid inaccurate inferences. Phylogeneticists rarely assess absolute fit between an assumed model of evolution and the data being analyzed. While an approach to assessing fit in a Bayesian framework has been proposed, it sometimes performs quite poorly in predicting a model’s phylogenetic utility. In Chapter 4, I propose and evaluate new test statistics for assessing phylogenetic model adequacy, which directly evaluate a model’s phylogenetic performance. / text