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

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance in living organisms. It has a long history of developing progressively more sophisticated stochastic models of evolution. Through a probabilist’s lens, this can be seen as a search for more appropriate ways to parameterize discrete state continuous time Markov chains to better encode biological reality, matching the historical processes that created empirical data sets, and creating useful tools that allow biologists to test specific hypotheses about the evolution of the organisms or the genes that interest them. This dissertation is an attempt to fill some of the gaps that persist in the literature, solving what we see as existing open problems. The overarching theme of this work is how to better model variation in the action of natural selection at multiple levels: across genes, between sites, and over time. Through four published journal articles and a fifth in preparation, we present amino acid and codon models that improve upon existing approaches, providing better descriptions of the process of natural selection and better tools to detect adaptive evolution. / AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer. Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer kan hierdie proses gesien word as ’n soektog na meer gepasde metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse met betrekking tot die evolusie van belanghebbende organismes of gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings wat in die literatuur bestaan in te vul en bestaande oop probleme op te los. Die oorkoepelende tema is verbeterde modellering van variasie in die werking van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter metodes om gevalle van aanpassing in evolusie te vind.