Evolutionary analyses rely on assumptions about the process of molecular evolution as well as the performance of the statistical methods. The rapid increase in DNA sequence data necessitates statistical methods that can accurately infer the evolutionary history of the sequences. However, it is often unclear how assumptions about the process of molecular evolution and the performance of the statistical methods affect evolutionary inferences.; Chapter one uses simulated four-taxon datasets to examine how the model of evolution affects maximum likelihood phylogenetic analyses. This study simulates datasets across a wide variety of tree shapes to determine how assumptions about the model of evolution affect the accuracy of phylogenetic inferences. Though parameter-rich, realistic models generally perform well in larger datasets, in small datasets, simpler models, especially models that do not incorporate rate variation among sites, occasionally infer the correct tree more often than a realistic of evolution. However, it is almost always beneficial to incorporate variation in the pattern of substitutions. The Goldman Yang Γ codon model generally performed as well as any simpler models, further indicating the importance of incorporating variation in the pattern of evolution into the likelihood model.; Chapter two uses simulations to examine the statistical properties of Bayesian phylogenetic methods. Bayesian analyses incorporate assumptions about the prior probability of the phylogenetic tree and its likelihood to calculate the posterior probability of the tree. The study first examines the effect of the prior probability of a tree on its posterior probability, finding that the effect of the prior is large in small datasets but is minimal in datasets over 500 bp. The second section finds that the model of evolution can strongly affect the posterior probability, and its effect can vary depending on the size of the dataset. Finally, the last section explores the relationship between likelihood nonparametric bootstrap values and the Bayesian posterior probability. The study emphasizes that a Bayesian approach provides an interpretable measure of phylogenetic uncertainty with less computational effort than maximum likelihood.; The last chapter surveys the evolutionary processes of four nuclear and four chloroplast loci within the grasses. It first finds that relatively simple nucleotide models of molecular evolution often fit the data as well as more complex models. Most of the eight loci also reject the molecular clock, though pairwise relative rate tests often detect little significant rate variation among lineages. There is little evidence of any change in selective pressure or locus-specific selection and no evidence of positive selection within the loci. Genome or lineage-specific factors appear to influence the patterns of at least synonymous rate variation in most loci.
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