Behavior and limitations of molecular and population-level models of evolution

Numerous models of molecular evolution have been developed over the years. Our knowledge of these models, while extensive in some aspects, is limited in others. Often models were developed independently of other models resulting in a lack of an understanding about how one model's parameters relate to the parameters in a different model. For example, some models work with codon sequences and others work with amino acid sequences. How the site-wise rates in an amino acid based model translate to the site-wise rates in a codon based model is unknown. It is also unclear how different parameters relate to the underlying evolutionary processes. For example, what physical quantities are measured by the site-wise rate of evolution is unclear. In Chapter 1, I introduce the concepts of modeling evolution and the principles of the inference of site-specific rates of evolution in a protein coding sequence. In Chapter 2, I determine the relationship between amino acid models and codon models of evolution. This relationship demonstrates how site-specific rates from a codon model relate to an amino acid model, and the deviations between the two estimates. This relationship also benchmarks empirical amino acid models against more mechanistic codon models. In Chapter 3, I establish how model choice affects maximum likelihood inference of site-specific rate of evolution. I analytically derive the site-wise rate under the assumptions of different substitution models. For the models where an analytically derived solution is not possible, I assess their effect on site-wise rates numerically. In Chapter 4, I demonstrate that when mutation can change epistatic interactions, small populations tend to evolve towards one of the two fixed points of epistasis. Our theory demonstrates that these points can be identified with mutation or drift robustness. Finally, in Chapter 5, I place these results in context, and I discuss future avenues to improve current models of evolution.Cellular and Molecular Biolog