Quantitative genetics and evolutionary inference in a phylogenetic context

Quantitative genetic theories for phenotypic evolution have received considerable attention in recent years. In this thesis, I examine the evolution of the central quantitative genetic parameter, the additive genetic variance-covariance matrix (G matrix), as well as the influence of G on the macroevolutionary pattern of phenotypic divergence among populations and species. In Chapters 1 and 2, I use empirical study and numerical simulations to examine the roles played by selection, correlated mutation, and genetic drift on the evolution of G. I find evidence that non-linear selection can influence the evolution of G in a natural population of Caribbean Anolis lizards (Chapter 1). Using numerical simulations (Chapter 2), I also show that the G matrix can be stable over a wider range of conditions than demonstrated in earlier studies, but I also identify factors that can induce substantial instability in G. In Chapters 3--6 I develop and apply new methods for the analysis of phenotypic diversification in the context of phylogenetic trees. I use these methods to explicitly test quantitative genetic predictions for morphological evolution. I empirically demonstrate that G has influenced the pattern of evolutionary differentiation among populations of a Caribbean lizard (Chapter 3). I then use computer simulations (Chapter 4) to show that phylogenetic methods outperform non-phylogenetic methods in identifying this type of pattern. Finally, I develop new likelihood methods (Chapters 5 and 6) to explicitly test quantitative genetic hypothesis in the context of phylogenetic trees, and show that these methods have high power and desirable error levels. Overall, in this work I explore the evolution of genetic constraint in the form of the G matrix over microevolutionary timescales to thousands of generations. I then examine the influence of G on the phenotypic divergence of populations and species. Across hierarchical levels this thesis unites microevolutionary processes operating on the evolution of G with macroevolutionary patterns in the differentiation of species.