Genes and environments: The evolution of phenotypic plasticity and epistasis

Traits never arise from single genes acting in isolation. Interactions among genes in a genome and between the genome and the environment are ubiquitous and play important roles in evolution. Only recently have theoretical biologists found the computational, tools to integrate such complex interactions into evolutionary models. Through four independent mathematical studies, this thesis explores the evolution of sensitivity to the environment, or phenotypic plasticity, and the evolution of intra-genomic interactions, or epistasis.;The first project considers the maintenance of phenotypic plasticity in a temporally heterogeneous environment. This model permits a quantitative dissection of population dynamics surrounding environmental transitions, and predicts an intuitive relationship between the rate of environmental stochasticity and the extent of phenotypic plasticity in a population. The second project uses a similar mathematical framework to argue that the evolvability of a population will depend on the extent of plasticity, the fitness costs of plasticity and the ruggedness of the map from phenotype to fitness.;A semi-empirical model of RNA secondary structure illuminates the relationship between environmental robustness, mutational robustness and modular organization. Computational evolution of RNA suggests that natural selection for thermodynamic stability of structures entails two surprising side effects: a loss of evolvability through increased mutational buffering and the origin of modular structure.;The last project offers a statistical model of interactions among amino acids in a single protein. Using two genetic algorithms, one to create fitness functions that approximate natural patterns of epistasis and a second to simulate the DNA shuffling protocol used by protein engineers, this work explores the effects of high rates of recombination and artificial selection regimes on the evolutionary search for novel function.