| Genetic systems under balancing selection maintain their polymorphism for long periods of time, and are therefore may be useful for inferring long-term evolutionary histories. However, many histories of interest, such as population structure or changing demographic and selective conditions, violate assumptions of existing theory of balancing selection, making inference difficult within the framework of that theory. Some aspects of data from natural populations, such as a surprisingly strong signal for population structure, and a consistent skew in the shape of reconstructed genealogies, suggest explanations based on these violations of model assumptions. These explanations, however, have been intuitive arguments, without a mathematical foundation. This problem is addressed here by the development of flexible models of balancing selection that incorporate deviations from ideal population assumptions. First, I examine the effect of population structure by developing a model of symmetric balancing selection in a finite island population. I next consider the effects of relaxing the assumption of fitness symmetry among alleles.; A Markov chain approach is used to model the dynamics of alleles under balancing selection, assuming a strong selection, weak mutation (SSWM) model. The rates of gain and loss of alleles are derived and used as the transition rates of the chain with the number of alleles in the population as the state. Next, the Markov chain is extended to more complex demographic and selective models. In the structured population model of Chapter 2, analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared among demes are derived, and checked against simulation results. Using the result that allocation of alleles among demes is independent of the strength and mode of balancing selection, I analyze data from MHC genes in a subdivided population of chinook salmon. Chapter 3 develops a model of asymmetric balancing selection, in which alleles are grouped into different lineages. The transition rates for the Markov chain are used to efficiently generate allelic genealogies. Equilibrium genealogical shape is found to be highly resistant to deviations from a strictly symmetric selection model. Non-equilibrium populations are then studied by introducing time-dependent changes in population size. |
