Frontiers in Coalescent Theory: Pedigrees, Identity-by-Descent, and Sequentially Markov Coalescent Models

Abstract

The coalescent is a stochastic process that describes the genetic ancestry ofindividuals sampled from a population. It is one of the main tools of theoretical population genetics and has been used as the basis of many sophisticated methods of inferring the demographic history of a population from a genetic sample. This dissertation is presented in four chapters, each developing coalescent theory to some degree. In the first chapter, I investigate how patterns of coalescence are affected by the population pedigree in structured populations, showing that the pedigree has longer-term effects in structured populations than in unstructured populations. Based on my findings, I develop a conceptual framework for jointly inferring population sizes, migration rates, and the recent pedigree of sampled individuals, and I demonstrate the efficacy of this approach in an application to simulated data. In Chapter 2, I present a theoretical study of the distribution of segments of identity-by-descent, showing how the accuracy of predictions made based on sequentially Markov coalescent models depends on the particular model being used as the basis of calculations. In the third chapter, I undertake a theoretical comparison of two approximations, termed the SMC and SMC', to the full model of coalescence with recombination. I derive new theoretical properties of the SMC' and use these properties to demonstrate that the SMC' is, in a well-defined sense, the most appropriate first-order approximation to the full coalescent with recombination. I also show that estimates of population size based on the SMC are statistically inconsistent. Finally, in Chapter 4, I develop a coalescent hidden Markov model approach to inferring the demographic and reproductive history of a triploid asexual lineage derived from a diploid sexual ancestor. The motivation for this project is an ongoing collaborative effort to sequence and analyze the genomes of sexual and asexual lineages of the New Zealand snail Potamopyrgus antipodarum. The method I present in this chapter will be applied to these genomes to infer when triploid asexual lineages were derived from sexual ancestors and to describe the demographic history of those sexual ancestors. Here, I investigate the this method with simulated asexual genomes.