Fredrik Olsson: Inbreeding, Effective Population Sizes and Genetic Differentiation - A Mathematical Analysis of Structured Populations

This thesis consists of four papers on various aspects of inbreeding, effective population sizes and genetic differentiation in structured populations, that is, populations that consist of a number of subpopulations. Three of the papers concern age structured populations, where in the first paper we concentrate on calculating the variance effective population size \((N_{eV})\) and how \(N_{eV}\) depends on the time between measurements and the weighting scheme of age classes. In the third paper we develop an estimation procedure of \(N_{eV}\)which uses age specific demographic parameters to obtain approximately unbiased estimates. A simulation method for age structured populations is presented in the fourth paper. It is applicable to models with multiallelic loci in linkage equilibrium.

In the second paper, we develop a framework for analysis of effective population sizes and genetic differentiation in geographically subdivided populations with a general migration scheme. Predictions of gene identities and gene diversities of the population are presented, which are used to find expressions for effective population sizes \((N_e)\) and the coefficient of gene differentiation \((G_{ST})\). We argue that not only the asymptotic values of \(N_e\) and \(G_{ST}\) are important, but also their temporal dynamic patterns.

The models presented in this thesis are important for understanding how different age decomposition, migration and reproduction scenarios of a structured population affect quantities, such as various types of effective sizes and genetic differentiation between subpopulations.