Stochastic modeling of multi-locus recombination in Mendelian populations

Abstract

Several mathematical models have been developed to describe the genetic structure of populations. Most of these models focus on only one, or few genetic loci. This thesis focuses on the models, which describe the dynamics of populations with respect to a large number of loci simultaneously. Such models are appropriate for recent large-scale studies of single nucleotide polymorphisms (SNPs). A random set representation of haplotypes in the population under study is proposed and the recursion equation for change of haplotype distributions in discrete time model is derived. A continuous time model for change of haplotype distributions is discussed and the solution to the differential equation describing change of probability measure is derived using the concept of blocks identical by descent (BID). The behavior of the solution is studied and a graph theoretical interpretation of the solution is investigated.