Sharif Digital Repository

This thesis is concentrated on some subjects on population genetics. In the rst part we give formulae including the expectation and variance of the height and the length of the ancestral recombination graph (ARG) and the expectation and variance of the number of recombination events and we show that the expectation of the length of the ARG is a linear combination of the expectation of the length of Kingman's coalescent and the expectation of the height of the ARG. Also we show give a relation between the expectation of the ARG and the expectation of the number of recombination events. At the end of this part we show that the ARG comes down from innity in the sense that we can dene it with X0... 

Population genetics studies the distribution and changes in allele frequencies under the influence of five main evolutionary processes: natural selection, genetic drift, mutation, gene flow, and recombination. Among these, the recombination process can influence a wide range of biological processes by rearranging genes, repairing DNA structure, and participating actively in cell division mechanisms. Recombination has the ability to create genetic diversity through gene rearrangement, which is the main reason for creating diversity and evolution in organisms. Models such as Hill-Robertson have proven the influential role of recombination in accelerating evolutionary mechanisms. Also,...