Algorithms for Genetics: Basics of Wright Fisher Model and Coalescent Theory

The Wright Fisher model of evolution attempts to simulate genetic drift wherein each individual in a generation produces an infinite and equal amount of gametes. The subsequent generation is a random draw of 2N gametes from this pool. In other words, the gene frequency in the next generation is composed of 2N draws from the gene frequency of the current generation. Mutations are randomly dropped into the gamete pool in the Wright Fisher model at a rate of mutations per individual per generation. The transition probability, which is the probability of a population drifting from a state having i copies to having j copies of a particular allele, can be obtained by the following expression.