Allele Based Inference on Evolution and Extinction; A Genetic Drift Approach

Abstract

In other to present a series of stochastic models from population dynamics capable of describing rudimentary aspects of genetic evolution, we studied two-allele Wright–Fisher and the Moran models for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size “simplest form, selection, and random mutation”. Principal results were presented in qualitative terms, illustrated by Monte Carlo simulations from R and http://www.radford.edu/~rsheehy/Gen_flash/popgen. Moran and the Wright-Fisher Models exhibited the same fixation probabilities, only that the Moran model runs twice as fast as the Wright-Fisher Model. A clue that can help us to understand this result is provided by the variance in reproductive success in the two models. Genetic changes due to drift were neither directional nor predictable in any deterministic way. Nonetheless, genetic drift led to evolutionary change in the absence of mutation (P=0.5), natural selection or gene flow. In general, alleles drift to fixation is significantly faster in smaller populations. Probability of fixation of an allele A was approximately equivalent to the initial frequency of that allele. With the inclusion of selection in our model, probability of fixation of a favoured allele due to natural selection increased with increase in fitness advantage and population size. The time taken to reach fixation is much slower, in case of no selective advantage, than a fixation under mutation with selective advantage.