A review on Monte Carlo simulation methods as they apply to mutation and selection as formulated in Wright-Fisher models of evolutionary genetics

Abstract

A case has made for the use of Monte Carlo simulation methods when the incorporation of mutation and natural selection into Wright-Fisher gametic sampling models renders then intractable from the standpoint of classical mathematical analysis. The paper has been organized around five themes. Among these themes was that of scientific openness and a clear documentation of the mathematics underlying the software so that the results of any Monte Carlo simulation experiment may be duplicated by any interested investigator in a programming language of his choice. A second theme was the disclosure of the random number generator used in the experiments to provide critical insights as to whether the generated uniform random variables met the criterion of independence satisfactorily. A third theme was that of a review of recent literature in genetics on attempts to find signatures of evolutionary processes such as natural selection, among the millions of segments of DNA in the human genome, that may help guide the search for new drugs to treat diseases. A fourth theme involved formalization of Wright-Fisher processes in a simple form that expedited the writing of software to run Monte Carlo simulation experiments. Also included in this theme was the reporting of several illustrative Monte Carlo simulation experiments for the cases of two and three alleles at some autosomal locus, in which attempts were to made to apply the theory of Wright-Fisher models to gain some understanding as to how evolutionary signatures may have developed in the human genome and those of other diploid species. A fifth theme was centered on recommendations that more demographic factors, such as non-constant population size, be included in future attempts to develop computer models dealing with signatures of evolutionary process in genomes of various species. A brief review of literature on the incorporation of demographic factors into genetic evolutionary models was also included to expedite and stimulate further development on this theme.