Simulating the Emergence of Mutations and Their Subsequent Evolution in an Age-Structured Stochastic Self-Regulating Process with Two Sexes

The stochastic process under consideration is intended to be not only partof the working paradigm of evolutionary and population genetics but also thatof applied probability and stochastic processes with an emphasis on computerintensive methods. In particular, the process is an age-structured self-regulatingmultitype branching process with a genetic component consisting of an autosomallocus with two alleles for females and males. It is within this simple contextthat mutation will be quantified in terms of probabilities that a given allele mutatesto the other per meiosis. But, unlike many models that are currentlybeing used in mathematical population genetics, in which natural selection isoften characterized in terms of parameters called fitness by genotype or phenotype,in this paper the parameterization of submodules of the model providesa framework for characterizing natural selection in terms of some of its components. One of these modules consists of reproductive success that is quantifiedin terms of the total expected number of offspring a female contributes to thepopulation throughout her fertile years. Another component consists of survivalprobabilities that characterize an individual’s ability to compete for limited environmentalresources. A third module consists of a parametric function thatexpresses the probabilities of survival in a birth cohort of individuals by age forboth females and males. A forth module of the model as an acceptance matrixof conditional probabilities such female may show a preference for the genotypeor phenotype as her male sexual partner. It is assumed that any force of naturalselection acts at the level of the three genotypes under consideration foreach sex. By assigning values of the parameters in each of the modules underconsideration, it is possible to conduct Monte Carlo simulation experiments designedto study the effects of each component of selection separately or in anycombination on a population evolving from a given initial population over somespecified period of time