Genetic polymorphism in an evolving population

Abstract

We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping diversity in the gene pool under abrupt environmental changes. The model provides reasonable estimates for the proportions of polymorphic and heterozygous loci and for the mutation rate, as observed in nature.PACS numbers: 87.10.+e, 02.70.Lq In the biological evolution process, it is known that the population remains polymorphic, consisting of two or more genotypes: Genetic variation thus persists [1,2]. Balanced polymorphism stands for that the population consists of two or more genotypes with the rate of the most frequent allele less than 95%. The proportion of polymorphic loci, measured by electrophoresis at allozyme loci in animal and plants, takes the values in the range between 0.145 and 0.587 [3,4]. Provided that one allele replicates faster than others, it increases in frequency at the expense of the others. It may completely replace other alleles, and make the population monomorphic, consisting of one genotype only. Often, however, the allele does not completely replace others but remain at a stable intermediate frequency, leaving the population polymorphic, although in nature the superficial similarity conceals the diversity of genotypes occurring among individuals within species. This is of importance in the light of the fact that the superiority of an allele holds only in certain environments, or at certain gene frequencies, or in conjunction with certain other alleles. In biology, how to maintain polymorphism is described in a phenomenological manner by introducing such assumptions as the balance of selection and recurrent mutation, selection balanced by gene flow, heterozygous advantage selection, frequency-dependent selection, and variable selection in time or space [1].Recently, a number of models for evolving population, including geographic speciation and conditions for adaptation of population, have been developed through the method of statistical mechanics [5,6]. In particular, Mróz et al. have introduced an interesting population model in which individuals are represented by their genotypes and phenotypes while the environment characterizes the ideal phenotype [6]. In this model, a random population must have the initial adaptation greater than a certain critical value in order to grow in an environment which does not change with time. In this paper, we attempt to describe genetic polymorphism, especially under the environmental change, by means of a population model which exhibits genetic polymorphism within itself. It is shown that the population which displays genetically polymorphic behavior is indeed advantageous for survival in the changing environment.We consider a population consisting of M individuals, each characterized by its sequence of genes with the size of the sequence given by N . Each gene is assumed to take two possible forms, i.e., there are...

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