A simple genealogical structure of strongly balanced allelic lines and trans-species evolution of polymorphism.

Abstract

Different alleles undergoing strong symmetric balancing selection show a simple genealogical structure (allelic genealogy), similar to the gene genealogy described by the coalescence process for a sample of neutral genes randomly drawn from a panmictic population at equilibrium. The only difference between the two genealogies lies in the different time scales. An approximate scaling factor for allelic genealogy relative to that of neutral gene genealogy is {fV/(2M)} [In{S/(16frM2)}13 2, where M = Nu and S = 2Ns (N, effective population size; u, mutation rate to selected alleles per locus per generation; s, selection coefficient). The larger the value of \/S/M (.100), the larger the scaling factor. These rindings, supported by simulation results, allow one to apply the theoretical results of the coalescence process directly to the allelic genealogy. Combined with the trans-species evolution of the major histocompatibility complex polymorphism for which balancing selection is believed to be responsible, allelic genealogy predicts that the number of breeding individuals in the human population could not be as small as 50-100 at any time of its evolutionary history. The analysis appears to contradict the founder principle as being important in recent mammalian evolution. It differs from the genealogy described by the linesof-descent process (5) in which coalescences of genes occurring within each line and the age of each line are the main interest, but the allelic genealogy are not taken into account. GeneAlthough allelic genealogy was developed to examine quantitatively the extraordinary polymorphism of the major histocompatibility complex (MHC) molecules (6-10), the study was largely based on computer simulation (4). In this paper, I show that there exists a simple mathematical structure of allelic genealogy under strong symmetric balancing selection and use this theory to discuss the evolutionary implication of transspecies mode of MHC polymorphisms (7).By balancing selection (one of the most efficient mechanisms to maintain polymorphism), I mean a collection of different selection schemes, all of which lead to the mean gene-frequency change given below. It has been shown that for this equation of the gene-frequency change, there can exist two fundamentally different selection models (4). In fact for any allele-frequency equation there are many alternative fitness models (11). This is unfortunate for the study of population genetics because simply observing a genefrequency change cannot identify the underlying mechanism. However, this is not the concern here (see ref. 4).Under balancing selection, alleles (allelic lines) can persist for a much longer time than neutral alleles, even in a relatively small population (12,13). Those selected alleles may therefore differ from each other by more than one nucleotide change. When new alleles are produced each with an initial frequency of 1/(2N), where N is the effective population size, they differ from their parental ones by single changes. If new alleles happen...

A population genetics study of the Familial Mediterranean Fever gene: evidence of balancing selection under an overdominance regime

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