Random fluctuation of selection coefficients and the extent of nucleotide variation in human populations

Abstract

It is well known that the selection coefficient of a mutant allele varies from generation to generation, and the effect of this factor on genetic variation has been studied by many theoreticians. However, no consensus has been reached. One group of investigators believes that fluctuating selection has an effect of enhancing genetic variation, whereas the other group contends that it has a diversity-reducing effect. In recent years, it has become possible to study this problem by using single nucleotide polymorphisms (SNPs) as well as exome sequence data. In this article we present the theoretical distributions of mutant nucleotide frequencies for the two models of fluctuating selection and then compare the distributions with the empirical distributions obtained from SNP and exome sequence data in human populations. Interestingly, both SNP and exome sequence data showed that the neutral mutation model fits the empirical distribution quite well. Furthermore, the mathematical models with diversity-enhancing and diversity-reducing effects also fit the empirical distribution reasonably well. This result implies that there is no need of distinguishing between the diversity-enhancing and diversity-reducing models of fluctuating selection and the nucleotide polymorphism in human populations can be explained largely by neutral mutations when long-term evolution is considered.

Keywords: allele frequency distribution; fluctuating selection coefficient; heterozygosity.

Fig. 1.

Theoretical distributions (spectra) of mutant allele frequencies (x) for various cases of random fluctuation of selection coefficient. Neutral, neutral mutations. S, S_A, S_B, and C refer to the models presented in Table S1. In C and D the number given for each curve stands for the NV_s value. Here is assumed.

Fig. 2.

Normalized distributions of mutant allele frequency (x) for various types of selection. p indicates the proportional frequency of polymorphic sites or heterozygosities rather than the absolute number.

Fig. 3.

Folded empirical distributions of mutant frequency (x) and heterozygosity for an African population (HapMap data) and an African American population (exome data). The allele frequencies considered are from 1/n to 0.5, where n is the sample size. p, proportion of heterozygous sites.

Fig. 4.

Theoretical and empirical distributions of mutant nucleotide frequency (x) and heterozygosity for the intergenic and protein-coding regions of HapMap data and the protein-coding region of exome data from human populations. The ordinate represents the number of polymorphic sites or heterozygous sites in proportion of the total number of sites. Here the allele frequency region of x = 0.2−0.8 is considered. p, proportional frequency rather than the absolute number.