Response to Comment on "Parasite Selection for Immunogenetic Optimality"

Abstract

Resistance to pathogens has been measured directly in several organisms by examining single-copy major histocompatibility complex (MHC) genes (1, 2). However, some MHC genes are found in multiple, tightly linked copies, as expected from gene duplication. Wegner et al. (3) reported that for a class IIB MHC gene with a variable number of copies (three to nine copies in different individuals) in the three-spined stickleback, individuals with an intermediate number of alleles (gene copies) appear to have the lowest parasite load in experimental immune challenges. To understand how such selection would influence genetic variation, I used a model in which an intermediate optimum is favored, similar to the quadratic deviations model (4, 5). Here, the fitness of the genotype with i alleles is wi 1 k (Pi Po)2, where Pi and Po are the phenotypes (number of alleles) for phenotype i and the optimum phenotype, respectively, and k is a constant determining the amount of selection. As assumed by Wegner et al. in (3), I assumed that all alleles were qualitatively similar—that is, all individuals with a given number of alleles had the same fitness, regardless of the identity of the alleles. Let us assume that the maximum fitness is for the phenotype with 5.82 alleles, which was the estimated minimal parasite load in (3), and assume that there are haplotypes with from one to five alleles. If we assume that k 0.01, then the fitness ranges from about 0.9 for a phenotype with either three or nine alleles to 1.0 for a phenotype with six alleles. With this model, selection results in a monomorphic population consisting of only haplotypes with three alleles. This theoretical result is consistent with that found in earlier research (4, 5) in which selection for an intermediate optimum does not generally maintain polymorphism and results in fixation of the haplotype that gives only phenotypes with the maximum fitness. This finding is in contrast to the distribution of haplotypes observed by Wegner et al. (3), in which the whole distribution of phenotypes from three to nine alleles was observed in 86 individuals (see Fig. 1) and the phenotypic diversity is 1 x i 2 0.822, where xi is the frequency of the ith phenotype. One way to counter the effect of selection reducing variation in the number of alleles is to incorporate mutation to chromosomes with different numbers of alleles (unequal crossing over to produce duplications or deficiencies). Let us assume that u is the rate of mutation from a haplotype with i alleles to a haplotypes with i 1 alleles and to i – 1 alleles (a proportion 1 – 2u do not mutate). If u 0.05, then the equilibrium distribution is as given in Fig. 1. This is similar to that observed and has a similar phenotypic diversity of 0.849. However, this rate of mutation is several orders of magnitude higher than observed for gene duplication and deficiency (6), so it seems unlikely that it is the basis of the distribution. Perhaps a more likely scenario is that the impact of stabilizing selection is even smaller than assumed here, which may make it of little influence in a finite population, and that nonselective forces primarily influence the distribution of allele number. Another possible explanation for the variation in allele numbers is that diversifying selection, either in space or time (2, 7), may maintain different alleles at a given locus. However, it is not clear how this could maintain different numbers of alleles within a population.