Are rare variants responsible for susceptibility to complex diseases?

Abstract

Little is known about the nature of genetic variation underlying complex diseases in humans. One popular view proposes that mapping efforts should focus on identification of susceptibility mutations that are relatively old and at high frequency. It is generally assumed-at least for modeling purposes-that selection against complex disease mutations is so weak that it can be ignored. In this article, I propose an explicit model for the evolution of complex disease loci, incorporating mutation, random genetic drift, and the possibility of purifying selection against susceptibility mutations. I show that, for the most plausible range of mutation rates, neutral susceptibility alleles are unlikely to be at intermediate frequencies and contribute little to the overall genetic variance for the disease. Instead, it seems likely that the bulk of genetic variance underlying diseases is due to loci where susceptibility mutations are mildly deleterious and where there is a high overall mutation rate to the susceptible class. At such loci, the total frequency of susceptibility mutations may be quite high, but there is likely to be extensive allelic heterogeneity at many of these loci. I discuss some practical implications of these results for gene mapping efforts.

Figure 1

Examples of the probability distribution of the overall frequency of susceptibility alleles at a locus (from Wright’s formula). In the upper plot, σ=0; in the lower plot, σ=12.0. Parameter values: β_S=3.0 (solid lines); β_S=1.0 (dotted lines); β_S=0.1 (dashed lines); β_N=0.01 throughout. Notice that the vertical scale differs by a factor of five between the plots. In the upper plot, virtually all of the probability mass is on values near 0 or 1 (see table 1).

Figure 2

Contribution to the additive genetic variance as a function of allele frequency. The plot shows how much of the (expected) additive genetic variance is due to alleles of a given frequency. The vertical axis is in units of 2δ², where δ is the marginal increase in penetrance caused by each susceptibility allele. The integral of each curve equals the expected additive genetic variance. The lines are labeled with the assumed values of σ: 0.0, 4.0, 12.0, 20.0, and 30.0; mutation rates are β_S=1.0, β_N=0.01 for all.

Figure 3

Probability distributions of the overall frequency of susceptibility alleles at each locus, under the multilocus model described in the text. In each plot, the solid line labeled “0” shows the unconditional distribution of allele frequencies. The lines labeled “1”,…,“5” show the frequency distributions at the five loci that contribute the most to the sibling recurrence risk: that is, line “i” gives the frequency distribution at the locus with the ith largest value of λ_s. Parameters: (top) K=0.01, Λ_s=10.0, L=5, and ; (bottom) K=0.0004, Λ_s=75.0, L=100, and .