Analysis of the estimators of the average coefficient of dominance of deleterious mutations

Abstract

We investigate the sources of bias that affect the most commonly used methods of estimation of the average degree of dominance (h) of deleterious mutations, focusing on estimates from segregating populations. The main emphasis is on the effect of the finite size of the populations, but other sources of bias are also considered. Using diffusion approximations to the distribution of gene frequencies in finite populations as well as stochastic simulations, we assess the behavior of the estimators obtained from populations at mutation-selection-drift balance under different mutational scenarios and compare averages of h for newly arisen and segregating mutations. Because of genetic drift, the inferences concerning newly arisen mutations based on the mutation-selection balance theory can have substantial upward bias depending upon the distribution of h. In addition, estimates usually refer to h weighted by the homozygous deleterious effect in different ways, so that inferences are complicated when these two variables are negatively correlated. Due to both sources of bias, the widely used regression of heterozygous on homozygous means underestimates the arithmetic mean of h for segregating mutations, in contrast to their repeatedly assumed equality in the literature. We conclude that none of the estimators from segregating populations provides, under general conditions, a useful tool to ascertain the properties of the degree of dominance, either for segregating or for newly arisen deleterious mutations. Direct estimates of the average h from mutation-accumulation experiments are shown to suffer some bias caused by purging selection but, because they do not require assumptions on the causes maintaining segregating variation, they appear to give a more reliable average dominance for newly arisen mutations.

Figure 1.—

(a) Distribution [f(s)] of mutational effects, s, for a gamma distribution with shape parameter β and mean effect . (b) Distribution [g(h)] of dominance coefficients following a beta distribution with mean and variance σ²_h of dominance coefficients. (c) Joint distribution of dominance coefficients, h, and mutational effects, s, for the model of dominance of Caballero and Keightley (1994). The values of h are sampled from a uniform distribution between 0 and the corresponding exponential curve. Parameters are: (1) ; (2) ; (3) ; and (4) .

Figure 2.—

Mutational parameters for newly arisen and segregating mutations for a model of dominance coefficients following a beta distribution with mean value and variance . Left, mutational model for λ = 0.2, . Right, mutational model for λ = 0.006, . Top, percentage of newly arisen (line) and segregating mutations (bars) for different classes of h. Bottom, average coefficient of selection of newly arisen (lines) and segregating mutations (bars) for different classes of h. Darkly shaded bars and solid lines, no correlation between s and h (r = 0); lightly shaded bars and dashed lines, r = −0.4. Results for newly arisen and segregating mutations are based on draws of 1,000,000 and 1000 mutations, respectively.