What does effective population size tell us about loss of allelic variation?

Abstract

There are two primary measures of the amount of genetic variation in a population at a locus: heterozygosity and the number of alleles. Effective population size (N _e) provides both an expectation of the amount of heterozygosity in a population at drift-mutation equilibrium and the rate of loss of heterozygosity because of genetic drift. In contrast, the number of alleles in a population at drift-mutation equilibrium is a function of both N _e and census size (N _C). In addition, populations with the same N _e can lose allelic variation at very different rates. Allelic variation is generally much more sensitive to bottlenecks than heterozygosity. Expressions used to adjust for the effects of violations of the ideal population on N _e do not provide good predictions of the loss of allelic variation. These effects are much greater for loci with many alleles, which are often important for adaptation. We show that there is a linear relationship between the reduction of N _C and the corresponding reduction of the expected number of alleles at drift-mutation equilibrium. This makes it possible to predict the expected effect of a bottleneck on allelic variation. Heterozygosity provides good estimates of the rate of adaptive change in the short-term, but allelic variation provides important information about long-term adaptive change. The guideline of long-term N _e being greater than 500 is often used as a primary genetic metric for evaluating conservation status. We recommend that this guideline be expanded to take into account allelic variation as well as heterozygosity.

Keywords: allelic variation; bottleneck; drift‐mutation equilibrium; effective population size; genetic drift; heterozygosity.

FIGURE 1

Average number of alleles expected per locus at mutation‐drift equilibrium for different census population sizes (N _C) under the infinite alleles model with a mutation rate of 10⁻⁵ (Equation 2) and different values of N _e. Heterozygosity is calculated with Equation (1); for example, H = 0.500 when μ = 10⁻⁵ and N _e = 25,000.

FIGURE 2

Simulation results (EASYPOP 2.0.1; Balloux, 2001) with 1000 repeats showing the mean allelic diversity (A _D) remaining after t generations of a reduced population size of 10 (N _e = N _C = 10) beginning with 2, 5, and 10 equally frequent alleles. The numbers below each line indicate the number of equally frequent alleles initially present. The dashed line shows the heterozygosity expected to be retained using Equation (4).

FIGURE 3

Simulation results (EASYPOP 2.0.1; Balloux, 2001) with 1000 repeats showing loss of allelic diversity in two populations with N _e = 4 having different values of N _C. Each population initially had 10 alleles at equal frequency. The upper line is a population with 99 females and 1 male. The lower line is a population with 2 females and 2 males. The dashed line shows the heterozygosity expected to be retained in both populations using Equation (4).

FIGURE 4

Bottleneck sizes that would retain a given proportion (25%, 50%, or 75%) of alleles. For example, the census size was N _C = 30.7 billion before the bottleneck in the Baltic herring. Retention of 50% of the alleles would require a minimum N _C = 15.4 billion after the bottleneck. The trajectories are constructed using N _e/N _C = 0.024 and μ = 10⁻⁷, assuming migration‐drift equilibrium before and after the bottleneck. The curves can be used for evaluating the expected effect of any change of N _C on allelic reduction as long as N _e/N _C remains the same over the bottleneck, and N _e μ is not too small (N _e μ > 1). See text for details.