SMALL POPULATION GENETIC VARIABILITY AT LOCI UNDER STABILIZING SELECTION.

Abstract

Genetic variability at a locus under stabilizing selection in a finite population is investigated using analytic methods and computer simulations. Three measures are examined: the number of alleles k, heterozygosity H, and additive genetic variance Vg. A nearly-neutral theory results. The composite parameter S = NVM /Vs (where N is the population size, VM the variance of new mutant allelic effects and Vs the weakness of stabilizing selection) figures prominently in the results. The equilibrium heterozygosity is similar to that of strictly neutral theory, H = 4Nμc / (1 + 4Nμc ), except that μc = μe=μ/1+cS where c is about 0.5. Simulations corroborate Vg=4μVs1+1/S except for very low N. Genetic variability attains similar equilibrium values at both a "lone" locus and at an "embedded" locus. This agrees with my earlier work concerning molecular clock rates. These results modify the neutralist interpretation of data concerning genetic variability and genetic distances between populations. Low H values are proportional not to N but to N. This may explain the narrow observed range of H among species. Heterozygosities need not be highly correlated to genetic variances. Genetic variances are not highly dependent on population size except in very small populations which are difficult to sample without bias because the smallest populations go extinct the fastest. Nearly neutral evolution will not be easily distinguished from strictly neutral theory under the Hudson-Kreitman-Aguade inter-/intraspecific variation ratio test, since a similar effective mutation rate holds for genetic distances and D = 2μc t, where μe=μ/1+S. As with strictly neutral theory, comparisons across loci should show D and H to be positively correlated because of the shared μc . But unlike neutral theory, for a given locus, comparisons across species should show D and H to be negatively correlated. There is no obvious threshold of population size below which genetic variability inevitably declines. Extinction depends on both genetic variation and natural selection. Neither theory nor observation presently indicates the measure of genetic variability (k, H, VG or other) that best indicates vulnerability of a small population to extinction.