RISK OF POPULATION EXTINCTION FROM FIXATION OF NEW DELETERIOUS MUTATIONS

Abstract

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, N_e, larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, \stackrel{}{t} , is asymptotically proportional to {\mathrm{e}}^{4N_{e^s}}/N_e for 4N_es > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes \stackrel{}{t} is about ŝ = 0.4/N_e. The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean \stackrel{}{s} and variance {?}_{\mathrm{s}}^2 . The mean time to extinction increases with variance in selection coefficients if \stackrel{}{s} is near ŝ, but can decrease greatly if \stackrel{}{s} is much larger than ŝ. For a given coefficient of variation of s,?c={?}_s/\stackrel{}{s} , the mean time to extinction is asymptotically proportional to N_e^{1+1/c^2} for 4N_e\stackrel{}{s}>1 . When s is exponentially distributed, (c = 1) \stackrel{}{t} is asymptotically proportional to N_e^2 . These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of N_e = 10³, may incur a substantial risk of extinction from the fixation of new mutations.