THE REDUCTION IN FIXATION PROBABILITY CAUSED BY SUBSTITUTIONS AT LINKED LOCI

The probability of fixation of a mutation with selective advantage s will be reduced by substitutions at other loci. The effect of a single substitution, with selective advantage S >> s, can be approximated as a sudden reduction in the frequency of the favourable allele, by a fraction w = 1-(s/S)(r/S) (where r is the recombination rate). An expression for the effect of a given sequence of such catastrophes is derived. This also applies to the ecological problem of finding the probability that a small population will survive, despite occasional disasters. It is shown that if substitutions occur at a rate Lambda, and are scattered randomly over a genetic map of length R, then an allele is unlikely to be fixed if its advantage is less than a critical value, s(crit) = (pi(2)/6)(2 Lambda S/(Rlog(S/s))). This threshold depends primarily on the variance in fitness per unit map length due to substitutions, var(W)/R = 2 Lambda S/R. With no recombination, the fixation probability can be calculated for a finite population. If Lambda > s, it is of the same order as for a neutral allele (approximate to Lambda/(2N(Lambda-s))), whilst if Lambda << s, fixation probability is much higher than for a neutral allele, but much lower than in the absence of hitch-hiking (1/2N << 2s/(4Ns)(Lambda/s) << 2s). These results suggest that hitch-hiking may substantially impede the accumulation of weakly favoured adaptations.