The reduction in fixation probability caused by substitutions at linked loci

Abstract

The probability of fixation of a mutation with selective advantageswill be reduced by substitutions at other loci. The effect of a single substitution, with selective advantage, can be approximated as a sudden reduction in the frequency of the favourable allele, by a fractionw= 1 −(s/S)^r/s(whereris the recombination rate). An expression for the effect of a given sequence of such catastrophes is derived. This also applies to the ecological prxoblem of finding the probability that a small population will survive, despite occasional disasters. It is shown that if substitutions occur at a rate Δ, and are scattered randomly over a genetic map of lengthR, then an allele is unlikely to be fixed if its advantage is less than a critical value,S_crit= (π²/6)(2ΔS/(Rlog(S/s))). This threshold depends primarily on the variance in fitness per unit map length dueto substitutions, var(W)/R= 2ΔS/R. With no recombination, the fixation probability can be calculated for a finite population. If Δ >s, it is of the same order as for a neutral allele ( ≈ Δ/(2N(Δ−s))), whilst if, fixation probability is much higher than for a neutral allele, but much lower than in the absence of hitch-hiking. These results suggest that hitch-hiking may substantially impede the accumulation of weakly favoured adaptations.