EVOLUTIONARILY STABLE MUTATION-RATES

I investigate the hypothesis that mutation rates in natural population s are determined by a balance between: (1) selection against deleterio us mutations favouring lower mutation rates, and (2) selection opposin g further reduction of the mutation rate, resulting from the costs inc urred by more stringent proof-reading and repair (for example, a reduc tion in the rate of DNA replication). The influence of advantageous mu tations is assumed to be negligible. In a previous paper, I analysed t he dynamics of a modifier of the mutation rate in a large sexual popul ation, where (infinitesimally rare) deleterious alleles segregate at a n infinite number of unlinked loci with symmetric multiplicative fitne ss effects. A simple condition was obtained for a modifier allele to i ncrease in frequency. Remarkably, this condition does not depend on th e allele frequencies at the modifier locus. Here, I show that (as a co nsequence), given any set of possible values of the mutation rate (any set of possible modifier alleles), there always exists a single globa lly stable value of the mutation rate. This is an unusually strong for m of ''evolutionarily stability'' for a sexual population. Less surpri singly the optimum mutation rate in an asexual population has similar stability properties. Furthermore, in the case of an asexual populatio n, it is not necessary to make any special assumptions about the selec tion acting against deleterious mutations, except that a deterministic mutation-selection equilibrium exists. I present a simple method for identifying the evolutionarily stable value of the mutation rate, give n the function alpha(U) relating the value of the mutation rate to the fitness cost of maintaining this rate. I also argue that if there is a highly conserved relationship between the rate of replication ptr ba se, and the rate of mutation per base, and if this relationship has th e form of a power law, then the remarkable uniformity of the per genom e mutation rate in DNA based microbes can be explained. (C) 1998 Acade mic Press.