Selection intensity against deleterious mutations in RNA secondary structures and rate of compensatory nucleotide substitutions

A two-locus model of reversible mutations with compensatory fitness interactions is presented; single mutations are assumed to be deleterious but neutral in appropriate combinations. The expectation of the time of compensatory nucleotide substitutions is calculated analytically for the case of tight linkage between sites. It is shown that selection increases the substitution time dramatically when selection intensity Ns > 1, where N is the diploid population size and s the selection coefficient. Computer simulations demonstrate that recombination increases the substitution time, but the effect of recombination is small when selection is weak. The amount of linkage disequilibrium generated in the process of compensatory substitution is also investigated. It is shown that significant linkage disequilibrium is expected to be rare in natural populations. The model is applied to the mRNA secondary structure of the bicoid 3' untranslated region of Drosophila. It is concluded that average selection intensity Ns against single deleterious mutations is not likely to be much larger than 1.