THE RATE OF COMPENSATORY EVOLUTION

A two-locus model is presented to analyze the evolution of compensator y mutations occurring in stems of RNA secondary structures. Single mut ations are assumed to be deleterious but harmless (neutral) in appropr iate combinations. In proceeding under mutation pressure, natural sele ction and genetic drift from one fitness peak to another one, a popula tion must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution , k(c), is then defined as the inverse of the expected transition time . When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombin ation generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linka ge, k(c) is given by the rate at which favorable combinations of doubl e mutants are produced by compensatory mutation. For r > 0, k(c) decre ases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substituti ons of compensatory mutants in relation to WRIGHT's shifting balance t heory of evolution and use our results to analyze the substitution pro cess in helices of mRNA secondary structures.