Epistasis and the mutation load: A measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is b ased on the assumptions of coupling equilibrium and that the interaction ef fects are multilinear. We find that the effect of m-order epistatic interac tions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interact ion density among loci is not too low. The solution suggests that synergist ic epistasis will decrease tile mutation load and that variation in epistat ic effects will elevate the load. Both of these results, however, are stric tly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selecti on equilibrium, only synergistic interactions among even numbers of genes w ill reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistas is and load at equilibrium. We argue that empirical estimates of gene inter action must pay attention to the genetic background in which the effects ar e measured and that it may; be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a sim ple criterion for the strength of epistasis that is necessary to overcome t he twofold disadvantage of sex.