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Conditions for invasion by a new allele that controls the recombination pattern among an arbitrary number of genes under viability selection are studied. The recombination pattern may include interference. The new allele increases if its appropriately averaged marginal fitness is greater than the mean fitness prior to its introduction. Under weak additive-by-additive epistatic selection, this condition involves a weighted average of the changes in pairwise recombination rates relative to those prior to the introduction of the modifier. The weights here are positive functions of the epistatic selection components. In particular, the modifier allele may succeed even if it increases recombination among some pairs of loci, provided the overall average effect is one of reduction.

Evolution of recombination among multiple selected loci: a generalized reduction principle.