Linkage disequilibrium requires epistatic fitness

The fitness models multiplicative and additive both result in equilibrial haplotype frequencies with zero linkage disequilibrium. Whenever, as is the case with these models, fitnesses are independent at the two loci, it will decay to zero as the generations pass through recombination.

In general, selection can only produce linkage disequilibrium at equilibrium when the fitnesses of the genotypes at different loci interact epistatically. Not all epistatic fitness interactions generate doubly polymorphic equilibria with linkage disequilibrium; but all such equilibria do have epistatic fitnesses. We shall describe epistatic fitness shortly.