Protected polymorphism in the two-locus haploid model with unpredictable fitnesses

In an unpredictable environment, the distributions of alleles from which polymorphism can be maintained forever belong to a certain set, the C-viability kernel. Such a set is calculated in the two-locus haploid model, as well as the corresponding fitnesses at any time which make this maintenance possible. The dependence of the C-viability kernel on the set U of admissible fitnesses and on the recombination rate r is studied. Notably, the C-viability kernel varies rapidly in the neighborhood of equal fitness of AB and ab; it becomes empty when ab has a fitness below a certain function, which is delineated, of the recombination rate. The properties of the two-locus model under constraints, out of equilibrium and with unpredictable selection are thus presented.