Minimal number of generations out of polymorphism in the one-locus two-allele model with unpredictable fertilities

Fertilities varying in time in an unpredictable manner raise the question of the maintenance of polymorphism, and the subsequent question of the minimal total number of generations spent by the system in impoverished polymorphism. In the one-locus two-allele model, level surfaces of this minimal time out of a given set K of constraints defining polymorphism are delineated. The surface of null minimal time is also the largest set of genotype frequencies from which there exists at least one route remaining in K forever. The influence of the range of admissible fertilities clarifies the trade-off between homozygotes and heterozygotes. Notably, ranges of fertility forbidding a system leaving K to ever return to it are determined. Generally, keeping a chance to regain polymorphism demands a sufficiently relatively high fertility for matings involving heterozygotes.