Cyclical environmental changes as a factor maintaining genetic polymorphism. 1. Two‐locus haploid selection

To classify different types of cyclic selection, a measure of fitness disequilibrium was used, and a class of systems were considered where this measure has the same sign in all states (sign‐concordant environments). The necessary conditions for existence of a fixed point (considering any moment within the period as a referring one) are obtained for sign‐concordant systems. However, analytical study of such systems, in the case of selection for equal additive genes, and numerical testing of more general situations, allowed us to conclude that no polymorphism is possible. In the alternative class of sign‐concordant systems, polymorphism is possible. However, we found that global stability is an exception rather than a rule for sign‐nonconcordant systems. Massive numerical simulations of selection in a four‐state environment were made for cycle lengths in the range 8–28 and with evenly distributed selection coefficients. The proportion of polymorphic regimes ranged up to about 1.5%, and was dependent on the recombination rate between the loci. It should be stressed, that polymorphism maintenance in the haploid systems, when it is possible, can not be considered as an effect derived from constant selection, or be a result of any hidden form of heterozygous advantage. In other words, polymorphism stability is causally connected with environmental fluctuations. Equally important is that this effect of fluctuations is only possible because of recombination: in single locus systems haploid cyclical selection is unable to produce protected polymorphism.