The dynamics of the rec-system in variable environments: Haploid selection in a cyclical two-state environment

The dynamics of a 3-locus infinite population with non-overlapping generations and panmixia was studied. Loci are di-allelic: two loci affect fitness under cyclical symmetric haploid selection while the third one is a modifier of recombination (rec-modifier). Selection favors alternatively haplotypes AB and ab or Ab and aB. It has been proven that under alternating selection (when period of selection consists of two generations) a dominant suppressor of recombination is displaced and the allele for non-zero recombination becomes fixed within the population. For populations with inversion heterozygosity within the selective system (i.e. with zero recombination in heterozygote for rec-modifier and non-zero for homozygotes) fixation of one of the alleles (depending on the initial point) at the rec-modifier locus is predicted. For other values of recombination parameters, the behavior of the system was studied numerically. A full bifurcation picture of parameters was obtained. Many of the results related to the case of a two-generation period hold also in the case of longer period lengths.