The Dynamics of Linkage Disequilibrium Under Temporal Environmental Fluctuations: Two-Locus Selection

Abstract

In this paper, we describe some regularities of the behavior of linkage disequilibrium, D, under temporal environmental fluctuations in infinite panmictic populations with non-overlapping generations and diploid and haploid selecton regimes. Different types of environmental variation ware considered. Our analysis shows that under two-locus haploid selection with any period length, there exists an environmental state (e.s.) where D can change the sign (between periods), but not more than once. The direction of this change is fully determined by a special quantity, "integral fitness disequilibrium coefficient," Δ, which is calculated from genotypic fitness in environmental states. If Δ = 0, then two e.s. exist with only one change of the sign in each. Special types of environments (sub- or super-multiplicative) common in theoretical modelling can be mentioned where the sign of D between periods behaves rather simply for any considered e.s. It can be shown that under sufficiently small rates of recombination r < r* for any period length p in every e.s. the sign of D can change no more than once; the border r* is calculated as a function of fitness values which decreases with decreased differences between the fitnesses. The obtained results were applied to various types of fitness functions. Thus, cases of additive effects of fitness loci on the selected trait under various hypotheses about the selection regime in changing environment were considered in detail. In particular, we showed that the sign of D generated by selection is, in a sense, a nonsymmetrical function when one considers possible forms of fitness dependence on the selected trait: negative D′s are more probable. These results are also extended to the diploid case with an additively formed selected trait.