Assessment of the ratio of pollen to seed flow in a cline for genetic variation in a quantitative trait

Abstract

A dispersal-selection cline model is analysed to evaluate the role of the ratio of pollen to seed flow (r) in spatial genetic variation, with a focus on clines in additive and dominant variances of major genes affecting a quantitative trait, assuming one locus with two alleles, no genetic drift and no mutation. It is shown that under weak selection, steady-state departures from the value at Hardy-Weinberg equilibrium (HWE) for genotype frequency (D) and additive variance (ΔVa) generally display a small value on one side of the selection boundary point, a high value around the point, and a moderate value on the other side of the boundary point. A large value of r can enhance formation of this pattern. However, this is not the case for clines in the average effect of a gene substitution (Δα) or in dominance variance (ΔVd), where large values of r can eradicate the clines. Direct use of their values at HWE to approximate the real case is acceptable. There is an expected turning point that divides clines of either additive variance or dominance variance into two subclines, each with a shorter width than that of allele frequency. Integration of these properties can help to indicate the existence of major genes affecting a quantitative trait.