Consequences of stabilising selection for polygenic variation. II. Any number of loci

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In effect, this paper is a continuation of Mather (1987), where it was demonstrated that, depending on the properties of a gene pair, stabilising selection could bring about a stable polymorphism, but would not always do so. The analysis is now extended to any number of loci acting simultaneously. Following the earlier paper, the effects of gene differences on the primary character are assumed to show neither non-allelic interaction nor disturbance due to linkage, but different gene pairs will generally show interaction in their effects on fitness which are assumed to be related to the square of primary phenotypic deviations from the optimum.It is shown that, in principle, the equilibrium allele frequencies at one locus are affected by the average deviation from the optimum of the three genotypes at each of the other polymorphic loci in the system. Thus stabilising selection acts not on individual loci independently, but on the system as an integrated whole: the response to selection at any one locus is affected by all the other loci and, in its turn, it affects response at all the other loci. The allele frequencies at any one locus will be adjusted by the allele frequencies at all the rest and the mean expression of the primary character will thus come to be at the optimum, subject, of course, to the effects of temporary environmental fluctuations.Published data from experiments based on the Texas cage population of Drosophila melanogaster agree with the theoretical expectations derived from this analysis.