Clines in polygenic traits

This article outlines theoretical models of dines in additive polygenic tra its, which are maintained by stabilizing selection towards a spatially vary ing optimum. Clines in the trait mean can be accurately predicted, given kn owledge of the genetic variance. However, predicting the variance is diffic ult, because it depends on genetic details. Changes in genetic variance ari se from changes in allele frequency, and in linkage disequilibria. Allele f requency changes dominate when selection is weak relative to recombination, and when there are a moderate number of loci. With a continuum of alleles, gene flow inflates the genetic variance in the same way as a source of mut ations of small effect. The variance can be approximated by assuming a Gaus sian distribution of allelic effects; with a sufficiently steep dine, this is accurate even when mutation and selection alone are better described by the 'House of Cards' approximation. With just two alleles at each locus, th e phenotype changes in a similar way: the mean remains close to the optimum , while the variance changes more slowly, and over a wider region. However, there may be substantial cryptic divergence at the underlying loci. With s trong selection and many loci, linkage disequilibria are the main cause of changes in genetic variance. Even for strong selection, the infinitesimal m odel can be closely approximated by assuming a Gaussian distribution of bre eding values. Linkage disequilibria can generate a substantial increase in genetic variance, which is concentrated at sharp gradients in trait means.