Genetic Drift Widens the Expected Cline but Narrows the Expected Cline Width

Abstract

Random genetic drift shifts clines in space, alters their width, and distorts their shape. Such random fluctuations complicate inferences from cline width and position. Notably, the effect of genetic drift on the expected shape of the cline is opposite to the naive (but quite common) misinterpretation of classic results on the expected cline. While random drift on average broadens the overall cline in expected allele frequency, it narrows the width of any particular cline. The opposing effects arise because locally, drift drives alleles to fixation--but fluctuations in position widen the expected cline. The effect of genetic drift can be predicted from standardized variance in allele frequencies, averaged across the habitat: <F>. A cline maintained by spatially varying selection (step change) is expected to be narrower by a factor of √1-<F> relative to the cline in the absence of drift. The expected cline is broader by the inverse of this factor. In a tension zone maintained by underdominance, the expected cline width is narrower by about 1-<F> relative to the width in the absence of drift. Individual clines can differ substantially from the expectation, and we give quantitative predictions for the variance in cline position and width. The predictions apply to clines in almost one-dimensional circumstances such as hybrid zones in rivers, deep valleys, or along a coast line and give a guide to what patterns to expect in two dimensions.