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: hF i. A cline maintained by spatially varying selection (step change) is expected to be narrower by a factor of ffiffiffiffiffiffiffiffiffiffiffiffiffi 12hFi p 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 -hF i 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.
WITHIN species, substantial genetic diversity may be maintained by the interaction between selection and gene flow. This may be manifest in gradients in heritable traits or in allele frequency (Endler 1977). Clines reflect the degradation by gene flow of adaptation to the local environment or genetic background, and they may be used to estimate the strength of selection experienced by natural populations. Often, it is assumed that the effects of drift on the realized clines can be neglected.Random genetic drift will shift clines from side to side, alter their width, and distort their shape (Felsenstein 1975;Slatkin and Maruyama 1975;Nagylaki 1978). Such random fluctuations complicate inferences from cline width and position, but may themselves be used to infer rates of gene flow, drift, and selection. More important, drift is expected to reduce local diversity and so to make selection less effective, thereby interfering with adaptation to local conditions. The common view is that genetic drift makes clines slightly shallower, because selection becomes less effective. This comes from a "generalization" of the effect of genetic drift on the "expected cline" as derived by Slatkin and Maruyama (1975) (see, e.g., Alleaume-Benharira et al. 2006). However, the characteristics of the expected cline do not necessarily give an adequate idea of the patterns we expect to see in specific clines. Here, we define the expected cline as the average allele frequency across independent realizations, taken at the same time, and so it includes the i...