Detecting Regions of Abrupt Change in Maps of Biological Variables

The areas where the rates of change of biological variables across space are particularly high may correspond to either steep ecological gradients or regions of limited admixture among demes. A method for detecting such biological boundaries was proposed by Womble (1951), who suggested averaging the absolute values of the derivatives of the functions describing biological variation in space at various locations. We present here algorithms that quantify both the mean magnitude and the mean direction of change in surfaces representing distributions of biological measures (such as gene frequencies, measures of quantitative traits, etc.). Inferences on the microevolutionary processes affecting the populations can be made by comparing the boundaries detected with the distribution of environmental characteristics, or with the location of factors that may have prevented population admixture. Examples of the application of this method to both simulated data and gene frequencies of two natural populations are given.