Geographic Patterns of (Genetic, Morphologic, Linguistic) Variation: How Barriers Can Be Detected by Using Monmonier's Algorithm

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Abstract
When sampling locations are known, the association between genetic and geographic distances can be tested by spatial autocorrelation or regression methods. These tests give some clues to the possible shape of the genetic landscape. Nevertheless, correlation analyses fail when attempting to identify where genetic barriers exist, namely, the areas where a given variable shows an abrupt rate of change. To this end, a computational geometry approach is more suitable because it provides the locations and the directions of barriers and because it can show where geographic patterns of two or more variables are similar. In this frame we have implemented Monmonier's (1973) maximum difference algorithm in a new software package to identify genetic barriers. To provide a more realistic representation of the barriers in a genetic landscape, we implemented in the software a significance test by means of bootstrap matrices analysis. As a result, the noise associated with genetic markers can be visualized on a geographic map and the areas where genetic barriers are more robust can be identified. Moreover, this multiple matrices approach can visualize the patterns of variation associated with different markers in the same overall picture. This improved Monmonier's method is highly reliable and can be applied to nongenetic data whenever sampling locations and a distance matrix between corresponding data are available.