Methods for geographic profiling of biological invasions with multiple origin sites.
Geographic profiling is a method that proved to be useful also in order to investigate the point of origin of a biological invasion. K-means clustering and Voronoi diagrams can partition a data set of geographic positions of populations invading a defined area and are, therefore, useful in cases in which an invasion had more introduction events as points of origin. One critical point of the method is to identify the right number of clusters in which to divide the starting data set formed by groups of points on a map. The Silhouette method proved to be capable of identifying the best number of subsets (clusters) of the general set of observations by providing different values for different subdivisions of the set of observations in clusters. For each cluster, the corresponding Voronoi tessellation was built on the starting map. To test the method, we did a simulation of clusters of data (points) on a map and we verified whether the proposed methods worked efficiently with the simulated data set with hundred repeats and using a varying number of clusters on the same map. The used techniques revealed to be efficient in finding the highest probability area of the map that would include the starting points for each cluster. A case study consisted in a known data set, that is, the spreading pattern of Caulerpa racemosa var. cylindracea (sea grapes), that was compatible (highest probability) with an original point of introduction in southern Italy and long distance (thousands of kilometers) secondary spreads via anthropic dispersal. The proposed techniques may also be applied to other kinds of data sets of biological data distributed on a map or in general on a geometrical surface.