A robust distance coefficient between distribution areas incorporating geographic distances.

At a biogeographical scale, incomplete sampling is a hardly avoidable problem. Incomplete sampling can result in artefacts in R-mode analysis of biogeographic data, i.e., in the quantification of the similarity or dissimilarity of distribution areas of different organisms. Consider, for example, the hypothetical case shown in Figure 1. There are four distribution areas. Three taxa have similar distribution areas (A, B, C) in the northwest of the study region, whereas the fourth distribution area (D) is far away in the southeast. A similarity or distance measure is necessary to quantify the similarity or dissimilarity. A wealth of binary similarity and distance coefficients is available for that purpose (e.g., Cheetham and Hazel, 1969; Hubalek, 1982; Gower and Legendre, 1986; Shi, 1993). In Figure 2 the resulting distance matrices for some distance coefficients are shown. We denote distribution areas as sets A of geographic units, which are subsets of the total region under study R = [r\,..., r^} with k geographic units. |y4| denotes the number of elements in A The Jaccard distance