Visualizing species richness and site similarity from presence-absence matrices

Species richness and similarity of biotas among distinct sites are important quantities in biogeography. Indices derived from presence-absence matrices are used to represent these quantities in so-called diversity-range plots.  The most commonly used diversity-range plot, however, has multiple special cases and its interpretation is cumbersome. Here we present an equivalent formulation that is geometrically simpler and has no special cases. In addition, we introduce a method to identify the statistical significance of the dispersion field, an index that represents how similar species composition is in a cell with respect to the whole area. The new diversity-range plot is a promising tool to explore biodiversity and endemism in a region as the values shown in this plot and whether they are statistically significant or not can also be represented in geography