Delimiting areas of endemism through kernel interpolation

Abstract

We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE), based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.

Figure 1. Step-by-step implementation of Geographic Interpolation of Endemism (GIE) analysis.

a: a centroid is estimated for the points of occurrence of each species. b: For each species, the distance between the centroid and its farthest point is measured. c: species are organized in groups, according to the distance measured in step b. d: This distance is used to define a circular area of influence around each species centroid. This procedure makes it possible to quantify the overlap between areas of distribution among species. e: The degree of overlap between species areas of influence is measured according to a Gaussian function around each species centroid. f: The density of species on each area of overlap, weighted by the degree of overlapping, is converted into interpolated curves using the kernel interpolation function (at left). These curves can be rasterized for display on maps.

Figure 2. Areas of endemism of spiders in Brazil, identified using GIE.

Shaded areas indicate the areas of endemism, dashed lines indicate the major areas of endemism delimited according to the kernel index. The insert shows the Brazilian biomes, discussed in the text.

Figure 3. Areas of endemism of spiders in Brazil identified using PAE.

a: Areas of endemism of spiders in Brazil identified using PAE, superimposed to the isolines of GIE’s areas of endemism depicted in Fig. 2. Colored polygons indicate areas of endemism composed by more than one grid cell, dark gray quadrats indicate areas that were restricted to a single, not clustered grid cell. b: PAE consensus cladogram obtained through parsimony analysis of the whole spider dataset. Colored branches indicate areas of endemism formed by more than two grid cells (same colors as the corresponding location on the map); gray terminal branches indicate areas that were restricted to a single, not clustered cell; white terminal branches indicate grid cells that did not form areas of endemism due to the absence of at least one endemic species.

Figure 4. Areas of endemism of spiders in Brazil identified using NDM.

Map showing some contiguous consensus areas of endemism identified by NDM analysis, indicated by colours.

Figure 5. The problems of using grid cells for delimitation of areas of endemism, illustrated by a hypothetical example.

a: Points of occurrence of three species (illustrated by different symbols) overlapped by a grid of large cells. The presence of an occurrence point inside a cell, even in its borders (as in the highlighted cells), is interpreted as if the species is present in the whole cell. b: As a consequence, areas of endemism delimited from the grid are overestimated. c: GIE optimization, which does not depend on grid cells, estimates areas of endemism with contours closer to the actual overlap between species distribution. d: Using a grid with smaller cells could generate more realistic areas of endemism, but it makes it more difficult to detect the overlap between the species distribution.