MINIMUM SPANNING TREE DISTANCE AND OTHER GEOGRAPHIC RANGE MEASURES AS PROXIES OF EXTINCTION RISK

While geographic range is recognized as a general property correlated with extinction risk across both fossil and modern taxa, there has been little work examining how the way it is measured affects analyses. I examined the behavior of six methods of measuring geographic range including convex hull area, latitudinal range, longitudinal range, maximum pairwise great circle distance, 5 x 5 degree cell count, and minimum spanning tree distance. The last measure has not been widely used and is the sum of the distance required to connect all occurrences without creating a loop. This represent the minimum distance a taxon must have crossed to achieve the observed distribution. Metrics for accuracy and precision were calculated for each geographic range measure across sample size in three datasets. A simulated dataset of two shapes (rectangle and horseshoe) with known areas, a fossil dataset of pre-Cenozoic brachiopod genera (n=370) from the Paleobiology Database, and a modern dataset of bird species (n=1297) from the eBird database associated with their current IUCN threat levels.

All three datasets showed similar patterns across measures in terms of accuracy and precision with sample size. Measures typically became more accurate and precise as sample size increased, with simple measures (latitudinal and longitudinal ranges) dropping very quickly, while the minimum spanning tree and 5 x 5 degree cell counts took longer to stabilize. However, the simulated dataset showed that the convex hull became less accurate and more precise as sample size increased in the horseshoe shape, greatly overestimating the true area even at small sample sizes. The six geographic range measures were all significant predictors of extinction risk in the fossil dataset but with large differences in magnitude. The minimum spanning tree was found to be the best predictor. Wilcox tests between IUCN categories found that all measures were consistent in direction, higher threat levels had smaller geographic ranges, on average. These results suggest that for categorical comparisons all six measures of geographic range are appropriate but that if magnitude of effects are to be considered the minimum spanning tree or cell count measures are favorable because the others may lack information or be seriously mislead under certain distribution shapes.