Quantifying geographic range measures and their utility as extinction risk proxies

Geographic range is used as a correlate of extinction risk for extant and extinct organisms across the fields of conservation and paleobiology. However, the exact method used to measure geographic range, the biases, and the limitations of each are rarely discussed explicitly despite their potential to impact conclusions. Here I examine and quantify properties of five commonly used measures of geographic range (convex hull area, maximum pairwise great circle distance, latitudinal range, longitudinal range, and cell count) along with a rarely used measure (minimum spanning tree distance) in the context of three datasets. A simulated dataset of two shapes with known areal limits, a paleontological occurrence dataset of pre-Cenozoic brachiopod genera from the Paleobiology Database (PBDB), and 50000 occurrence records of birds species in the western hemisphere from the eBird database. Simulated distributions indicate that when a distribution is simple (i.e. a rectangle) all measures are similarly accurate and precise at varying sample sizes and all measures converge toward the true value with increasing sample size. However, given a more complex distribution (i.e. horseshoe shape) the convex hull area becomes increasingly inaccurate as sample size increases even as it becomes more precise. Within the PBDB dataset the minimum spanning tree was heavily favored by Akaike Information Criterion as the most effective predictor of extinction risk. Analysis of the eBird data set indicated differences between IUCN Red List Categories were significant for all geographic range measures. Overall, these results suggest that for the purpose of categorical comparisons, such as those between victims and survivors of an extinction event, all six geographic range measures are interchangeable. However, the magnitude of the relationship between geographic range and extinction risk is strongly dependent on the choice of measure. Simple linear measures, such as latitudinal range, were relatively poor predictors while minimum spanning tree and cell count measures were strong predictors, especially after sampling was accounted for. The minimum spanning tree measure was found to perform at the same level or better than most other measures with the main drawback being that it is computationally expensive.