Quantifying species’ geographic range changes: conceptual and statistical issues

Geographic range is an important metric used to evaluate species’ environmental relationships. Additionally, a very small or rapidly shrinking range may indicate elevated extinction risk. However, a species does not fully occupy its range in the way a lake fills a basin and is instead best thought of as a cloud of points rather than an area per se. Samples of species presence or abundance are subject to issues of both inherent detectability and stochastic detectability due to sample locations in space and time. In addition, populations fluctuate in space and time. These factors mean that the population centroid, range area, and range margin are not deterministic. Examples from the literature demonstrate that multidirectional range changes are ubiquitous due to stochastic effects. Confounding factors, particularly due to human activities such as land use change, also complicate inference about range changes. Herein, statistical tests for centroid and margin changes in the context of stochastic fluctuations of clouds of points and sample error are demonstrated. Scale‐dependent area analysis and tests for range area change are presented along with tests for responses at the community level (suites of species). This test allows for evaluation of change in spatial pattern for patchy populations with or without outliers. Geographic range change can reliably be tested with statistics based on distributions of clouds of observed points rather than bounded areas per se, if potential confounding is taken into account.