hyperoverlap : Detecting biological overlap in n ‐dimensional space

Comparative biological studies often investigate the morphological, physiological or ecological divergence (or overlap) between entities such as species or populations. Here we discuss the weaknesses of using existing methods to analyse patterns of phenotypic overlap and present a novel method to analyse co‐occurrence in multidimensional space. We propose a ‘hyperoverlap’ framework to detect qualitative overlap (or divergence) between point datasets and present the hyperoverlap r package which implements this framework, including functions for visualization. hyperoverlap uses support vector machines (SVMs) to train a classifier based on point data (such as morphological or ecological data) for two entities. This classifier finds the optimal boundary between the two sets of data and compares the predictions to the original labels. Misclassification is an evidence of overlap between the two entities. We demonstrate the theoretical and practical advantages of this method compared to existing approaches (e.g. single‐entity hypervolume models) using the bioclimatic data extracted from global occurrence records of conifers. We find that there are instances where single‐entity hypervolume models predict overlap, but there are no observations of either entity in the shared hypervolume. In these instances, hyperoverlap reports nonoverlap. We show that our method is stable and less likely to be affected by sampling biases than current approaches. We also find that hyperoverlap is particularly effective for situations involving entities with a small number of data points (e.g. narrowly endemic species) for which single‐entity models cannot be reliably constructed. We argue that overlap can be reliably detected using hyperoverlap , particularly for descriptive studies. The method proposed here is a valuable tool for studying patterns of overlap in a multidimensional space.