hyperoverlap: Detecting biological overlap in n‐dimensional space

Abstract

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.

Concepts and applications in functional diversity

“…Thus, probabilistic hypervolumes reflect the notion that not all areas within the boundaries of a given trait space are filled with the same intensity. The popularity of probabilistic hypervolumes is steadily increasing in functional ecology, as testified by the number of R algorithms published in recent years allowing to delineate and/or analyze probabilistic hypervolumes Blonder et al, 2018; M. J. M. Brown, Holland, & Jordan, 2020;Carmona, de Bello, Mason, & Lepš, 2019;Junker, Kuppler, Bathke, Schreyer, & Trutschnig, 2016;Swanson et al, 2015).…”

Habitat Specificity, Host Plants and Areas of Endemism for the Genera-Group Blepharida s.l. in the Afrotropical Region (Coleoptera, Chrysomelidae, Galerucinae, Alticini)

“…Statistical analyses were performed using NCSS11 software (NCSS, LLC, Kaysville, UT, USA). Finally, to detect the possibility of a niche overlap driven by climate, we evaluated the target flea beetle and plant occurrences by using the “hyperoverlap” package [ 46 ] in R environment [ 47 ]. This tool permits the evaluation of overlap or divergence between point datasets, such as in our case, using support vector machines to find the best classification (linear or polynomial), giving a classification matrix, for any n-dimensional set of point attributes [ 46 ].…”

“…Finally, to detect the possibility of a niche overlap driven by climate, we evaluated the target flea beetle and plant occurrences by using the “hyperoverlap” package [ 46 ] in R environment [ 47 ]. This tool permits the evaluation of overlap or divergence between point datasets, such as in our case, using support vector machines to find the best classification (linear or polynomial), giving a classification matrix, for any n-dimensional set of point attributes [ 46 ]. The “hyperovelap_detect” function, which has proven to be resistant to sampling biases and to small numbers of points [ 46 ], was used to find climatic niche overlap for the aforementioned pairs, while the “hyperovelap_lda” function was used to obtain the three-dimensional plots (reporting a combined linear discriminant analysis, PCA 1 and PCA 2 residuals) resulting from the classification.…”

“…This tool permits the evaluation of overlap or divergence between point datasets, such as in our case, using support vector machines to find the best classification (linear or polynomial), giving a classification matrix, for any n-dimensional set of point attributes [ 46 ]. The “hyperovelap_detect” function, which has proven to be resistant to sampling biases and to small numbers of points [ 46 ], was used to find climatic niche overlap for the aforementioned pairs, while the “hyperovelap_lda” function was used to obtain the three-dimensional plots (reporting a combined linear discriminant analysis, PCA 1 and PCA 2 residuals) resulting from the classification. This last function was needed because four of the Worldclim climatic variables were used for this analysis, namely, BIO1 (mean annual temperature), BIO7 (temperature annual range), BIO14 (precipitation of the driest month) and BIO18 (precipitation of the warmest quarter), identified to be the most relevant variables from the species distribution models built by D’Alessandro et al [ 8 ], shared among Afroblepharida , Blepharidina and Calotheca .…”

Niche dynamics in amphitropical desert disjunct plants: Seeking for ecological and species‐specific influences

“…Hutchinson (1957) defined the niche as the set of environmental conditions under which a species can persist, and made the distinction between the ‘fundamental niche’ and the ‘realized niche’ of a species, with the former referring to the abiotic conditions, and the latter including also the biotic ones (Whittaker et al., 1973). In the last 20 years, advancements in the characterization and comparison of realized niches have been possible by the availability of species’ presence data and environmental variables in publicly accessible online databases (Broennimann et al., 2012; Brown et al., 2020; A. T. Peterson & Soberón, 2012). As species’ niches are n ‐dimensional (Hutchinson, 1957) and are the result of complex interactions (Wiens, 2011), they can be studied by multivariate techniques to disentangle potential influences among interacting variables.…”