Dynamic range boxes – a robust nonparametric approach to quantify size and overlap of n‐dimensional hypervolumes

Abstract

Summary n‐dimensional hypervolumes are commonly applied in ecology and evolutionary studies to describe and compare niches, trait spaces characterizing phenotypes or the functional composition of communities. Classical ecological surveys, modern analytical tools and the establishment of online data bases will produce large multivariate data sets, which demands robust statistical tools to analyse and interpret hypervolumes. Existing approaches often have weaknesses; for example, they rely on multivariate normally or elliptically distributed data, perform poorly in higher dimensions, or their outputs vary arbitrarily with parameter choice. Here we introduce dynamic range boxes as a robust nonparametric approach to quantify size and overlap of n‐dimensional hypervolumes. Dynamic range boxes (implemented in the r package dynRB) improve the concept of multivariate range boxes by accounting for the distribution of the data within their range, while still no assumptions on the underlying distributions are needed. In addition to calculating the whole n‐dimensional hypervolume, the package dynRB also provides functions for a coordinate‐wise analysis and interpretation of the data. The concept of dynamic range boxes reliably computes sizes and overlaps of n‐dimensional hypervolumes, which makes dynamic range boxes readily applicable for a broad range of data sets to answer questions related to various disciplines.

Biotic interactions in species distribution models enhance model performance and shed light on natural history of rare birds: a case study using the straight‐billed reedhaunter Limnoctites rectirostris

“…Therefore, we first modeled SDMs of E. pandanifolium (n = 107), E. horridum (n = 69) and E. eburneum (n = 57) using occurrence data sourced from Global Biodiversity Information Facility (), and used them as inputs into the straight‐billed reedhaunter SDM. Straight‐billed reedhaunter occurrence data (n = 166) were obtained from literature records (Gould 1839, Sanborn , Daguerre , Pereyra , Esteban , Escalante , Zorrilla de San Martín , Gerzenstein and Achával , Canevari et al 1991, Krapovickas et al , Chébez , Ricci and Ricci , Babarskas and Fraga 1998, López‐Lanús et al , Sagrera , Accordi and Barcellos , Accordi and Hartz , Pacheco and Olmos , Aldabe et al , Brummelhaus et al , Gonçalves et al ), Global Biodiversity Information Facility () and eBird () (Fig. 2).…”

Elevation predicts the functional composition of alpine plant communities based on vegetative traits, but not based on floral traits

“…The abundance weighted mean in the trait characteristics within a community defines the mean functional position of each community. First, we quantified the size vol(p n ) and overlap port(p n , p m ) of the community-specific trait spaces using the approach dynamic range boxes (dynRB, Junker et al 2016), which is a robust non-parametric approach to quantify the size and overlap of n-dimensional hypervolumes. dynRB accounts for the distribution of the data within their range, while no assumptions on the underlying distribution are required.…”

“…The framework of n-dimensional hypervolumes considers, unlike other multivariate approaches, each trait equally, does not reduce the number of dimensions, and thus represents a direct representation of functional community composition (Barros et al 2016;Carmona et al 2016;Junker et al 2016;Kuppler et al 2017;Lamanna et al 2014). Accordingly, hypervolumes have been shown to be a valuable approach to track changes in community composition (Barros et al 2016).…”

“…Accordingly, hypervolumes have been shown to be a valuable approach to track changes in community composition (Barros et al 2016). Although the framework of n-dimensional hypervolumes has been proposed 60 years ago to describe niches (Hutchinson 1957), just recently, it became accessible through the development of statistical approaches that calculate the size and overlap of n-dimensional hypervolumes (for description of the different available approaches, see Blonder et al 2014;Carmona et al 2016;Junker et al 2016;Swanson et al 2015). The available approaches differ in the definition of the geometry of hypervolumes, in the number of dimensions that can be considered, and in the assumptions on the underlying distribution of the data.…”

Evaluation and selection of functional diversity metrics with recommendations for their use in life cycle assessments

“…However, this is a relatively new metric which has yet to undergo the assessment stipulated by Table 3 and it is still unclear whether this metric satisfies other properties. In addition to the n-dimensional hypervolume, other recent developments include; Range box (Qiao et al 2017), Minimum ellipse (Swanson et al 2015), Dynamic range box (Junker et al 2016) and Probabilistic hypervolume (Carmona et al 2016). However, these metrics also have yet to undergo stringent tests to reveal whether they conform to important properties or have a link to ecosystem functioning.…”