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

1. 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. 2. 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. 3. 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. 4. The concept of dynamic range boxes reliably computes sizes and overlaps of n-dimensional hypervolumes, whichmakes dynamic range boxes readily applicable for a broad range of data sets to answer questions related to various disciplines.