New approaches for delineating n‐dimensional hypervolumes

Abstract

Hutchinson's n‐dimensional hypervolume concept underlies many applications in contemporary ecology and evolutionary biology. Estimating hypervolumes from sampled data has been an ongoing challenge due to conceptual and computational issues. We present new algorithms for delineating the boundaries and probability density within n‐dimensional hypervolumes. The methods produce smooth boundaries that can fit data either more loosely (Gaussian kernel density estimation) or more tightly (one‐classification via support vector machine). Further, the algorithms can accept abundance‐weighted data, and the resulting hypervolumes can be given a probabilistic interpretation and projected into geographic space. We demonstrate the properties of these methods on a large dataset that characterises the functional traits and geographic distribution of thousands of plants. The methods are available in version ≥2.0.7 of the hypervolume r package. These new algorithms provide: (i) a more robust approach for delineating the shape and density of n‐dimensional hypervolumes; (ii) more efficient performance on large and high‐dimensional datasets; and (iii) improved measures of functional diversity and environmental niche breadth.

hyperoverlap: Detecting biological overlap in n‐dimensional space

“…We can use hypervolume concepts to analyse patterns of overlap between sets of point data in multidimensional space (e.g. Blonder et al, ). Current hypervolume approaches first map each observation in an n ‐dimensional space, where the dimensions are the chosen variables.…”

“…MaxEnt; Phillips, Anderson, & Schapire, ); to classify points in ecological space as ‘in’ or ‘out’ of the modelled niche (e.g. hypervolume_exclusion_test; Blonder et al, ); or to define the boundary of the niche in n‐dimensional space (e.g. hypervolume_svm; Blonder et al, ).…”

“…hypervolume_exclusion_test; Blonder et al, ); or to define the boundary of the niche in n‐dimensional space (e.g. hypervolume_svm; Blonder et al, ). Once described by an appropriate model, two hypervolumes may be compared and the volumes of the overlapping and unique regions can be measured (see hypervolume_set, hypervolume_overlap_statistics functions; Blonder et al, ).…”

“…Because many biological variables are strongly correlated, this method is limited in the variables that can be analysed. Blonder's hypervolume package (Blonder, Lamanna, Violle, & Enquist, ; Blonder et al, ) includes a range of functions for hypervolume modelling and comparison. In both hypervolume and hyperoverlap the shape of the hypervolume is not defined by a priori expectations, so we have used hypervolume as a standard to evaluate the performance of hyperoverlap .…”

Model‐based hypervolumes for complex ecological data

“…Accounting for data structure is possible in non‐parametric approaches by incorporating a weighting structure (Breunig , Blonder et al. ) so that observations do not all contribute equally to the calculated hypervolume. We aim to demonstrate that multidimensional parametric approaches can be generalized to account for complex data structures in an analogous way to incorporating data structure into univariate models.…”