A unifying framework for quantifying and comparing n-dimensional hypervolumes

Muyang Lu, Ecology and Evolutionary Biology, Yale Unversity, New Haven, CT, Kevin Winner, Ecology & Evolutionary Biology, Yale University, New Haven, CT and Walter Jetz, Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT

Background/Question/Methods The quantification of Hutchison’s n-dimensional hypervolume has enabled substantial progress in community ecology, species niche analysis and beyond. While non-parametric methods for quantifying and comparing hypervolumes are popular, they do not support a partitioning of the different components and drivers of hypervolume variation. Here, we propose as alternative the use of multivariate normal distributions for the assessment and comparison of niche hypervolumes and introduce this as the multivariate-normal hypervolume (MVNH) framework.The framework provides parametric measures of the size and dissimilarity of niche hypervolumes, each of which can be partitioned into biologically interpretable components. Specifically, We use 1) the determinant of the covariance matrix (i.e. the generalized variance) of a MVNH as a measure of total niche size, which can be partitioned into the components of univariate niche variances and a correlation component; and 2) the Bhattacharyya distance between two MVNHs as a measure of niche dissimilarity, which can be partitioned into the components of Mahalanobis distance between hypervolume centroids and the determinant ratio which measures hypervolume size difference.
Results/Conclusions Our approach overcomes several operational and computational limitations of non-parametric methods and provides a framework that offers both unification and granularity in the assessment of niche volumes and differences, which has wide implications for understanding niche evolution, niche shifts and expansion during biotic invasions etc.