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Title: A unifying framework for quantifying and comparing n‐dimensional hypervolumes
Abstract

The quantification of Hutchinson's n‐dimensional hypervolume has enabled substantial progress in community ecology, species niche analysis and beyond. However, most existing methods do not support a partitioning of the different components of hypervolume. Such a partitioning is crucial to address the ‘curse of dimensionality’ in hypervolume measures and interpret the metrics on the original niche axes instead of principal components. Here, we propose the use of multivariate normal distributions for the comparison of niche hypervolumes and introduce this as the multivariate‐normal hypervolume (MVNH) framework (R package available onhttps://github.com/lvmuyang/MVNH).

The framework provides parametric measures of the size and dissimilarity of niche hypervolumes, each of which can be partitioned into biologically interpretable components. Specifically, the determinant of the covariance matrix (i.e. the generalized variance) of a MVNH is a measure of total niche size, which can be partitioned into univariate niche variance components and a correlation component (a measure of dimensionality, i.e. the effective number of independent niche axes standardized by the number of dimensions). The Bhattacharyya distance (BD; a function of the geometric mean of two probability distributions) between two MVNHs is a measure of niche dissimilarity. The BD partitions total dissimilarity into the components of Mahalanobis distance (standardized Euclidean distance with correlated variables) between hypervolume centroids and the determinant ratio which measures hypervolume size difference. The Mahalanobis distance and determinant ratio can be further partitioned into univariate divergences and a correlation component.

We use empirical examples of community‐ and species‐level analysis to demonstrate the new insights provided by these metrics. We show that the newly proposed framework enables us to quantify the relative contributions of different hypervolume components and to connect these analyses to the ecological drivers of functional diversity and environmental niche variation.

Our approach overcomes several operational and computational limitations of popular nonparametric methods and provides a partitioning framework that has wide implications for understanding functional diversity, niche evolution, niche shifts and expansion during biotic invasions, etc.

 
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NSF-PAR ID:
10377326
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley-Blackwell
Date Published:
Journal Name:
Methods in Ecology and Evolution
Volume:
12
Issue:
10
ISSN:
2041-210X
Page Range / eLocation ID:
p. 1953-1968
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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