The n-dimensional hypervolume

Authors

  • Benjamin Blonder,

    Corresponding author
    1. Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ, USA
    2. Rocky Mountain Biological Laboratory, Crested Butte, CO, USA
    3. Center for Macroecology, Evolution, and Climate, University of Copenhagen, Copenhagen, Denmark
    • Correspondence: Benjamin Blonder, Department of Ecology and Evolutionary Biology, University of Arizona, 1041 E Lowell Street, Tucson, AZ 85721, USA.

      E-mail: bblonder@email.arizona.edu

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  • Christine Lamanna,

    1. Rocky Mountain Biological Laboratory, Crested Butte, CO, USA
    2. Sustainability Solutions Initiative, University of Maine, Orono, ME, USA
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  • Cyrille Violle,

    1. Centre d'Ecologie Fonctionnelle et Evolutive-UMR 5175, CNRS, Montpellier, France
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  • Brian J. Enquist

    1. Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ, USA
    2. Rocky Mountain Biological Laboratory, Crested Butte, CO, USA
    3. The Santa Fe Institute, Santa Fe, NM, USA
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  • Editor: José Alexandre Diniz-Filho

Abstract

Aim

The Hutchinsonian hypervolume is the conceptual foundation for many lines of ecological and evolutionary inquiry, including functional morphology, comparative biology, community ecology and niche theory. However, extant methods to sample from hypervolumes or measure their geometry perform poorly on high-dimensional or holey datasets.

Innovation

We first highlight the conceptual and computational issues that have prevented a more direct approach to measuring hypervolumes. Next, we present a new multivariate kernel density estimation method that resolves many of these problems in an arbitrary number of dimensions.

Main conclusions

We show that our method (implemented as the ‘hypervolume’ R package) can match several extant methods for hypervolume geometry and species distribution modelling. Tools to quantify high-dimensional ecological hypervolumes will enable a wide range of fundamental descriptive, inferential and comparative questions to be addressed.

Ancillary