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Preparation of Free-Surface Hyperbolic Water Vortices
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Do Hypervolumes Have Holes?

Benjamin Blonder

    The American Naturalist
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    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new mathematical method to detect "holes" or vacant spaces within ecological niches, even in high dimensions. This tool helps identify unconsidered ecological or evolutionary factors influencing species distributions.

    Keywords:
    Hutchinsongeometryholehypervolumeinvasionnichevacant niche

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    Area of Science:

    • Ecology and Evolutionary Biology
    • Quantitative Biology
    • Niche Modeling

    Background:

    • Hypervolumes are essential for visualizing species and community niches and trait distributions.
    • While some niches are convex (fundamental, potential), observed niches (realized) can exhibit 'holes'—unoccupied hyperspace.
    • These holes may indicate unconsidered ecological or evolutionary processes, but detecting them in >2D has been challenging.

    Purpose of the Study:

    • To develop a novel mathematical approach for inferring holes in high-dimensional hypervolumes.
    • To implement this method in the 'hypervolume' R package for practical application.
    • To demonstrate the utility of hole detection by assessing vacant niches in a Galapagos finch community.

    Main Methods:

    • Development of a new mathematical framework to identify unoccupied regions within hypervolumes.
    • Implementation of the algorithm within the 'hypervolume' R package.
    • Application of the method to a dataset of Galapagos finches on Isabela Island to detect vacant niches.

    Main Results:

    • A functional mathematical approach and software tool ('hypervolume' R package) for detecting holes in high-dimensional hypervolumes were successfully developed.
    • The analysis of the Galapagos finch community provided a demonstration of detecting evidence for vacant niches.
    • The developed methods offer new capabilities for exploring ecological and evolutionary questions related to niche structure.

    Conclusions:

    • The developed mathematical and computational tools enable the detection of holes in multidimensional ecological niches for the first time.
    • This advancement provides a novel approach to investigate deviations from expected niche shapes, potentially revealing hidden ecological or evolutionary dynamics.
    • The findings have broad implications for research in ecology and evolutionary biology, offering new avenues for understanding species distributions and community assembly.