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The Geometry of Macroevolution: Phenotypic Evolution on Non-Euclidean Manifolds.

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Title: The Geometry of Macroevolution: Phenotypic Evolution on Non-Euclidean Manifolds.
Authors: Boyko, James D.1 (AUTHOR) jboyko@umich.edu, Rabosky, Daniel L.1,2 (AUTHOR)
Source: American Naturalist. Jun2026, Vol. 207 Issue 6, p751-762. 12p.
Subject Terms: Non-Euclidean geometry, Geodesics, Machine learning, Evolutionary theories, Phenotypes, Phylogeny, Dimensional reduction algorithms, Macroevolution
Abstract: Phylogenetic comparative methods typically rely on an often unstated and potentially unrealistic assumption: that phenotypes evolve within a flat Euclidean space. We advocate for explicitly considering the "geometry of macroevolution," proposing that complex developmental and genetic constraints may cause phenotypes to evolve on curved, non-Euclidean manifolds. On such manifolds, the shortest path between two forms (the geodesic) is not a straight line. We demonstrate how measuring evolutionary divergence on a curved manifold with an inappropriate Euclidean metric can systematically underestimate true path lengths, creating analytical artifacts. Specifically, this geometric distortion can produce the appearance of declining evolutionary rates over time, offering a novel complementary explanation for widely observed patterns like age-rate scaling. Characterizing this geometry can be approached through a priori theoretical models or empirically through data-driven manifold learning. The convergence of large-scale phenomic datasets and machine learning is making it increasingly feasible to infer this geometric structure directly from data. Our goal is to encourage the field to move from implicitly assuming a geometry to deliberately characterizing it, ensuring that inferred macroevolutionary patterns reflect biological reality rather than the constraints of our analytical framework. [ABSTRACT FROM AUTHOR]
Copyright of American Naturalist is the property of University of Chicago and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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PubType: Academic Journal
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  Data: The Geometry of Macroevolution: Phenotypic Evolution on Non-Euclidean Manifolds.
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  Data: <searchLink fieldCode="AR" term="%22Boyko%2C+James+D%2E%22">Boyko, James D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jboyko@umich.edu</i><br /><searchLink fieldCode="AR" term="%22Rabosky%2C+Daniel+L%2E%22">Rabosky, Daniel L.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22American+Naturalist%22">American Naturalist</searchLink>. Jun2026, Vol. 207 Issue 6, p751-762. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Non-Euclidean+geometry%22">Non-Euclidean geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesics%22">Geodesics</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Evolutionary+theories%22">Evolutionary theories</searchLink><br /><searchLink fieldCode="DE" term="%22Phenotypes%22">Phenotypes</searchLink><br /><searchLink fieldCode="DE" term="%22Phylogeny%22">Phylogeny</searchLink><br /><searchLink fieldCode="DE" term="%22Dimensional+reduction+algorithms%22">Dimensional reduction algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Macroevolution%22">Macroevolution</searchLink>
– Name: Abstract
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  Data: Phylogenetic comparative methods typically rely on an often unstated and potentially unrealistic assumption: that phenotypes evolve within a flat Euclidean space. We advocate for explicitly considering the "geometry of macroevolution," proposing that complex developmental and genetic constraints may cause phenotypes to evolve on curved, non-Euclidean manifolds. On such manifolds, the shortest path between two forms (the geodesic) is not a straight line. We demonstrate how measuring evolutionary divergence on a curved manifold with an inappropriate Euclidean metric can systematically underestimate true path lengths, creating analytical artifacts. Specifically, this geometric distortion can produce the appearance of declining evolutionary rates over time, offering a novel complementary explanation for widely observed patterns like age-rate scaling. Characterizing this geometry can be approached through a priori theoretical models or empirically through data-driven manifold learning. The convergence of large-scale phenomic datasets and machine learning is making it increasingly feasible to infer this geometric structure directly from data. Our goal is to encourage the field to move from implicitly assuming a geometry to deliberately characterizing it, ensuring that inferred macroevolutionary patterns reflect biological reality rather than the constraints of our analytical framework. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of American Naturalist is the property of University of Chicago and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1086/740145
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 751
    Subjects:
      – SubjectFull: Non-Euclidean geometry
        Type: general
      – SubjectFull: Geodesics
        Type: general
      – SubjectFull: Machine learning
        Type: general
      – SubjectFull: Evolutionary theories
        Type: general
      – SubjectFull: Phenotypes
        Type: general
      – SubjectFull: Phylogeny
        Type: general
      – SubjectFull: Dimensional reduction algorithms
        Type: general
      – SubjectFull: Macroevolution
        Type: general
    Titles:
      – TitleFull: The Geometry of Macroevolution: Phenotypic Evolution on Non-Euclidean Manifolds.
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            NameFull: Boyko, James D.
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            NameFull: Rabosky, Daniel L.
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          Dates:
            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 207
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              Value: 6
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            – TitleFull: American Naturalist
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