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Morphometric Spaces, Shape Components and the Effects of Linear Transformations

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Advances in Morphometrics

Part of the book series: NATO ASI Series ((NSSA,volume 284))

Abstract

The various types of mathematical spaces used in morphometrics are reviewed with emphasis given to the distinctions between the physical space of the organism, shape space and tangent spaces. The effects of linear transformations of the coordinates of the landmarks (on the specimens or the reference) on various statistical analyses and estimates of the uniform and nonaffine components of shape variation are presented. It is shown why statistical analyses of the estimates of the nonaffine components of shape variation are sensitive to affine transformations of the reference or the specimens (which may seem counterintuitive). Some implications of these results on the choices of methods for the study of shape are discussed.

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Author information

Authors and Affiliations

  1. Department of Ecology and Evolution, State University of New York, Stony Brook, New York, 11794-5245, USA

    F. James Rohlf

Authors
  1. F. James Rohlf
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Editor information

Editors and Affiliations

  1. Department of Biology, Mail: Dept. Invertebrates, Queens College of the City University of New York, Flushing, New York, USA

    Leslie F. Marcus

  2. American Museum of Natural History, CPW at 79th Street, 10024, New York, New York, USA

    Leslie F. Marcus

  3. Dipartimento di Biologia Animale e dell’Uomo, University of Rome “La Sapienza”, via Borelli 50, 00161, Rome, Italy

    Marco Corti

  4. University of Rome “La Sapienza”, Rome, Italy

    Anna Loy

  5. Department of Biology, Osborn Memorial Laboratory, Yale University, P.O. Box 208104, 06520-8104, New Haven, Connecticut, USA

    Gavin J. P. Naylor

  6. Department of Ecology and Evolution, State University of New York, 11794, Stony Brook, New York, USA

    Dennis E. Slice

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© 1996 Springer Science+Business Media New York

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Rohlf, F.J. (1996). Morphometric Spaces, Shape Components and the Effects of Linear Transformations. In: Marcus, L.F., Corti, M., Loy, A., Naylor, G.J.P., Slice, D.E. (eds) Advances in Morphometrics. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9083-2_11

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  • DOI: https://doi.org/10.1007/978-1-4757-9083-2_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9085-6

  • Online ISBN: 978-1-4757-9083-2

  • eBook Packages: Springer Book Archive

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