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Morpho-Functional Analysis Using Procrustes Superimposition by Static Reference

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Abstract

In conventional geometric morphometric analyses of limb long bones, differences in the evolutionary capacity of articular surfaces and non-articular structures often remain unrecognised. It can be shown that areas of high spatial variance dominate shape data, which is problematic for the functional interpretation of limb long bone shape. We herein introduce Procrustes superimposition by static reference (PSSR), a novel analysis strategy that aims to facilitate morpho-functional inference. This procedure exploits the spatial constraint of some reference structures (in our case, articular surfaces) for the superimposition of other subareas (e.g. muscle attachment sites) in relation to that static reference. PSSR allows for the transformation of raw scan data, enabling researchers to extract geometric models of two- and three-dimensional substructures that cannot effectively be integrated with landmarks. As we demonstrate by a simple model analysis for one muscle attachment site, this procedure can yield measures of direct functional relevance. Multivariate analysis of an extensive set of subareas indicates how this type of data relates to conventional shape coordinates. The shape evolution of xenarthran humeri, which has previously been subject to a detailed study (Milne et al., J Zool 278(1):48–56, 2009), serves as a test case. The concept of a variance-based separation of landmark subsets expands mathematical methods by incorporating knowledge about evolutionary constraints. PSSR could therefore find application far beyond the intuitive case study of long bone shape.

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Acknowledgements

We would like to thank Maja Mielke and Jan Wölfer for useful feedback on an early version the manuscript. We appreciate the detailed review and constructive suggestions by Julien Claude and one anonymous reviewer. The following curators/collection managers granted access to specimens that were used in this study, for which we are very thankful: Gerhard Scholtz (Zoologische Lehrsammlung der Humboldt-Universität zu Berlin), Frieder Mayer, Christiane Funk and Steffen Bock (Museum für Naturkunde, Berlin), Thomas M. Kaiser (Centrum für Naturkunde, Universität Hamburg), Anneke H. van Heteren (Zoologische Staatssammlung München), Irina Ruf and Katrin Krohmann (Senckenbergmuseum Frankfurt) and Stefan Merker (Staatliches Museum für Naturkunde, Stuttgart). Funded by the German Research Council (DFG EXC 1027 to FM and JAN and DFG AM 517/1-1 to EA) and by the Alexander von Humboldt Foundation (to EA).

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Author notes

  1. Eli Amson and John A. Nyakatura have contributed equally.

Authors and Affiliations

  1. AG Morphologie und Formengeschichte, Institut für Biologie, Humboldt Universität zu Berlin, Philippstr. 12/13, 10115, Berlin, Germany

    Falk Mielke, Eli Amson & John A. Nyakatura

  2. “Bild Wissen Gestaltung. Ein interdisziplinäres Labor”, Humboldt Universität, Sophienstr. 22a, 10178, Berlin, Germany

    Falk Mielke, Eli Amson & John A. Nyakatura

  3. Applied Veterinary Sciences and Functional Morphology, Universiteit Antwerpen, Universiteitsplein 1, 2610, Wilrijk, Belgium

    Falk Mielke

  4. Museum für Naturkunde, Leibniz-Institut für Evolutions- und Biodiversitätsforschung, Invalidenstr. 43, 10115, Berlin, Germany

    Eli Amson

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  1. Falk Mielke
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Correspondence to Falk Mielke.

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Electronic supplementary material

Below is the link to the electronic supplementary material.

Online Resource S1

: List of scans. (XLSX 11 KB)

Online Resource S2

: List of landmarks. (XLSX 10 KB)

Online Resource S3

: List of subareas. (XLSX 8 KB)

Online Resource S4

: Subarea Selection tool (VTK, python) that uses surface colouration by curvature. (PY 32 KB)

Online Resource S5

: Python Jupyter Notebook tutorial for the processes of PSSR and subarea PCA. (ZIP 232 KB)

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Mielke, F., Amson, E. & Nyakatura, J.A. Morpho-Functional Analysis Using Procrustes Superimposition by Static Reference. Evol Biol 45, 449–461 (2018). https://doi.org/10.1007/s11692-018-9456-9

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