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Inferring the Nature of Allometry from Geometric Data

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Abstract

The form of an organism is the combination of its size and its shape. For a sample of forms, biologists wish to characterize both mean form and the variation in form. For geometric data, where form is characterized as the spatial locations of homologous points, the first step in analysis superimposes the forms, which requires an assumption about what measure of size is appropriate. Geometric morphometrics adopts centroid size as the natural measure of size, and assumes that variation around the mean form is isometric with size. These assumptions limit the interpretation of the resulting estimates of mean and variance in form. We illustrate these problems using allometric variation in shape. We show that superimposition based on subsets of relatively isometric points can yield superior inferences about the overall pattern of variation. We propose and demonstrate two superimposition techniques based on this idea. In subset superimposition, landmarks are progressively discarded from the data used for superimposition if they result in significant decreases in the variation among the remaining landmarks. In outline superimposition, regularly distributed pseudolandmarks on the continuous outline of a form are used as the basis for superimposition of the landmarks contained within it. Simulations show that these techniques can result in dramatic improvements in the accuracy of estimated variance-covariance matrices among landmarks when our assumptions are roughly satisfied. The pattern of variation inferred by means of our superimposition techniques can be quite different from that recovered from full generalized Procrustes superimposition. The pattern of shape variation in the wings of drosophilid flies appears to meet these assumptions. Adoption of superimposition procedures that incorporate biological assumptions about the nature of size and of the variation in shape can dramatically improve the ability to infer the pattern of variation in geometric morphometric data.

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Acknowledgments

We thank D. Adams, E. Marquez, F. J. Rohlf, and M. Zelditch for discussions and a reviewer and B. Hallgrimsson for their comments on the manuscript. This work was funded by NSF grant DEB-0129219 to D.H. and by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant U54 RR021813. Information on the National Centers for Biomedical Computing can be obtained from http://nihroadmap.nih.gov/bioinformatics.

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  1. Department of Biological Science, Florida State University, 319 Stadium Drive, Tallahassee, FL, 32306-4295, USA

    Kim van der Linde & David Houle

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  1. Kim van der Linde
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Correspondence to Kim van der Linde.

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van der Linde, K., Houle, D. Inferring the Nature of Allometry from Geometric Data. Evol Biol 36, 311–322 (2009). https://doi.org/10.1007/s11692-009-9061-z

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