Inferring the Nature of Allometry from Geometric Data |
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Authors: | Kim van der Linde David Houle |
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Institution: | (1) Department of Biological Science, Florida State University, 319 Stadium Drive, Tallahassee, FL 32306-4295, USA |
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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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Keywords: | Allometry Drosophila Geometric morphometrics Identifiability problem Variance-covariance matrix Wing shape |
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