Seattle, January 15, 2023
Dear MorphMetters,
First, may all of us have a happy, healthy 2023.
I'm writing to alert you to an item of mine just posted at
arxiv.org. "Reworking geometric morphometrics into a methodology
of transformation grids" began as a years-long conversation with
Joe Felsenstein (Seattle) that prodded me into a deep critique
about what we mean by "orientation" in Procrustes. From
there it was a natural extension to more closely examine what
is implied by Procrustes centering and scaling, and then to suss out
why thin-plate splines are often so difficult to
either summarize in words or to translate into hypotheses.
Once I had proceeded as far as Figure 4, the manuscript's argument
took on a life of its own. Some of the references are current, but
(typically for my recent papers) some are over a century old.
The arxiv post is a modest modification of a manuscript I submitted to
Evolutionary Biology earlier this month --- anyone who gets that piece for
review will notice the changes, mainly a softening of its main homily.
In either version the central argument evinces my customary skepticism:
to be a source of useful insights for evolutionary or developmental
biology, GMM needs to supersede the Procrustes toolkit in toto and
should complement the interpolating thin-plate spline by a regression-
based fitting tool not pinned to the exact landmark locations.
Whether you agree, disagree, claim priority for yourself,
Peter Sneath, or somebody else, or have modifications or extensions
to suggest, I'd be pleased to receive any comments on the argument.
And if I use them in any revision I will acknowledge you by name
if you wish me to do so. You can find this arxiv version
(not far from the one under review by the journal) at
http://arxiv.org/abs/2301.05623
which lets you request a .pdf for download.
If you wish to cite it before it is (I hope) ultimately
accepted at the journal, you can use the DOI
https://doi.org/10.48550/arXiv.2301.05623
Here's wishing a year of meaningful coordinate grids
for us all. Fred Bookstein
ABSTRACT:
Today's typical application of geometric morphometrics to
a quantitative comparison of organismal anatomies begins by
standardizing samples of homologously labelled
point configurations for location, orientation, and scale, and then
renders the ensuing comparisons graphically by thin-plate spline
as applied to group averages, principal components,
regression predictions, or canonical variates. The scale-standardization
step has recently come under criticism as unnecessary and
indeed inappropriate, at least for growth studies. This essay
argues for a similar rethinking of the centering and rotation, and
then the replacement of the thin-plate spline interpolant of the
resulting configurations by a different strategy
that leaves unexplained residuals at every landmark individually in
order to simplify the interpretation of the displayed grid as a whole,
the ``transformation grid'' that has been highlighted as the true
underlying topic ever since D'Arcy Thompson's celebrated exposition of 1917.
For analyses of comparisons involving gradients at large
geometric scale, this paper argues for
replacement of all three of the Procrustes conventions by a version
of my two-point registration of 1986 (originally
Francis Galton's of 1907). The choice of the two points interacts
with another non-Procrustes concern, interpretability of the
grid lines of a coordinate system deformed according to a fitted
polynomial trend rather than an interpolating thin-plate spline.
The paper works two examples using previously published midsagittal cranial
data; there result new findings pertinent to the
interpretation of both of these classic data sets.
A concluding discussion considers the possibility that the current
toolkit of geometric morphometrics, centered on Procrustes shape
coordinates and thin-plate splines, is too restricted to suit many of the
interpretive purposes of evolutionary and developmental biology.
Our morphometrics needs to borrow more broadly
from the range of geometric ideas.
KEYWORDS:
Procrustes analysis, thin-plate spline, geometric morphometrics,
Vilmann neurocranial octagons, anthropoid midsagittal crania,
transformation grids, quadratic fits, bilinear maps, cubic fits,
two-point shape coordinates, modularity, baseline registration,
D'Arcy Thompson.
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