February 1, 2024
Dear MorphMetters,
Happy new year, everybody. I'm pleased to announce
that my article "Quadratic trends: a morphometric tool both
old and new" has been posted over at Evolutionary Biology,
the journal where so much of our important GMM work appears
these days.
The new article drives deeply into rules
for reporting the simplest nonlinear patterns of shape change
over the organism: not only the patterns Julian Huxley called
"growth gradients" back in 1932 but also the polynomial "trend
surfaces" Peter Sneath explored for phylogenetic comparisons
and numerical taxonomy in 1967.
It is a sequel to my article "Reworking geometric
morphometrics" last year that explained why you should always
freely rotate your Cartesian coordinate system before trying
to interpret any deformation of that grid: now we can see exactly
how some important algebraic aspects of descriptions like that depend
on the rotation, and why that dependence matters.
First I introduce a new
application of ellipses -- they can represent the simplest (quadratic)
version of these gradients. Then I explore
their relation to GPA (none), their dependence on choice of
a two-point baseline (through the centroid, please),
their ordination by several new diagrams and versions of PCA
(none involving either Procrustes distance or thin-plate-spline
bending energy), their elaboration for
longitudinal data, and their relation to higher-order methods like
cubic polynomials or quadratic-trend splines. Finally, I suggest
one further way to generate new morphometric characters by
closely examining the azimuthal curves (deformed circles) of an
originally polar coordinate system.
My purpose throughout is to replace the current rhetorical
context of GMM, one mainly concerned with the idea of
"statistical testing" copied from multivariate analysis,
by D'Arcy Thompson's original idea that diagrams should
serve the purpose of _generating_ morphogenetic hypotheses
instead of "testing" hypotheses that arose somewhere else.
I think it will be worth your time to browse all
these new GMM tools and themes.
You can download the paper from
https://link.springer.com/content/pdf/10.1007/s11692-023-09621-4
or write me for a copy. It is Open Access -- download is free to
everybody, along with re-use of words and figures under the usual rules.
As always I welcome your thoughts, favorable or un-,
about any aspect of its formulas, diagrams, or arguments.
With every good wish for a productive 2024, Fred Bookstein
[email protected],[email protected]
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