Dear MorphMetters,

Some of you may have been in the auditorium in the Department of Botany, 
University of Vienna, back in March when Philipp Mitteroecker and I were 
the two scheduled discussants for the conference "GMAustria19" on 
applications of geometric morphometrics.  Several of the papers delivered 
there used between-group principal components analysis (bgPCA), and after 
each of those papers I mentioned in the course of my commentary that bgPCA 
was fatally flawed in applications to most GMM data sets and should NEVER 
be used here. In my keynote address, which closed the meeting, I had one 
cryptic slide about this assertion, with an example that flashed on the 
screen but was immediately replaced by the next slide.
The typical response to both my own talk and my criticism of the talks of 
others, as far as bgPCA was concerned, was along the lines of "Hunh?" or 
sometimes "What are you blathering about this time? Isn't bgPCA in the 
standard toolkit?" I answered that the Bookstein paper they should read was 
just then being written, as one of a pair jointly arising from 
conversations with Andrea Cardini, Jim Rohlf, and Paul O'Higgins following 
an original hunch of Cardini's, and that my argument would be pretty 
convincing once it was actually written down.  The claim isn't that people 
are using bgPCA incorrectly. They're using it according to the published 
formulas, yes, but the method itself yields biological nonsense much too 
That was March.  In April, two different articles in Nature (one by Detroit 
et al., one by Chen et al.) buttressed claims about sister species of Homo 
sapiens using the bgPCA method, and so suddenly it became clear that we 
authors had to do something quickly lest this become an epidemic of bad 
biometrics. So we accelerated our writing. My paper was the first to be 
finished, probably because it is a single-authored item by an emeritus with 
no other obligations, and it seemed like a good idea to upload the final 
draft to even before submitting the paper, so that 
any letter to the editors of Nature could include a link to  the argument 
as to exactly WHY bgPCA is nearly always unsound and its inferences invalid 
for applications in contemporary GMM. 
That is the draft that has just appeared as

For those of you who were at the March meeting, this is the argument 
(complete with formulas) defending my stern condemnation there. I won't try 
to summarize it in this morphmet note -- if you're interested, just read 
the abstract on page 1 of the link.  For those of you who have already 
published bgPCA analyses, you know who you are -- my paper argues strongly 
that you need to go back and revisit the inferences of those papers in a 
mood of much more intense multivariate skepticism.  For the rest of you, 
please consider this draft manuscript to be a wake-up call. A technique 
that has appeared in dozens of papers and that was, alas, specifically 
praised by Mitteroecker and Bookstein personally (back in 2011) could 
nevertheless, when examined closely (for the first time!), turn out to be 
algebraic garbage when applied to data sets where there are far more shape 
coordinates than specimens. But isn't that the usual situation in GMM these 
As always, I welcome all responses, both positive and negative. The biorxiv 
posting is permanent, but there is plenty of time for me to make changes 
before the paper is published (at present it has not yet even been 
submitted anywhere), so feel free to try to find the flaws in my argument.  
But I hope you will want to try some of these simulations on your own 
before you argue against mine. You will also want to study the companion 
piece by Cardini, O'Higgins, and Rohlf that should likewise be available 
for download before too long.        
Fred Bookstein

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