Seems be a good time to take a step back and discuss what is or is not possible
using Procrustes based morphometrics (a subset of GMM). In addition to trying
to assess variation at a single landmark, there is also a problem with studying
covariation among landmarks. Because p landmarks yields 2p coordinates (in a 2D
study) that raw data are points in a 2p dimensional figure space. After
Procrustes points are in a 2p-4 dimensional space. That means that there must
be correlations among landmarks so that variation is just in a 2p-4 dimensional
space. Perhaps less obvious is that it also constrains the patter of variation
at different landmarks (a function of their distance to the centroid). I wrote
the tpsTri software to allow users to investigate some of these properties for
the simplest case of just 3 landmarks. Perhaps it could be made easier to use
but it can be used to visualize some of these constraints - at least for those
that can be shown for 3 landmarks in 2D. Because it is just for 3 points it
cannot illustrate analyses of variation at different scales. Need more tutorial
software to illustrate principles.
These limitations call into question some methods used in studies on the very
popular topics of integration and modularity. GMM is an excellent tool but it
cannot do the impossible. The fact that one can compute interesting statistics
does not mean that they are reasonable.
Jim
F. James Rohlf
Distinguished Professor, Emeritus and Research Professor
Depts: Anthropology and Ecology & Evolution
Stony Brook University
On 5/13/2021 10:02:53 AM, Polly, P. David <[email protected]> wrote:
I want to second what Chris said (as well as Andrea and others): all
interpretations in geometric morphometric must involve change in one subset of
landmarks relative to another because the Procrustes coordinate system is
arbitrary and scale-less.
I've attached a diagram from one of my lectures that illustrates why that means that you
should not measure an evolutionary rate (or any other kind of change) from one landmark
by itself (if you don't see an attachment, scroll to bottom of thread and see if it is
embedded there). It is derived from the classic "Pinocchio" example and shows
two triangles that represent shapes at the tips of two phylogenetic branches. Procrustes
superimposition minimizes the shape distance between them, but, as Chris said, shape is a
concept that necessarily involves at least three landmarks and a difference in shape is a
shift of one or more of those relative to the others. If you measured a rate of
evolutionary change in each Procrustes superimposed landmark, the rates would be exactly
the same in this example (but opposite in direction). But the biological process that
produced the evolutionary change may not have affected each landmark equally. The other
two superimpositions in my diagram are biologically 100% compatible with the Procrustes
superimposition (they all involve exactly the same relative change between the three
landmarks), but they have drastically different implications for evolutionary rate.
You can measure the rate at which A shifts relative to B&C, but you cannot with
Procrustes based methods ever tell which shifted more or faster. Similarly you
cannot tell which landmark is more variable, only whether one varies relative to
others. Like Chris, I wish I could retract my very first paper using GMM (1998)
because in it I looked at correlation in variance in superimposed molar landmarks
with the variance expected from the developmental process that generates tooth
shape. It was a good idea (I like to think) but the results are nonsense. In 2005
I finally published another paper where I tried to do it right. Unfortunately the
first paper got a lot more attention because the second was necessarily more
esoteric in its methods.
With best wishes,
David
P. David Polly
Earth and Atmospheric Sciences
Biology and Anthropology
Indiana University
1001 E. 10th Street
Bloomington, IN 47405-1405
[email protected] [mailto:[email protected]]
+1 (812) 855-7994
https://pollylab.indiana.edu
On 13 May 2021, at 8:54 AM, Chris Klingenberg <[email protected]
[mailto:[email protected]]> wrote:
Dear morphometricians
I think most of us agree that analyses of landmarks one at a time are not a
good idea. We've all been told this over and over and, if we are teaching
morphometrics, we routinely tell it to our students. But it is actually not
that easy to justify why not.
I think one important point is to think about the language. When we say we are interested
"what landmark X does" or want to know "how landmark Y varies", I think we are
using a linguistic shortcut. Actually, I think we really do not care at all what landmarks do or
how they vary per se. What we are interested in is what they do in relation to the surrounding
morphological structures or how their positions vary in relation to the anatomical axes of the
structure to which they belong.
What we are interested in for most morphological studies is the locations of
landmarks and variation in those locations after we have stripped away the
information of where the specimen is and which way it points. It is not quite
accidental that this is essentially the definition of form (conformation,
size-shape, size-and-shape, or whatever name you may prefer). Whether we are
interested in this or in shape, after size information has also been stripped
away, is a question that depends on the particular research question.
For shape variables (the same is true with some differences for
form/conformation etc.) it is also possible to show formally that it's not
possible for just one landmark in a configuration to change so that the
resulting change is just a shape change. Whatever change you might make to any
landmark, there is always some change in the non-shape components of size,
position and/or orientation. In my (obviously biased) view, the most accessible
explanation for this is Figure 3 in the paper freely available via this link:
https://link.springer.com/article/10.1007/s11692-020-09520-y
[https://link.springer.com/article/10.1007/s11692-020-09520-y]
Even the suggestions of Pietro and Paolo are not about the variation of a
landmark on its own. A distance measurement inevitably involves *two* landmarks
and for each of them is relative to the other one. The local measures of
deformation all are based on calculations involving all the landmarks and a
method for interpolating between them, so again is inherently relative to the
whole configuration.
As a consequence, we can't ever really separate, either logically or
technically via morphometric analyses, how each landmark varies on its own. It
is always the landmark of interest relative to all others. And as a result, we
should not do analyses of morphometric data (superimposed or not) landmark by
landmark, as Andrea and the others in this discussion have agreed.
Of course, there are analyses like this out there (including a particular table
in an old paper of mine -- I wish I could 'unpublish' that table...). If you
encounter them in the literature, ignore them and look at those parts of the
respective studies that do not rely on them. And of course we should not add
new analyses of that kind.
And because language has a role in this, we should also pay attention (as
authors, reviewers or editors of morphometrics papers) to how shape changes are
described in relation to landmarks. Shifts of landmarks are always relative
shifts, and this should be mentioned for all of them. This may require
repeating the word 'relative' rather a lot in some passages, but as this
discussion shows, it is something that can help everyone in the field.
I hope this helps.
Best wishes
Chris
--
***********************************
Christian Peter Klingenberg
School of Biological Sciences
University of Manchester
Michael Smith Building
Oxford Road
Manchester M13 9PT
United Kingdom
Web site: https://morphometrics.uk
E-mail: [email protected]
Phone: +44 161 2753899
Skype: chris_klingenberg
***********************************
-----Original Message-----
From: <[email protected]> on behalf of Diego Astua de Moraes
<[email protected]>
Date: Thursday, 13 May 2021 at 02:09
To: andrea cardini <[email protected]>
Cc: "[email protected]" <[email protected]>
Subject: Re: [MORPHMET2] WE AGREE IT IS STILL WRONG TO DO analyses of landmarks
one at a time in Procrustes shape data
Dear AndreaRegarding your last paragraph, but it also concerns your problem
(1), I am under the impression, totally a guess, I admit that these mistakes
are not necessarily more frequent now, but probably are (and will be) a
recurrent issue that is likely to resurface from time to time. I guess when
less people were in the field, it was easy for everyone to reach out to
everyone and discuss dos and don'ts. The more there are people using GM, and we
can now consider it is a fairly widespread approach, the more it is likely that
one or another error/mistake/misinterpretation will occur again. More people
means more literature, meaning more to read to be actually up to date on
everything. I know some problems lie within the basics of the method, and
should be solved simply by reading the basic literature and textbooks, but more
people also mean more people approaching the method by themselves without any
guidance. One thing is what we teach our own students, another is what can be
expected from a wide variety of students/professionals using the methods and
learning by themselves. If some basic issues in other long established fields
(let's say, the use of proper terms in phylogenetic systematics, or proper
approaches in basic taxonomy) that should be settled for good keep resurfacing
here and there, I guess these problems also will in GM.
However, why they are made by experienced researchers in top journals is
beyond my guess!
Cheers,
Diego
Diego Astúa, D.Sc.
Professor Associado & Curador da Coleção de Mamíferos UFPE
Associate Professor & Curator of Mammals UFPE
_____________________________________________
e-mail: [email protected] / [email protected]
Personal: CV Lattes <http://lattes.cnpq.br/3461530401338795> | ResearchGate
<https://www.researchgate.net/profile/Diego_Astua> | Publons/ResearcherID
<http://www.researcherid.com/rid/A-3583-2010> | ORCID <http://orcid.org/0000-0002-9573-6437> |
Google Scholar <https://scholar.google.com/citations?user=KOaSIDEAAAAJ>
Lab: Website <https://www.ufpe.br/mastozoologia> | Facebook
<https://www.facebook.com/mastozoologiaufpe/> | Instagram
<http://www.instagram.com/labmasto.ufpe>
Em qua., 12 de mai. de 2021 às 11:35, andrea cardini <[email protected]>
escreveu:
Dear All,
many thanks for your replies and thoughts.
I'd split the problem in two (I talk about landmarks but it's similar
with semilandmarks):
1) There are things that simply cannot be done (they're wrong and deeply
misleading at least in biology): interpreting the variance of single
landmarks after a common superimposition with the aim of telling whether
this or that landmark varies more than others; computing the
evolutionary rate of single landmarks one at a time etc. etc. This is
something on which all morphometricians, who developed the methods we're
using and whom I bothered with questions since the end of '90s, agree
and have agreed for a very long time. I am glad to see there's no change
on this issue and simply one should avoid making those mistakes or
following those who keep making them (including in very prestigious
journals).
2) There might be methods that help to guess whether a specific region
(not a single landmark!) is particularly affected by change. Pietro,
Philipp and Paolo mentioned some possibilities. There might be problems
and difficulties here too, but there could be solutions or at least
approximations. I am agnostic on this (with apologies to Paolo, whose
paper has been on my reading list for quite a while: I'll get there, I
promise!).
Right now, however, my worry was about the first issue and those who
answered confirm that nothing revolutionary happened: those were and
still are big mistakes.
Carmelo raised an interesting question about whether this is more or
less common than in the past. Hard to say without a huge review of the
literature. But 30 years after the "revolution" in morphometrics, those
mistakes should not happen at all. Yet, they occur and, when made by
experienced morphometricians and published in top journals, set a very
bad example.
Thanks again for your comments.
Cheers
Andrea
On 12/05/2021 15:11, Paolo Piras wrote:
"Of course, there can be exceptions and a biological signal can be local
and be represented well by a single landmark or a single interlandmark
distance."
I think that a proper evaluation of local deformation could be effective in
interpreting the "localness" of both shape and deformation differences...
*Piras P.*, Profico A., Pandolfi L., Raia P., Di Vincenzo F., Mondanaro
A., Castiglione S., Varano V. (2020). Current options for visualization of
local deformation in modern shape analysis applied to paleobiological case
studies. *Frontiers in Earth Science*, 8:66. doi: 10.3389/feart.2020.00066
IF: 2.689
ATB
Paolo
Il giorno mer 12 mag 2021 alle ore 14:10 [email protected] <
[email protected]> ha scritto:
Dear Andrea,
In principle, I agree that one should avoid interpreting single landmarks
or shape coordinates because
- landmarks are not geometrically independent after GPA (loss of degrees
of freedom)
- landmark displacement vectors depend on the superimposition and, hence,
the other landmark positions (Pinocchio effect)
- often the shape features are not that local but involve a joint shift of
multiple landmarks; in this case, the actual shape patterns cannot be
inferred from looking at each landmark separately.
Formal statistical analyses (e.g., regressions, significance tests) of
each landmark or shape coordinate separately can hardly be interpreted and
are subject to the multiple comparison problem. This is why we have
multivariate stats and GMM. With proper visualizations, such as TPS
deformation grids or series of reconstructed shapes, the Pinocchio effect
does not apply and one can observe even complex shape or form differences.
Of course, there can be exceptions and a biological signal can be local
and be represented well by a single landmark or a single interlandmark
distance. But one cannot know about this before analyzing all the landmarks
jointly!
Best,
Philipp Mitteroecker
On Tuesday, May 11, 2021 at 6:18:33 PM UTC+2 [email protected] wrote:
Dear Dr. Andrea, Fruciano, and Pietro,
I asked a question on integration/modularity in geomorph google forum. I
benefit hugely from Mike's reply.
That post is somewhat related to the current post. So I am here to let
you aware and please feel free to comment further there if you have
interest.
Link to my question:
https://groups.google.com/u/3/g/geomorph-r-package/c/VKpAxHnVW1U
On Tuesday, May 11, 2021 at 7:52:05 PM UTC+8 Carmelo Fruciano wrote:
Dear Andrea,
I've seen this from time to time, but I am not too sure there's been a
recent increase in this.
Some of the most striking cases in my own literature searches and
reading involve genetic mapping of one coordinate at a time (post-GPA) -
as if each coordinate were a separate trait, which is (IMHO) nonsensical.
This is obviously biased because of my own research interests (i.e., I
have seen more in this area because I've read a bit more in this area
than in others, not because they are more frequent in genetic mapping
than in other areas). But these papers are fairly spread over time and I
didn't catch any particular increase in their frequency as of late.
I understand this does not exactly address what you were asking but I
still hope it helps,
Carmelo
--
==================
Carmelo Fruciano
Italian National Research Council (CNR)
IRBIM Messina
http://www.fruciano.org/
==================
On 10 May 2021 14:49, andrea cardini <[email protected]> wrote:
Dear All,
I have the impression that studies analyzing one landmark at a time
after a Procrustes superimposition (plus a possible sliding of
semilandmarks) are beginning to pop up here and there in the biological
literature.
I wonder whether there's some revolutionary evidence, which was
published and I missed, that contradicts a most basic principle of
Procrustes shape analysis: never to analyze Procrustes shape variables
one at a time, including especially the case of pairs or triplets of
2D-3D landmark Procrustes shape coordinates. This is nicely summarized
by Paul in J. Anat. (2000) 197, pp. 103–120; exemplified in Fig. 9 of
doi:10.1371/journal.pone.0025630; related to the problem of analyzing
one PW at a time discussed by Jim (Syst. Biol. 47(1):147± 158, 1998);
and most likely known since the early days of Procrustes GMM.
I would be astonished to find that this is not longer true but I am
happy to be surprised.
Many thanks in advance for refs and feedback.
Please, if you reply directly to me, let me know if I can share your
answer.
Cheers
Andrea
--
Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di
Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 4223140
Adjunct Associate Professor, Centre for Forensic Anthropology, The
University of Western Australia, 35 Stirling Highway, Crawley WA 6009,
Australia
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