Dear All,
I am really grateful to all those who contributed to this discussion,
which I found really helpful, mostly clear and certainly rich of well
made points.
I am glad that I don't need to go back to 'esoteric' literature, because
the explanations many of you have provided (here and in previous
publications for biologists), in plain language and with clear examples,
do not require a deep knowledge of maths, which I don't have.
One should know her/his target readership/audience, and adapt the
message. When I was a student, the vast majority of biology and natural
science students were terrorized by maths and stats; 30 years after the
situation hasn't changed. Most mathematicians and statisticians in Italy
can't teach biologists, but luckily this isn't inevitable. The
Anglosaxon literature for 'non-numerically oriented' readers is full of
excellent textbooks which have abandoned the ineffective formal
traditional way of teaching and adopted a descriptive 'problem-based'
approach with plain language, simple well described examples and very
few equations. What's best in theory (assuming it is not a matter of
opinion) may not be what's best in practice, which reminds of the old
academic joke about the famous professor: "We made him/her Professor of
X ... but now we have to hire someone else who could teach students".
Science should be understandable by a majority, and not just a few who
are gifted or blessed by having the chance to go to the best schools.
That works at all levels. In the journal club I organize with some of my
former students, and in which we read on all topics (except
morphometrics!), they clearly spot leading scientists who can deliver
intuitive messages even when using highly quantitative methods, as well
as others who totally fail and seem to write for a tiny circle of
experts despite publishing in journals with very broad readerships.
This brings me back memories of when, in 2005 in York, we were reading
together some of the chapters of the Green Book, which had just been
published: regardless of whether we agreed or not with the authors on
everything, we were all impressed by how well written the book was (with
the maths available but organized in subsections that could be initially
skipped and read later after gaining a basic understanding of a method).
How much that book, even with some potential inaccuracies, has helped
GMM to become a popular analytical tool in biology is likely
underestimated.
I apologize with those whose papers I forgot to mention (certainly, but
not only, Chris' contribution, whose fig. 3 now I appreciate better). On
the limitations of analyses and interpretations of Procrustes shape data
there are several other very good refs, some which are probably more
recent and I am simply less familiar with.
I liked a lot David's slide, that makes the point about the misleading
interpretation of evolution one landmark at a time very clear.
Leandro raised the important point of 'data dredging'. One should
measure what's relevant, instead of measuring as much as possible and
maybe then mine the data until something is found. This was also an
implication of Pietro's comment about the usefulness of traditional
morphometrics: with my series of papers on evolutionary allometry in
mammalian crania, it took me a long time to understand that all I was
able to say was simply in relation to the relative size of the snout and
the braincase. Procrustes shape analysis using dozens of landmarks was
either inappropriate or simply not necessary, which is why in the end I
omitted all of that from the 'big' study in Evol. Biol.: the answers
were the same, but GMM added irrelevant complexity for that specific
study question.
Thanks Jim for mentioning that the point I raised also relates to the
problems with analyses of integration and modularity using Procrustes
shape data. In fact, that was another issue in some of the papers with
analyses of landmarks one at a time. Although it may or may not have
practical relevance depending on the specific dataset, to my knowledge,
the problems I stressed in the paper on spurious results (also in Evol.
Biol. and later in Zoomorphol.) are still there and should be at least
discussed when using those methods. Indeed, with slid semilandmarks,
inaccurate spurious results may occur also with the partial warp
integration/disintegration approach, as I showed in the last example of
the paper.
Cheers
Andrea
PS
Norm, we once jacknifed landmarks to test the sensitivity of results to
the specific choice of the configuration. I think it was in Cardini &
Elton, 2008, Biol. J. Linn. Soc. I see that approach as simply checking
precision or the robustness of results in relation to that specific
configuration: it is useful but, if we had chosen the 'wrong' set of
points, our results could be robust and yet inaccurate.
I guess you're suggesting it as a way to exclude subsets of landmarks to
check if a specific finding depends on measuring (or not) certain
regions of a structure. It could be interesting but I am not sure
whether there might be other issues: the relationship of other points to
those which are left out is no longer measured and data are in a
different shape space (Chris' comment is probably relevant here).
On 14/05/2021 23:16, [email protected] wrote:
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 <(812)%20855-7994>
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 <+44%20161%20275%203899>
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,
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Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 4223140
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