Perhaps one of the reasons why analysis of landmarks one at a time is constantly seen nowadays, even after decades' proposal against it, is that researchers are really tempted to follow this approach because the questions that can be answered are sometimes of interest to researchers. Knowing alternative approaches is therefore an important way to help researchers get out of this pitfall!
Here is a scenario where researchers may be tempted to do per-landmark analysis: I am interested in changes of endocranial morphology from 14 to 25 years . I want to know which endocranial region demonstrates the largest morphological change during the investigative period. Certainly one may perform Procrustes ANOVA to test statistical significance of endocranial shape difference between 14 and 25 years and use heatmap to visualize shape differences. But what if researchers are interested in comparing the relative magnitude of shape change across regions? For example, one may wish to ask *if the changes in the frontal region are larger than the changes in the occipital region?* Merely looking at the heatmap might be helpful but some quantitative answer is surely wanted. Tempted by curiosity for this question while not aware of any other possible solutions, researchers may choose to do analysis of landmarks one at a time. This is one typical scenario where researchers can easily fall into the pifall of per-landmark analysis. So here are the questions: (1) Is it a legitimate question that could be answered by Procrustes shape coordinates? (2) If yes, what to do other than per-landmark analysis? I hope answers to this question will stimulate researchers to be better aware of not just what should not be done, but also what are the alternatives. Best regards, Lv On Monday, 17 May 2021 at 19:11:57 UTC+8 [email protected] wrote: > 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, > > Australia > > > > E-mail address: [email protected], [email protected] > > WEBPAGE: https://sites.google.com/view/alcardini2/ > > or https://tinyurl.com/andreacardini > > > > FREE Yellow BOOK on Geometric Morphometrics: > > https://tinyurl.com/yellowmorphobook > > > > ESTIMATE YOUR GLOBAL FOOTPRINT: > > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > > SUPPORT: secondwarning.org <http://secondwarning.org> > > > > -- > > You received this message because you are subscribed to the Google > > Groups "Morphmet" group. > > To unsubscribe from this group and stop receiving emails from it, send > > an email to [email protected] <mailto: > morphmet2%[email protected]>. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/morphmet2/7e5da2bd-3026-12df-522e-a17eed006d24%40gmail.com > . > > > > > > > > -- > > > > You received this message because you are subscribed to the Google Groups > > "Morphmet" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to [email protected] <mailto: > morphmet2%[email protected]>. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/morphmet2/c1b99d79-5ada-44ef-abd3-3068675d23a9n%40googlegroups.com > > < > https://groups.google.com/d/msgid/morphmet2/c1b99d79-5ada-44ef-abd3-3068675d23a9n%40googlegroups.com?utm_medium=email&utm_source=footer > > > > . > > > > > > > > > > -- > > 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 > > > > E-mail address: [email protected], [email protected] > > WEBPAGE: https://sites.google.com/view/alcardini2/ > > or https://tinyurl.com/andreacardini > > > > FREE Yellow BOOK on Geometric Morphometrics: > > https://tinyurl.com/yellowmorphobook > > > > ESTIMATE YOUR GLOBAL FOOTPRINT: > > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > > SUPPORT: secondwarning.org <http://secondwarning.org> > > > > -- > > You received this message because you are subscribed to the Google > Groups "Morphmet" group. > > To unsubscribe from this group and stop receiving emails from it, > send an email to [email protected] <mailto: > morphmet2%[email protected]>. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/0ecfa3dd-800a-e2c6-2f96-3c43fc2d2476%40gmail.com > . > > > > > > > > -- > > You received this message because you are subscribed to the Google > Groups "Morphmet" group. > > To unsubscribe from this group and stop receiving emails from it, > send an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/CAD6G%3DqrPYG_GwQdE%2BSoPaSgQnY8kY9_oVSx8y2nDan_JefRaBA%40mail.gmail.com > > < > https://groups.google.com/d/msgid/morphmet2/CAD6G%3DqrPYG_GwQdE%2BSoPaSgQnY8kY9_oVSx8y2nDan_JefRaBA%40mail.gmail.com?utm_medium=email&utm_source=footer > >. > > > > -- > > You received this message because you are subscribed to the Google > Groups "Morphmet" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/013E8344-A51F-4F70-976F-F06A084EA228%40manchester.ac.uk > . > > > > -- > 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 > > E-mail address: [email protected], [email protected] > WEBPAGE: https://sites.google.com/view/alcardini2/ > or https://tinyurl.com/andreacardini > > FREE Yellow BOOK on Geometric Morphometrics: > https://tinyurl.com/yellowmorphobook > > ESTIMATE YOUR GLOBAL FOOTPRINT: > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > SUPPORT: secondwarning.org > -- You received this message because you are subscribed to the Google Groups "Morphmet" group. 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