Perhaps, but Procrustes superimposition already adds lots of covariances also. It is a bit tricky (meaning that I do not know of a good solution) to preserve the "real" covariances and distinguish them from artifacts of fitting. GM works well for testing differences among means of groups but studying covariances among shape variables is a much more difficult problem. Some ML approaches have been suggested that could minimize the covariances due to superimposition but the ones I have looked at require some very unreasonable biological assumptions about their statistical properties.

Such discussions will not die until there are good solutions or else someone proves that no good solution is possible. I still have hope for some clever idea. _ _ _ _ _ _ _ _ _ F. James Rohlf, Distinguished Prof. Emeritus Depts. of Anthropology and of Ecology & Evolution -----Original Message----- From: alcardini <alcard...@gmail.com> Sent: Tuesday, November 6, 2018 12:35 PM To: F. James Rohlf <f.james.ro...@stonybrook.edu> Cc: mitte...@univie.ac.at; MORPHMET <morphmet@morphometrics.org> Subject: Re: [MORPHMET] Re: semilandmarks in biology Yes, but doesn't that also add more covariance that wasn't there in the first place? Neither least squares nor minimum bending energy, that we minimize for sliding, are biological models: they will reduce variance but will do it in ways that are totally biologically arbitrary. In the examples I showed sliding led to the appearance of patterns from totally random data and that effect was much stronger than without sliding. I neither advocate sliding or not sliding. Semilandmarks are different from landmarks and more is not necessarily better. There are definitely some applications where I find them very useful but many more where they seem to be there just to make cool pictures. As Mike said, we've already had this discussion. Besides different views on what to measure and why, at that time I hadn't appreciated the problem with p/n and the potential strength of the patterns introduced by the covariance created by the superimposition (plus sliding!). Cheers Andrea On 06/11/2018, F. James Rohlf <f.james.ro...@stonybrook.edu> wrote: > I agree with Philipp but I would like to add that the way I think > about the justification for the sliding of semilandmarks is that if > one were smart enough to know exactly where the most meaningful > locations are along some curve then one should just place the points > along the curve and computationally treat them as fixed landmarks. > However, if their exact positions are to some extend arbitrary > (usually the case) although still along a defined curve then sliding > makes sense to me as it minimizes the apparent differences among > specimens (the sliding minimizes your measure of how much specimens differ > from each other or, usually, the mean shape. > > > > _ _ _ _ _ _ _ _ _ > > F. James Rohlf, Distinguished Prof. Emeritus > > > > Depts. of Anthropology and of Ecology & Evolution > > > > > > From: mitte...@univie.ac.at <mitte...@univie.ac.at> > Sent: Tuesday, November 6, 2018 9:09 AM > To: MORPHMET <morphmet@morphometrics.org> > Subject: [MORPHMET] Re: semilandmarks in biology > > > > I agree only in part. > > > > Whether or not semilandmarks "really are needed" may be hard to say > beforehand. If the signal is known well enough before the study, even > a single linear distance or distance ratio may suffice. In fact, most > geometric morphometric studies are characterized by an oversampling of > (anatomical) landmarks as an exploratory strategy: it allows for > unexpected findings (and nice visualizations). > > > > Furthermore, there is a fundamental difference between sliding > semilandmarks and other outline methods, including EFA. When > establishing correspondence of semilandmarks across individuals, the > minBE sliding algorithm takes the anatomical landmarks (and their > stronger biological homology) into account, while standard EFA and > related techniques cannot easily combine point homology with curve or > surface homology. Clearly, when point homology exists, it should be > parameterized accordingly. If smooth curves or surfaces exists, they > should also be parameterized, whether or not this makes the analysis slightly > more challenging. > > > > Anyway, different landmarks often convey different biological signals > and different homology criteria. For instance, Type I and Type II > landmarks (sensu Bookstein 1991) differ fundamentally in their notion of > homology. > Whereas Type I landmarks are defined in terms of local anatomy or > histology, a Type II landmark is a purely geometric construct, which > may or may not coincide with notions of anatomical/developmental > homology. ANY reasonable morphometric analysis must be interpreted in > the light of the correspondence function employed, and the some holds > true for semilandmarks. For this, of course, one needs to understand > the basic properties of sliding landmarks, much as the basic > properties of Procrustes alignment, etc.. For instance, both the > sliding algorithm and Procrustes alignment introduce correlations > between shape coordinates (hence their reduced degrees of freedom). > This is one of the reasons why I have warned for many years and in > many publications about the biological interpretation of raw > correlations (e.g., summarized in Mitteroecker et al. 2012 Evol Biol). > Interpretations in terms of morphological integration or modularity > are even more difficult because in most studies these concepts are not > operationalized. They are either described by vague and biologically > trivial narratives, or they are themselves defined as patterns of > correlations, which is circular and makes most "hypotheses" untestable. > > > > The same criticism applies to the naive interpretation of PCA scree > plots and derived statistics. An isotropic (circular) distribution of > shape coordinates corresponds to no biological model or hypothesis > whatsoever (e.g., Huttegger & Mitteroecker 2011, Bookstein & > Mitteroecker 2014, and Bookstein 2015, all three in Evol Biol). > Accordingly, a deviation from isometry does not itself inform about > integration or modularity (in any reasonable biological sense). > > The multivariate distribution of shape coordinates, including > "dominant directions of variation," depend on many arbitrary factors, > including the spacing, superimposition, and sliding of landmarks as > well as on the number of landmarks relative to the number of cases. > But all of this applies to both anatomical landmarks and sliding > semilandmarks. > > > > I don't understand how the fact that semilandmarks makes some of these > issues more obvious is an argument against their use. > > > > Best, > > > > Philipp > > > > > > > > > > > > > > > Am Dienstag, 6. November 2018 13:28:55 UTC+1 schrieb alcardini: > > As a biologist, for me, the question about whether or not to use > semilandmarks starts with whether I really need them and what they're > actually measuring. > > On this, among others, Klingenberg, O'Higgins and Oxnard have written > some very important easy-to-read papers that everyone doing > morphometrics should consider and carefully ponder. They can be found at: > https://preview.tinyurl.com/semilandmarks > > I've included there also an older criticism by O'Higgins on EFA and > related methods. As semilandmarks, EFA and similar methods for the > analysis of outlines measure curves (or surfaces) where landmarks > might be few or > missing: if semilandmarks are OK because where the points map is > irrelevant, as long as they capture homologous curves or surfaces, the > same applies for EFAs and related methods; however, the opposite is > also true and, if there are problems with 'homology' in EFA etc., > those problems are there also using semilandmarks as a trick to discretize > curves and surfaces. > > Even with those problems, one could still have valid reasons to use > semilandmarks but it should be honestly acknowledged that they are the > best we can do (for now at least) in very difficult cases. Most of the > studies I know (certainly a minority from a now huge literature) seem > to only provide post-hoc justification of the putative importance of > semilandmarks: there were few 'good landmarks'; I added semilandmarks > and found something; therefore they work. > > > > From a mathematical point of view, I cannot say anything, as I am not > a mathematician. On this, although not specific to semilandmarks, a > fundamental reading for me is Bookstein, 2017, Evol Biol (also > available for a few days, as the other pdfs, at the link above). That > paper is one of the most inspiring I've ever read and it did inspire a > small section of my recent Evol Biol paper on false positives in some > of the tests of modularity/integration using Procrustes data. For > analyses using sliding semilandmarks, the relevant figures are Figs > 4-5, that suggest how tricky things can be. If someone worries that > that's specific to my example data (and it could be!), the experiment > is trivial to repeat on anyone's own semilandmark data. > > Taken from the data of the same paper, below you find a PCA of rodent > hemimandibles (adults, within a species) using minBE slid > semilandmarks or just 9 'corresponding' landmarks. The advantage of > semilandmarks, compared to the 9 landmarks, is that they allow to > capture a dominant direction of variation (PC1 accounting for 14% of > shape variance), whose positive extreme (magnified 3 times) is shown > with a really suggestive deformation grid diagram. In comparison, 9 > landmarks do not suggest any dominant direction of variation (each PC > explaining 9-5% of variance), the scatterplot is circular and the TPS shape > diagram much harder to interpret. > > What these two PCAs have in common is that they are both analyses of > random noise (multivariate random normally distributed numbers added > to a mean shape). > > > > All the best > > > > Andrea > > > > 9 LANDMARKS PLUS 22 SLID SEMILANDMARKS > > > <https://groups.google.com/a/morphometrics.org/group/morphmet/attach/d > cce33d95d952/oclbeaidoponnmni.jpeg?part=0.1.1&view=1&authuser=0> > > > 9 LANDMARKS > > > <https://groups.google.com/a/morphometrics.org/group/morphmet/attach/d > cce33d95d952/pebddfgpogepigmi.jpeg?part=0.1.2&view=1&authuser=0> > > > -- > > 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 2058472 > > Adjunct Associate Professor, School of Anatomy, Physiology and Human > Biology, The University of Western Australia, 35 Stirling Highway, > Crawley WA 6009, Australia > > E-mail address: alca...@gmail.com <javascript:> , > andrea....@unimore.it <javascript:> > WEBPAGE: https://sites.google.com/site/alcardini/home/main > > FREE Yellow BOOK on Geometric Morphometrics: > https://tinyurl.com/2013-Yellow-Book > > ESTIMATE YOUR GLOBAL FOOTPRINT: > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > > -- > MORPHMET may be accessed via its webpage at > http://www.morphometrics.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 morphmet+unsubscr...@morphometrics.org > <mailto:morphmet+unsubscr...@morphometrics.org> . > > -- > MORPHMET may be accessed via its webpage at > http://www.morphometrics.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 morphmet+unsubscr...@morphometrics.org. > -- 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 2058472 Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: alcard...@gmail.com, andrea.card...@unimore.it WEBPAGE: https://sites.google.com/site/alcardini/home/main FREE Yellow BOOK on Geometric Morphometrics: http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf ESTIMATE YOUR GLOBAL FOOTPRINT: http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ -- MORPHMET may be accessed via its webpage at http://www.morphometrics.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 morphmet+unsubscr...@morphometrics.org.