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.



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
> -- 
> 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
> http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/

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