Dear All,
Lea's message has generated a very interesting discussion, which as usual has been very instructive for me.

My points were really basic ones. I am not worried about semilandmarks (although when I read something like "... subjects were analyzed to collect between 2700 and 10 400 homologous landmarks from each rib ..." I do worry a little). My real concern is about first having clear ideas about why one is measuring something and only then deciding how to measure it. This was indirectly said by Mike's sentence "If I suspect curvature is important ...", which implies that only if it is important I try to measure it.

With faces, Jim's example, I may get a very detailed description (Pilipp's point) using many points. However, if all I am interested in is how relatively wide and long faces are, maybe I can get that information with just 4 points. A much nicer example on the specificity of what one measures is Charles and Paul's one on bird wings in one the two papers I mentioned.

Even if I need a very detailed description and I have 10000 points on faces, the average of my face, Jim, Mike and Philipp's faces, in a study on human population biology, is still just 4 people out of millions and cannot be an accurate estimate in that context. Good if better measurements (more but also specifically tailored for my aim) increase power, but they won't allow to get away with the need of large samples for robust results when I am studying small differences. When, many years ago, in my second publication ever in geometric morphometrics, I wrote that the mandible of the Vancouver Island marmot was the most distinctive among all marmot species (despite being the youngest population), I was far too optimistic. It's a tiny population and one of the most endangered north American mammals, and all I had was 8 specimens (mostly collected in the same years from probably just a couple of localities). Only years later when we managed to measure some 50 specimens, including subfossils, from several localities and found the same results (including the same unusual coronoid process), I became more confident that those results were robust. Of course, even 50 is not a really big sample size when comparing closely related species, and I'd be happier with many more specimens. Besides, that landmark configuration wasn't great and probably today I would also consider adding some semilandmarks on curves.



On 31/05/17 16:42, Mike Collyer wrote:
Dear Lea,

I see others have responded to your inquiry, already.  I thought I would add an 
additional perspective.

Your question about statistical significance requires asking a follow-up 
question.  What statistical methods would you intend to use to evaluate 
“significance”?  If you are worried about the number of landmarks, your concern 
suggests you might be using parametric test statistics frequently associated 
with MANOVA, like Wilks lambda or Pilai trace.  Indeed, when using these 
statistics and converting them to approximate F values, one must have many more 
specimens than landmarks (more error degrees of freedom than shape variables, 
to be more precise), if “significance” is to be inferred from probabilities 
associated with F-distributions.  Therefore, limiting the number of landmarks 
might be a goal.

When using resampling procedures to conduct ANOVA, using fewer landmarks can 
paradoxically decrease effect sizes, as an overly simplified definition of 
shape becomes implied.  We demonstrated this in our paper: Collyer, M.L., D.J. 
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for 
phenotypes described by high-dimensional data. Heredity. 115: 357-365.  This is 
consistent with Andrea’s comment about quality over quantity with the caveat 
that limited quantity precludes quality.  In other words, too few landmarks 
translates to limited ability to discern shape differences, because the shape 
compared is basic.  In the paper, we used two separate landmark configurations: 
one with few landmarks and the other with the same landmarks plus sliding 
semilandmarks between fixed points, on different populations of fish.  We found 
that adding the semilandmarks increased the effect size for population 
differences and sexual dimorphism.  But if we constrained our analyses to 
parametric MANOVA for our small samples, we would have to use the simpler 
landmark configurations and live with the results.

I do not wish to suggest that adding more landmarks is better.  Overkill is 
certainly a concern.  I would suggest though that statistical power would be 
for me less of a concern than a proper characterization of the shape I wish to 
compare among samples.  If I suspect curvature is important but am afraid to 
use (semi)landmarks that would allow me to assess the curvature differences 
among groups, opting instead to use just the endpoints of a structure because I 
am worried about statistical power, then I just allowed a statistical procedure 
to take me away from the biologically relevant question I sought to address.  
Andrea is correct that quality is better than quantity, but quantity can be a 
burden in either direction (too few or too many).  Additionally, statistical 
power will vary among statistical methods.  Reconsidering methods might be as 
important as reconsidering landmarks configurations.


On May 4, 2017, at 5:19 AM, Lea Wolter <> wrote:

Hello everyone,

I am new in the field of geometric morphometrics and have a question for my 
bachelor thesis.

I am not sure how many landmarks I should use at most in regard to the sample 
size. I have a sample of about 22 individuals per population or maybe a bit 
less (using sternum and epigyne of spiders) with 5 populations.
I have read a paper in which they use 18 landmarks with an even lower sample 
size (3 populations with 20 individuals, 1 with 10). But I have also heard that 
I should use twice as much individuals per population as land marks...

Maybe there is some mathematical formula for it to know if it would be 
statistically significant? Could you recommend some paper?

Because of the symmetry of the epigyne I am now thinking of using just one half 
of it for setting landmarks (so I get 5 instead of 9 landmarks). For the 
sternum I thought about 7 or 9 landmarks, so at most I would also get 18 
landmarks like in the paper.

I would also like to use two type specimens in the analysis, but I have just 
this one individual per population... would it be totally nonesens in a 
statistical point of view?

Thanks very much for your help!

Best regards

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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

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