Dear Lea,

Unfortunately, there isn't (yet) a magic mathematical formula to determine 
whether you've sampled enough landmarks, but there are some exploratory 
approaches you can take to see if you're landmark sampling is converging to 
the "true" shape variation. One simple thing you can do is sample as many 
landmarks as you can on a representative sampling of specimens, then create 
a PC morphospace. Then, subsample the landmarks (e.g., 75%, 50%, 25% of the 
landmarks) and see if the PC morphospace from these subsampled 
datasets mirror the distribution of shapes of the full dataset. If 
the morphospaces begin deviating from the PC morphospace of the full 
dataset, then you have a visual cue that the subsampling is not adequately 
characterizing the shape variation of your specimens. In terms of a 
statistically significant test for landmark sampling, I suppose one can 
test for correlation between subsampled and full dataset, but because the 
subsampled and full dataset will be auto-correlated to some extent, the 
null would have to reflect this.

Alternatively, I have a script that automatically subsamples the landmarks 
of a given dataset and creates a plot to see how well the subsampled 
datasets converge to the point distribution of the full dataset. If you are 
interested, I would be happy to describe the technique in more detail 
and/or run the analysis on your dataset if you don't mind sending me the 
data. The script is currently under review for a journal, so it's not 
available yet to the public.

Also, as you mention, having more shape variables (i.e., number of 
landmarks x 2 or 3 depending on 2-D or 3-D landmarks) than the number of 
specimens will generally reduce the power of statistical tests. There are 
ways to counter this issue (e.g., Q-mode approach recently proposed by Dean 

Now, concerning the sampling of bilateral landmarks, Andrea Cardini has 
recently written a nice pair of papers on the subject:

Cardini, A. 2016. Left, right or both? Estimating and improving accuracy of 
one-side-only geometric morphometric analyses of cranial variation. J Zool 
Syst Evol Res.

Cardini, A. 2016. Lost in the other half: improving accuracy in geometric 
morphometric analyses of one side of bilaterally symmetric structures. Syst 

These papers highlight the artifact that originates from performing 
Procrustes alignment on "one-side-only" datasets. At least for alignment 
purposes, I suggest sampling both sides of bilaterally symmetric structures.

Hope this helps.

All the best,

On Tuesday, May 9, 2017 at 12:26:04 PM UTC+1, 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 
> Lea

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