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
> 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
MORPHMET may be accessed via its webpage at http://www.morphometrics.org
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