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 Adams). 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 Biol. 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, Aki 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 -- 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.
