I agree with Michael, you cannot have too many semilandmarks. Additional (semi)landmarks may not necessarily add much new information (e.g., they may not change a PCA ordination), but they typically add anatomical details. Usually, this is helpful for reconstructing shapes and for interpretation of results. By contrast, adding variables cannot make statistical results worse. For instance, Rao (1948) has proven that Mahalanobis distances cannot become smaller when adding variables, and hence classification rates and p-values typically become better.

Procrustes shape coordinates are not of full rank, thus statistical methods like ANOVA, DA, and many significance tests require prior reduction to PCs anyway, regardless of the number of semilandmarks. This is also relevant in CVA ordinations, where the number of cases should be several times more the number of variables (see Mitteroecker & Bookstein 2011; alternatives are ordinary PCA or between-group PCA).

You do have to use the same number of semilandmarks per specimen.  I do not agree that one could use too many semilandmarks.  If one performs PCA on Procrustes residuals projected into tangent space, redundancies generated by using more than needed semilandmarks would be revealed by eigenvalues of 0, and these PCs could be removed as shape variables.  Performing ANOVA on the resulting PC scores or Procrustes ANOVA on original Procrustes residuals will produce the same results, projection distortion notwithstanding. But using too many semilandmarks will have no statistical limitation, unless one wishes to use only parametric methods.

Thank you very much for your suggestions, Michael.

I agree with Michael, you cannot have too many semilandmarks. Additional (semi)landmarks may not necessarily add much new information (e.g., they may not change a PCA ordination), but they typically add anatomical details. Usually, this is helpful for reconstructing shapes and for interpretation of results. By contrast, adding variables cannot make statistical results worse. For instance, Rao (1948) has proven that Mahalanobis distances cannot become smaller when adding variables, and hence classification rates and p-values typically become better.

Procrustes shape coordinates are not of full rank, thus statistical methods like ANOVA, DA, and many significance tests require prior reduction to PCs anyway, regardless of the number of semilandmarks. This is also relevant in CVA ordinations, where the number of cases should be several times more the number of variables (see Mitteroecker & Bookstein 2011; alternatives are ordinary PCA or between-group PCA).

Dear Philipp, thank you very much for your answer. I will try to use less landmarks to digitize this curve.

I tried to explain that you do not need to reduce your landmarks.

Dear Philipp and Micheal, thanks again for your attention.  For my situation, the start point and end point are easy to localize, they are homologous among specimens, the entire region I want to study has large morphological change, but they are all derived from the lateral side of the same bone in different species. This region is taxonomically and functionally important. In the first version of the MS, I used 148 semilandmarks along this curve and with the start point and end point as fixed landmarks. The reviewer suggested that I need to test out the number of semilandmarks to include  in analysis. I wonder whether there is a better way to digitize this region. And how could I determine the number of landmarks (should I use landmarks, instead of semilandmarks?) been sampled along this region? Thanks again.   

Dear all,

If I correctly understood Michael and Philip, there is no problem in selecting a large number of landmarks or semilandmarks, even if they exceeded the number of specimens under study, because anyway one should reduce dimensions by means of PCA or similar, am I right?

And that parametric tests are affected but nonparametric ones are not (by the selection of too many landmarks)?

Thanks Deyan for your interesting question!