Adding more (semi)landmarks inevitably increases the spatial resolution and
thus allows one to capture finer anatomical details - whether relevant to
the biological question or not. This can be advantageous for the
reconstruction of shapes, especially when producing 3D morphs by warping
dense surface representations. Basic developmental or evolutionary trends,
group structures, etc., often are visible in an ordination analysis with a
smaller set of relevant landmarks; finer anatomical resolution not
necessarily affects these patterns. However, adding more landmarks cannot
reduce or even remove any signals that were found with less landmarks, but
it can make ordination analyses and the interpretation distances and angles
in shape space more challenging.

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An excess of variables (landmarks) over specimens does NOT pose problems to
statistical methods such as the computation of mean shapes and Procrustes
distances, PCA, PLS, and the multivariate regression of shape coordinates
on some independent variable (shape regression). These methods are based on
averages or regressions computed for each variable separately, or on the
decomposition of a covariance matrix.
Other techniques, including Mahalanobis distance, DFA, CVA, CCA, and
relative eigenanalysis require the inversions of a full-rank covariance
matrix, which implies an access of specimens over variables. The same
applies to many multivariate parametric test statistics, such as
Hotelling's T2, Wilks' Lambda, etc. But shape coordinates are NEVER of full
rank and thus can never be subjected to any of these methods without prior
variable reduction. In fact, reliable results can only be obtained if there
are manifold more specimens than variables, which usually requires variable
reduction by PCA, PLS or other techniques, or the regularization of
covariance matrices (which is more common in the bioinformatic community).
For these reasons, I do not see any disadvantage of measuring a large
number of landmarks, except for a waste of time perhaps. If life time is an
issue, one can optimize landmark schemes as suggested by Jim or Aki.
Best,
Philipp
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