I'd like to add a few comments on sampling (landmarks but also
specimens). I hope that some of the other subscribers, who know much
more than I do about morphometrics, will refine and correct my points.
A very short one on my two papers. They make a very simple point: if one
is landmarking just one side of a structure with object symmetry simply
to speed up data collection, then mirror-reconstructing the missing side
will make a nicer visualization and probably make shape data which are
closer to those obtained by landmarking both sides. The difference may
be tiny and I said "probably" because I am reporting results of
empirical studies: out of 11-12 datasets, all but one had shape
distances closer to those of the full bilateral landmark data after
mirror-reconstructing the missing side. This did not work in one dataset
which happened to have a very large amount of fluctuating asymmetry.
To what extent these results are generalizable, I can't say but everyone
can plan a small preliminary analysis to check it in her/his own data.
I fully agree with Aki that, if time, money etc. are not a constraint,
even when one is not interested in asymmetry, it is better to measure
both sides. That's in fact true also for structures with matching symmetry.
In terms of the choice of landmarks, I wish to stress (once more!) that
quality may be more important than quantity: first one should think well
about what she/he wants to measure, which will relate to the specific
question being asked, and then decide about where and how many landmarks
to use. There are at least two wonderful papers I suggested several
times on this issue:
Oxnard & O'Higgins, 2009, Biological Theory 4(1), 84–97.
Klingenberg, 2008, Evol Biol 35:186–190
Then, especially for semilandmarks, I guess that as Aki (and others
before) suggested, one can see what a good compromise is between
information and the number of points (maybe considering also, but not
principally, the visualization).
For sample size, one should consider whether differences are presumably
big (and a small sample might be OK...ish) or small (as in most
microevolutionary studies, which generally require large N). I believe
that Rohlf, already in the early days of geometric morphometrics, had
written a software for exploring statistical power in shape data
(TPSPower) but I am not sure if he kept developing it. In any case,
power and sensitivity (to sampling) analyeses are certainly available in R.
With small differences, although resampling methods may allow to perform
tests even with tiny samples, power will be low and estimates (say, mean
size and shape, variance and covariance etc.) will be likely inaccurate.
Unfortunately, often, the most interesting taxa are rare populations (or
fossils) for which specimens are difficult to find.
A couple of people told me that there's an important paper coming out
soon on sampling error in geometric morphometrics and it might suggest
that one really needs huge samples. I would not be surprised and suspect
that the few empirical studies we did (a couple of papers in
Zoomorphology) were overoptimistic despite already suggesting (more or
less) that one might need several dozens of specimens even when
differences are relatively large and the number of landmarks was not
particularly large. Again, they were empirical studies and one cannot
say how generalizable they are.
Anyway, I look forward to this new paper and hope it will be announced
in MORPHMET, as well as I look forward to Aki's paper.
On 29/05/17 18:35, Aki Watanabe wrote:
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,
On Tuesday, May 9, 2017 at 12:26:04 PM UTC+1, Lea Wolter wrote:
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!
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