Dear All,
Lea's message has generated a very interesting discussion, which as
usual has been very instructive for me.
My points were really basic ones. I am not worried about semilandmarks
(although when I read something like "... subjects were analyzed to
collect between 2700 and 10 400 homologous landmarks from
each rib ..." I do worry a little). My real concern is about first
having clear ideas about why one is measuring something and only then
deciding how to measure it. This was indirectly said by Mike's sentence
"If I suspect curvature is important ...", which implies that only if it
is important I try to measure it.
With faces, Jim's example, I may get a very detailed description
(Pilipp's point) using many points. However, if all I am interested in
is how relatively wide and long faces are, maybe I can get that
information with just 4 points.
A much nicer example on the specificity of what one measures is Charles
and Paul's one on bird wings in one the two papers I mentioned.
Even if I need a very detailed description and I have 10000 points on
faces, the average of my face, Jim, Mike and Philipp's faces, in a study
on human population biology, is still just 4 people out of millions and
cannot be an accurate estimate in that context. Good if better
measurements (more but also specifically tailored for my aim) increase
power, but they won't allow to get away with the need of large samples
for robust results when I am studying small differences.
When, many years ago, in my second publication ever in geometric
morphometrics, I wrote that the mandible of the Vancouver Island marmot
was the most distinctive among all marmot species (despite being the
youngest population), I was far too optimistic. It's a tiny population
and one of the most endangered north American mammals, and all I had was
8 specimens (mostly collected in the same years from probably just a
couple of localities). Only years later when we managed to measure some
50 specimens, including subfossils, from several localities and found
the same results (including the same unusual coronoid process), I became
more confident that those results were robust. Of course, even 50 is not
a really big sample size when comparing closely related species, and I'd
be happier with many more specimens. Besides, that landmark
configuration wasn't great and probably today I would also consider
adding some semilandmarks on curves.
Cheers
Andrea
On 31/05/17 16:42, Mike Collyer wrote:
Dear Lea,
I see others have responded to your inquiry, already. I thought I would add an
additional perspective.
Your question about statistical significance requires asking a follow-up
question. What statistical methods would you intend to use to evaluate
“significance”? If you are worried about the number of landmarks, your concern
suggests you might be using parametric test statistics frequently associated
with MANOVA, like Wilks lambda or Pilai trace. Indeed, when using these
statistics and converting them to approximate F values, one must have many more
specimens than landmarks (more error degrees of freedom than shape variables,
to be more precise), if “significance” is to be inferred from probabilities
associated with F-distributions. Therefore, limiting the number of landmarks
might be a goal.
When using resampling procedures to conduct ANOVA, using fewer landmarks can
paradoxically decrease effect sizes, as an overly simplified definition of
shape becomes implied. We demonstrated this in our paper: Collyer, M.L., D.J.
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for
phenotypes described by high-dimensional data. Heredity. 115: 357-365. This is
consistent with Andrea’s comment about quality over quantity with the caveat
that limited quantity precludes quality. In other words, too few landmarks
translates to limited ability to discern shape differences, because the shape
compared is basic. In the paper, we used two separate landmark configurations:
one with few landmarks and the other with the same landmarks plus sliding
semilandmarks between fixed points, on different populations of fish. We found
that adding the semilandmarks increased the effect size for population
differences and sexual dimorphism. But if we constrained our analyses to
parametric MANOVA for our small samples, we would have to use the simpler
landmark configurations and live with the results.
I do not wish to suggest that adding more landmarks is better. Overkill is
certainly a concern. I would suggest though that statistical power would be
for me less of a concern than a proper characterization of the shape I wish to
compare among samples. If I suspect curvature is important but am afraid to
use (semi)landmarks that would allow me to assess the curvature differences
among groups, opting instead to use just the endpoints of a structure because I
am worried about statistical power, then I just allowed a statistical procedure
to take me away from the biologically relevant question I sought to address.
Andrea is correct that quality is better than quantity, but quantity can be a
burden in either direction (too few or too many). Additionally, statistical
power will vary among statistical methods. Reconsidering methods might be as
important as reconsidering landmarks configurations.
Regards!
Mike
On May 4, 2017, at 5:19 AM, Lea Wolter <leawolter...@gmail.com> 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
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