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Subject: arching effect and allometry in fish geometric morphometrics
Date: Tue, 16 Nov 2010 07:22:42 -0500
From: Rebeca <[email protected]>
To: <[email protected]>
Dear all,
I am using landmark –based geometric morphometrics to study the
population structure of a marine fish and identify the different stocks
(populations) that dwell around the Iberian Peninsula.
To do this, I have fish samples from several areas but they differ in
size composition (in some areas fish are mostly small whereas in other
the samples consist of large specimens). Thus, it is clear that I need
to correct my dataset for allometry before I compare the shape of the
fish from different areas (using a canonical variate analysis). However,
I recently read about other artifacts in shape studies involving fish,
such as the “arching effect” described in Valentin et al. 2008 (Valentin
et al., 2008. Arching effect on fish body shape in geometric
morphometric studies. Journal of Fish Biology, 73(3):623). According to
these authors, the arching effect refers to the upward and downward
arching of the fish body during landmark capture (when taking the photo)
and is due to slight posture differences between fishes because their
body is flexible.
In this paper, they assess the strength of the arching effect in a
dataset as follows:
First, a series of deformation models is generated by taking pictures of
10 specimens in 20 different arching postures (i.e. , a single specimen
is photographed 20 times in different bending postures, then the next
specimen is photographed in 20 postures and so on). For each deformation
model a Principal component analysis (PCA) is done, where the first
eigenvector summarizes the variation related to upward or donward
bending (around 95% of the total shape variation). Then, the mean first
eigenvector is calculated using the first eigenvector of the 10
deformation models.
After this, a PCA is done for the complete dataset used in the study of
the fish population structure. Then, to see if there is a strong arching
effect in the dataset used to study the population structure of the
fish, the angle between the mean first eigenvector of the deformation
model and the first eigenvector of the dataset is computed. If the angle
between these eigenvectors is small, it would indicate a strong arching
effect in the dataset that needs to be removed before the comparison of
the fish from different areas.
Thus, I started studying the possibility of having an arching effect in
my dataset and after doing some tests, I realized that the strenght of
the arching effect could be also related to the size of the fish
specimens (small specimens are more rigid than medium and large sized
specimens, which tend to bend more easily). Therefore, to understand
better what is happening, I would like to test if the arching effect is
related to size and if the deformtion model (1^st mean eigenvector) and
the allometric vector (regression vector of the regression of shap on
size) are related, to determine what is the best approach to correct the
shape variables before the comparison of fish from different areas, I
mean, if I need to correct for allometry and for the arching effect
separately or if both explain similar shape changes and when I correct
for allometry I also eliminate some of the variability due to the
arching effect.
So, to see if the deformation model is related to size, I was planning
to do a regression of the scores of the first PC of the deformation
model on size (centroid size) and to check if the deformation model
(1^st mean eigenvector) and the allometric vector are related I was
thinking of simply calculating the angle between these two vectors.
Since I am not an expert in these subjects, I would really appreciate
your comments or ideas on this.
Thanks,
Rebeca
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Rebeca P. Rodriguez Mendoza
Marine Research Institute – CSIC
Marine Resources and Ecology Department
Fisheries Unit
Eduardo Cabello 6, 36208.
Vigo, (Pontevedra) Spain.
Tlf. (+34) 986 231 930 Ext. 240
