Table I
|
|
tangent
approx.:
|
Porch '88
|
U.Tenn.
|
Canton S
|
| Procrustes: |
|
m |
f |
m |
f |
m |
f |
| Porch
'88 |
m |
0 |
15.00 |
24.59 |
19.54 |
20.32 |
21.79 |
|
f |
15.00 |
0 |
33.85 |
23.70 |
27.65 |
20.03 |
| U.
Tenn. |
m |
24.59 |
33.86 |
0 |
14.06 |
21.44 |
29.39 |
|
f |
19.54 |
23.70 |
14.06 |
0 |
19.22 |
20.01 |
| Canton
S |
m |
20.32 |
27.66 |
21.45 |
19.23 |
0 |
14.89 |
|
f |
21.79 |
20.03 |
29.40 |
20.01 |
14.90 |
0 |
Table
I. Morphological distance matrix of Procrustes distances (lower triangular
matrix) and tangent space approximations (upper triangular matrix) between
averaged landmark coordinates of the two sexes (m/f) of three Drosophila
melanogaster strains. The tabulated distances are seen to be not exactly
symetrical due to the fact that differences in tangent space are exhibited
as rotations of landmarks on a spherical surface while Procrustes distances
are measured as differences on a plane in Euclidean space. A chord
connecting points on the sphere underestimates the surface distance between
two points moreso for distant points on the sphere. When shape differences
are small, as is the case with the Drosophila wing dimorphisms,
the difference between the two measures is very small (here seen as at
most a unit smaller difference in the fourth significant digit of the larger
approximations). This was confirmed by application of the tpsSmall
program which measured the correlation between Procrustes and tangent space
differences to be very close to unity. The calculated distances
for Procrustes (shape
space) and its tangent
approximation (tangent
space) are by deffinition not equal, but are usually close
to equal when differences in shape are small. This direct confirmation
of the close equivalence of Procrustes distances and their tangent space
approximations further argues that the proceding analysis using thin plate
splines (done in tangent space) is not a distortion of reality. Trees
were subsequently built using the Phylip distance matrix algorithms from
symetric Procrustes matrices. It is seen that similarly small Procrustes
distances are obtained by comparing male and females within each strain.
Last Update: 97/06/16
Name: Joe Kunkel