Biology Reference
In-Depth Information
TABLE 11.7
Two-way Multivariate Analysis of Variance (MANOVA) of Rodent Craniofacial Shape
Between Species (“Taxa”) and Ages (“Age”)
Effect
df
Pillai's Trace
Approx F
Num df
Den df
P
Taxa
1
0.97848
748.46
13
214
,
0.0001
Age
8
2.56727
8.03
104
1768
,
0.0001
taxa:level
4
1.06715
6.07
52
868
,
0.0001
Residuals
226
pairs of species differ in their ontogenies, but based on the tiny angles, the differences
appear very small.
To determine whether scaling might be the dominant cause of morphological variation
we conduct a PCA of the covariance matrix of the log-transformed measurements and
compare the eigenvalues for the first two axes. In the case of the two piranhas, the eigen-
value of PC1 is 2.61; this axis accounts for 99.9%. For PC2, the eigenvalue is 0.010 and this
axis accounts for just 0.4% of the variance. Thus, ontogenetic scaling (and the differential
extension/truncation of ontogenetic allometry) appears to account for nearly all the varia-
tion in the data. This dominance of scaling is evident in the plot of the PC scores for the
two species (
Figure 11.13
). We obtain a similar result for the two rodents. The eigenvalue
of PC1 is 0.915; this axis accounts for 95.5% of the variation in the data. For PC2, the eigen-
value is 0.017 and this axis accounts for merely 1.8% of the variance. Thus, PC1 accounts
for an overwhelming proportion of the variance. As evident from the plot, the older house
mice overlap the neonatal cotton rats along PC1, due to the enormous size difference
between the species (
Figure 11.14
) and the two species are separated along PC2. The onto-
genetic trajectories are slightly oblique to PC1, suggesting that the two species differ in
allometries and not just by a consistent difference in shape (a consistent difference would
be perpendicular to PC1). Thus, for both species, we could conclude that the data are
explained well by a hypothesis of ontogenetic scaling even though the ontogenetic trajecto-
ries are not strictly the same.
Repeating these same analyses using geometric data, we obtain strikingly different
results. In the comparison of ontogenetic trajectories between the two piranhas we obtain an
angle of 34.9
, corresponding to a correlation of 0.819. The angle is large relative to those
obtained by resampling (11.0
, 16.6
). A permutation test similarly determines that the spe-
cies differ significantly (P
0.001). The statistical result agrees with what we obtained from
the traditional morphometric data, but an angle of 35.0
is not small. Analysis of the two
rodent ontogenies yields an angle of 42.7
between the two species, corresponding to a cor-
relation of 0.74, which again are larger than those obtained by resampling within-species
(13.2
, 10.4
). A permutation test similarly determines that the species are more different
than expected by chance (P
,
0.001). Again, the statistical result agrees with what we
obtained from the traditional morphometric data, but an angle of 42.7
is not small.
We can obtain further insight into the meaning of the angles by testing the other null
hypothesis, i.e. that the vectors are no more similar than expected by chance. For the com-
parison between the piranhas,
,
the angles between randomly permuted vectors of
