Biology Reference
In-Depth Information
youngest and oldest ages are most easily done by calculating the predicted shape for that
stage (from the regression equation) then adding the residuals around the regression line
to the predicted shape. The lengths of the trajectories can be calculated from the distance
between the predicted shapes at the youngest and oldest stages, and the comparison
between distances can be done by computing the distance between the shapes at the two
stages, testing the null hypothesis that the distances do not differ.
Example: Ontogeny of Shape and Disparity
In this example, we combine a comparative analysis of ontogeny with an analysis of shape
disparity, measured at two developmental stages
at the transition from larval to juvenile
growth and at maximum adult body size. We use the approach presented by
Adams and
Collyer (2009)
for the comparison of phenotypic trajectories. We begin with a Multivariate
Analysis of Variance (MANOVA, see Chapter 9). Just as we did in the analysis of traditional
morphometric data, in this one we use MANOVA rather than MANCOVA because we are
comparing the mean shapes for each species at two developmental stages rather than using a
continuous factor (size) as a covariate. We find that both factors, plus the interaction term, are
highly significant statistically (
Table 11.8
). The species all differ statistically significantly in
shape at the transition from larval to juvenile growth; some of the distances between species
are large (
Table 11.9
). All but two species differ in their ontogenetic trajectories of shape
(
Table 11.10
) and several (but not all) also differ in lengths of the trajectories (
Table 11.11
). The
trajectories for all nine species are shown in the space of the first two principal components
for body shape (
Figure 11.20
); this plot obviously cannot do justice to the complexity of these
data. Nevertheless, it does show that three species on the left side of the plot (S. manueli,
S. gouldingi and S. elongatus) have distinctive juvenile shapes and two of them, but not the
third (S. elongatus), develop in the direction of the other Serrasalmus.
To determine what impact that combination of modifications has on disparity, we will
compute the disparity of body shape at the transition from larval to juvenile development
and again at maximum adult size. To do this, we will estimate the predicted shape at the
two developmental stages and compute disparity of the means for each stage. Disparity is
calculated as the square root of the average of the squared distances from each species to
the mean of the distribution (see Chapter 10 for further discussion of measuring disparity).
To determine if the disparities of juveniles and adults differ significantly, we can repeat-
edly resample individuals within species and repeat the calculation of the predicted values
TABLE 11.8
Two-way Multivariate Analysis of Variance (MANOVA) of Piranha Body Shape Across Species
(“Taxa”) and Developmental Stage (“Stage”)
Effect
Df
Pillai's Trace
Approx F
Num Df
Den Df
P
Taxa
8
5.461
49.60
256
5904
2.2e
16
,
Stage
1
0.99
2343.08
32
731
2.2e
16
,
Taxa:Stage
8
5.04
39.26
256
5904
2.2e
16
,
Residuals
762
