Biology Reference
In-Depth Information
direction across a sequence of age-specific optima because it could change direction
from age to age, as in the case of the cotton rat discussed above. The direction of the
trajectory, as well as the rate at which shape develops, may be related, in part, to age-
specific functional demands or mortality rates. Curving trajectories for shape have
been documented for several mammalian species (
Zelditch et al., 2003a
; Tanner et al.,
2010b;
La Croix et al., 2011a
), although linear trajectories are detected or assumed in others
(e.g.
Monteiro et al., 1999; Ponce de Leon and Zollikofer, 2001; Strand Vioarsdottir et al.,
2002; Bastir and Rosas, 2004
). In organisms that undergo metamorphosis, transitions in
direction may be abrupt, decoupling larval from juvenile morphogenesis (
Strauss and
Altig, 1992; Ivanovic et al., 2007, 2011
). Whether trajectories are linear, smoothly curving
or abruptly reorienting can have important implications for the evolution of morphology
because the decoupling between phases could allow for their independent evolution.
For example, one study of scapular ontogeny concludes that the shape of the infant
constrains that of the adult (
Young, 2008
)
the shape of the infant is hypothesized
to drive the pattern of postnatal growth. Another view of constraints limiting the
evolutionary flexibility of ontogenetic allometries is based on analyses of craniofacial
form in muroid rodents; according to this hypothesis, functional constraints of later
development, more specifically those due to the biomechanics of mastication, lead to
conserved postweaning ontogenies. Early ontogenies are more flexible, being less con-
strained by function.
In studies that emphasize the biomechanical or other functional interpretations of scal-
ing coefficients, the ratios between linear, areal and volumetric measurements are biologi-
cally meaningful. There are theories that predict the expected values, so it is those values
that need to be measured. Allometric coefficients are also interpretable developmentally,
and many studies of allometry are concerned with the developmental interpretation of the
coefficients. To lay the foundation for that interpretation we introduce the conventional
formalisms for studies of ontogenetic allometry.
FORMALISMS FOR THE ANALYSIS OF ONTOGENETIC ALLOMETRY:
TRADITIONAL MORPHOMETRIC DATA
The traditional formalism for the study of allometry relates the increase in size of one
part (Y) to that of another (X). Often, X is intended to represent the size of the whole
organism. To make our discussion of allometry as concrete as possible, and to ease the
transition from geometric to traditional morphometric data, we will focus on the case of
the piranha, Serrasalmus gouldingi, one of the examples we have used throughout this text.
To analyze its ontogenetic allometry using traditional morphometric data we measure a
variety of lengths and depths (
Figure 11.6
). For our measure of body size we will use the
measurement extending from landmark 1 to landmark 7, which is termed “standard
length” (SL) and is frequently used as the measurement of body size in studies of teleosts,
so, in our example, X
SL. The other 29 measurements are the measures represented by
5
the vector {Y
1
, Y
2
, Y
3
,
Y
29
}. We first discuss the mathematical analysis of allometry,
then follow this with an interpretation of the coefficients obtained by the analysis, and
then consider their developmental significance.
...
