Biology Reference
In-Depth Information
trajectories, we also incorporate analyses of disparity to dissect the developmental sources
of disparity. These analyses are done without any information about age, so we next con-
sider hypotheses that require age data to test, and how to test them when species differ in
their ontogenetic trajectories. Finally, we discuss the disparity of ontogeny itself.
WHY
ALLOMETRY IS INTERESTING IN ITS OWN RI
GHT
On purely biomechanical grounds, we often expect organisms to change shape when
they change size in either ontogeny or evolution. Were organisms to grow (or evolve to a
larger size) without changing shape, they would likely decrease their ability to perform
such vital functions as respiration, locomotion and feeding. That is because, under geomet-
ric scaling, a length of x scales to an area of x
2
and a volume of x
3
. To see why that might
impair performance, consider the cross-sectional area of a weight-bearing limb bone. If the
length, area and mass of a small organism are in the proportions of 2:4:8, those for a some-
what larger organism would be 4:16:64, and for a much larger organism they would be
10:100:1000. Thus, length has increased fivefold whereas area increased 25-fold and
volume increased 125-fold. Geometric scaling could cause limbs to buckle under the more
rapidly increasing mass, and also cause bones loaded by force-generating muscles to bend.
For that reason, changes in size are expected to lead to changes in shape to maintain
functional equivalence. This reasoning does not predict changes in proportions of length
measurements (because they scale to the same power). They are functionally equivalent
at constant proportions, i.e. two jaws with the same ratio between input and output
lever arms are equal in their mechanical advantage.
Allometric scaling maintains functional equivalence over a range of sizes for
certain basic physical properties (such as surface area:volume relationships). These might
be expected to scale predictably over an entire ontogenetic series even though young
animals are not just small they are also young and often ecologically different than
older (larger) members of their own species. For that reason, they do not face the same
functional demands but they might for length:surface area or for surface area:volume rela-
tionships. Otherwise we might expect scaling relationships that alter proportions by more
(or less) than predicted from the scaling of lengths to areas to volumes. That by itself is
interesting because it means that, over an individual's life-time, it is increasing its size,
changing its shape, and experiencing transitions in functional demands and that, at every
age, the organism must be competent to perform whatever functions it currently has while
it is continually changing both form and function. How these transformations in
size, shape and function are interrelated is a central question in studies of ontogenetic
allometry.
One question is whether the ontogenetic trajectory is directed towards the optimal
adult shape or instead towards an optimum weighted in favor of the most vulnerable
age. The trajectory may be oriented towards the adult morphology because that mor-
phology is stable for longest, at least in organisms that have determinate morphogenesis.
It may therefore be more consequential to fitness than the morphologies that precede
it. Yet the adult shape will never be reached at all if organisms do not survive vulnerable
pre-adult phases. However, the direction of the trajectory may represent a compromise
