Biology Reference
In-Depth Information
Returning to our squirrel jaw example, we may wish to consider other factors besides
climate, which may seem to be only indirectly associated with jaw shape. We might
instead prefer to characterize the differences in what is eaten (hard vs soft, tough vs brittle,
thin shell vs thick). Given that most animals have varied diets, we might choose to classify
diets according to preferred foods or the preponderance of foods eaten, or the ones that
are critical to winter survival. Care must be taken in the construction of these variables to
ensure that the variables and the scores on those variables are independent. For example,
scoring diet components as percentages of the total (e.g. 10% vertebrates, 50% arthropods,
40% vegetation) could produce errors of inference from miscounting the number of inde-
pendent variables (and thus, degrees of freedom) as well as incurring the other problems
that arise from the use of ratios (Atchley et al., 1976).
Correlation of jaw shape with material properties of food may still be too indirect
an explanation for variation in shape. We may still question why squirrels that eat a high
proportion of hard foods have differently shaped jaws from those that eat a low pro-
portion of hard foods. To answer this question, it may be necessary to measure jaw
performance directly (e.g., the relationship between forces exerted by muscles and those
applied to the food, or the deformations experienced by the bone when muscles contract).
Correlations of these performance measures with shape may still not answer our ecomor-
phological question because shape may not directly translate into a relevant functional
parameter like mechanical advantage
a ratio of two lever arm lengths. Indeed, if the
answer to the question lies in an analysis of variables that are not shape and is sufficiently
addressed by them, then a geometric analysis of shape differences may be uninformative
or even misleading. On the other hand, if those non-shape parameters are only part of the
answer, then a shape analysis may capture both the changes in those parameters and the
broader morphological context that frames the transformation.
Use of shape analysis to answer a functional morphology question can be illustrated
by examples from our study of squirrel jaws. There are several ways to change a jaw so
the animal can produce a larger bite force and eat harder foods than the competition
can. Many of the alternatives involve moving muscles or their lines of action farther
from the joint, increasing the mechanical advantage of the jaw by reducing the length of
the output arm relative to the input arm reducing its length, thereby increasing output
force relative to input. Another possibility is to shorten the distal part of the jaw, bring-
ing the teeth closer to the muscles (shortening the output arm). Even if these changes
havethesameeffectonbiteforce,theymaydifferinnetadaptivevaluebecausesome
ofthesechangesmightreducegapemorethan others, which would be detrimental if
the harder items in the diet are also the largeritems.Yetanotherwaytoincrease
output force for eating harder foods would be to increase the thickness of the jaw and
change the curvature of the incisor, allowing it to bear larger loads. This may be less effi-
cient with respect to input
output ratio, but more productive in evolutionary terms
because it allows feeding on harder foods within imposing a smaller gape that might
limit choices.
For rigid structures like individual bones or fixed composites like most mammalian
skulls, it is easy to conceive of the structure having a shape and to frame a question in
terms of changing that shape in response to ecological or functional demands. In contrast,
flexible or articulated structures (e.g. limbs) may not be seen to have “a” shape, but rather
