Biology Reference
In-Depth Information
variation; he emphasizes the dynamics and complexity of development, and the fact
that the structure of variation is an outcome of multiple variance-generating processes
(
Hallgr
ยด
msson et al., 2007a,b, 2009
). Those processes may partially overlap spatially, ampli-
fying each other in some regions and canceling out in others. Even if each individual
process is modular, their net effect on variation need not be. We might also anticipate a
non-modular organization of variation when functional complexes are not modular
(
Zelditch et al., 2008, 2009
). Due to the dynamics and complexity of development, and/or
the functional organization of morphology, we might find integration but not modularity.
The methods that we describe below test hypotheses of modularity. Although there are
methods for exploring the data to find the best-fitting model (one of these is discussed
below), the methods are used primarily to test hypotheses derived from developmental
biology, functional morphology or any other source of theory that predicts the structure of
variation. An important methodological consideration when it comes to choosing a
method is the array of hypotheses against which your
a priori
hypothesis is tested.
Regardless of the method you choose, it is important to remember that the best-fitting
hypothesis is the best in a specific context
the alternatives that you entertained.
A Brief Overview of Methods for Analyzing Modularity
All three of the methods that we describe below require stating a hypothesis that pre-
dicts the modular structure of the data. In all three cases that is done by subdividing a
configuration of landmarks into two or more subsets. For example, we can subdivide the
mandible into two subsets of landmarks (plus semilandmarks) according to the hypothesis
of mandibular modularity favored by quantitative genetic studies. The hypothesis posits
two modules, one the tooth-bearing region, the other the muscle-bearing region (
Cheverud
et al., 1997, 2004; Mezey et al., 2000; Ehrich et al., 2003; Cheverud, 2004; Klingenberg et al.,
2004
). The division is usually made at the point where the molar alveolus separates
from the coronoid process, and where the angular process can be distinguished from the
horizontal ramus (
Figure 12.14
). (For brevity, we refer to this as the Front/Back model.)
FIGURE 12.14
A hypothesis
of mandibular modularity. The
Front/Back hypothesis predicts
that there are two modules, one
comprising the tooth-bearing
region of the jaw, the other com-
prising the muscle-bearing region
of the jaw.
