Biology Reference
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and Houle (2003) , when the organization of the genotype
phenotype map is modular, the
effects of a group of genes are limited to distinct aspects of the phenotype.
The idea that effects of groups of genes are restricted to functionally coupled traits is
not always incorporated in the definition of modularity. One alternative definition empha-
sizes the structural property of modularity, i.e. that modules are highly integrated inter-
nally and (quasi)-autonomous with respect to other modules. By this definition, it is not
necessary for modules to contain functionally related traits, but it is necessary that they be
conditionally independent of each other. The requirement of conditional independence
also comes from the theoretical analysis of evolvability; Hansen and colleagues ( Hansen,
2003; Hansen et al., 2003 ) define the “relevant evolvability” of a trait as its ability to
respond to directional selection when the other traits are under stabilizing selection. Thus,
it is the ability of one trait (or complex) to evolve when others are held constant that mat-
ters to evolvability. Two traits might be correlated and therefore each seems to lack the
independence required to evolve individually when the other is held constant, but if their
correlation is due to the mutual dependence on some other trait, the two may be indepen-
dent when holding that third trait constant. If so, they are conditionally independent. A
strong and purely structural definition of modularity is that modules comprise traits that
are all mutually informative (conditionally dependent) and conditionally independent of
the traits within other modules ( Magwene, 2001 ). This structural definition is depicted in
Figure 12.12 . This figure shows a graph, in which each trait is a node; the edges between
nodes connect conditionally dependent traits. In the absence of an edge, the traits are con-
ditionally independent. Within each module there is an edge between every pair of traits,
but between modules there are no edges. A weaker structural definition of modularity
relaxes the requirement that all the traits within a module be mutually informative.
A third definition of modularity reframes the concept by highlighting its developmental
origins ( Figure 12.13 ; after Klingenberg, 2008 ). One notable distinction between this dia-
gram and the one shown in Figure 12.11 is that this one replaces functional with develop-
mental modules (M1, M2). A second distinction is that this diagram shows genes affecting
developmental pathways rather than traits
the dotted lines show the genetic effects, the
solid lines show the architecture of the pathways. Adding the pathways to the diagram
rather than leaving them implicit makes it possible to depict two ways in which genetic
correlations arise developmentally. One is by the same gene being expressed at two (or
more) times or places, which Klingenberg terms “parallel variation”. The other is by direct
FIGURE 12.12 The structural concept of modularity. The nodes of the
graph represent traits (T1
T10); those that are independent of each other,
controlling for all others, are connected by an edge. Modules comprise traits
that are all directly connected to each other. No edges connect the two mod-
ules; they are conditionally independent.
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