pleiotropy

Welch JJ & Waxman D 2003 Modularity and the cost of complexity. Evolution 57:1723-1734.

• we examine the claim that the rate of evolution of complex phenotypes could be accelerated through some sort of phenotypic modularity

• we consider the process of adaptation as a single-mutant adaptive walk in a population of haploids
• at any instant there is, at most, one mutation segregating in the population
• this approach, related to the strong-selection-weak-mutation approximation of Gillespie (1983, 1991), is common to most of the recent work on Fisher's model and other unrelated work
• we use the approach to remove the influence of mutation rate, levels of dominance, population size, and reproductive mode, all of which influence the rate of adaptation, but are not the focus here

• we collect the n trait values and the n changes due to mutation into n-dimensional vectors
• it is this picture of the phenotypic state of an organism as a point in an n-dimensional space and a mutation as a vector of change in that space that makes the model geometrical

• Orr's (2000) identification of an important evolutionary advantage to reducing the number of effectively independent characters comprising an organism, remains compelling
• he suggests that this might be achieved by developmentally "building" characters, and relates this to the notion of "modularity" as present in the work of Wagner and others
• Barton and Partridge (2000) make a similar claim, suggesting that many of the regulatory processes listed by Kirschner and Gerhard (1998) as facilitating the evolvability of metazoans, could be modeled as a reduction in the dimensionality of Fisher's model
• the notion that features of the developmental system act to somehow facilitate adaptive evolution, or to increase "evolvability," has been a much discussed topic within evolutionary developmental biology
• modularity has been a central concern
• the key idea is that further adaptation should not undo adaptation previously achieved, that a change to one part should not disrupt the whole system

• the Fisher model in its original formulation included universal pleiotropy
• some authors have considered Fisher's model with no pleiotropy in the context of drift load
• there have been no considerations of immediate levels of pleiotropy in this model
• we introduce modular pleiotropy, as depicted in Figure 4c, to determine the extent to which it might reduce the cost of complexity

• modular architectures are thought to be favored when some traits are maladapted but others are not
• modularity then allows adaptation to take place without undoing the adaptation achieved elsewhere

• a higher level of modularity will be favored when only a single trait is maladapted
• the cost of complexity cannot be eliminated with modular pleiotropy
• a minimum cost of n^{− 1} always applies
• under some conditions, modularity can retard the rate of adaptation

• it is this ruggedness that is often meant by the term "complexity" in discussions of biological evolution (e.g., Kauffman and Levin 1987), rather than the dimensionality of the landscape

• a population trapped at a local fitness optimum in n-dimensional space might find that the addition of extra dimensions enabled further adaptive evolution along those dimensions
• this could increase the rate of evolution for organisms characterized by more phenotypic dimensions (higher n)