Both modes of evolving modularity, parcellation and integration, consist of a formally equivalent "sorting" of gene effects. Genetic effects not "in line" with the directional selection on a set of functionally coupled characters become "aligned." For instance parcellation consists of the differential suppression of pleiotropic effects among characters from different character complexes and the maintenance of pleiotropic effects on characters within each complex. Integration results in correlations between characters which prevents non adaptive independent variation of the individual characters (Riedl, 1975). The challenge is to find a class of selection forces that have these differential effects on the structure of the genotype-phenotype map. Four possible candidates are found in the literature: 1) selection based on the rate of adaptation (Riedl, 1975; Rechenberg, 1972); 2) constructional selection (Altenberg, 1994); 3) stabilizing selection (Cheverud, 1984); and 4) a combination of stabilizing and directional selection.
Selection for adaptation rate is based on the fact that modularity can enhance the rate of evolution, because it avoids interference between different functional systems. If there are genotypes in a population that differ in their rate of adaptation to an environmental challenge then the faster class of genotypes will reach higher fitness values more quickly and thereby gain a selective advantage over the "slower" class of genotypes. This mode of selection works particularly well in the absence of recombination (Wagner, 1981). It is in principle also possible in sexually reproducing populations, but requires strong linkage disequilibrium (Wagner and Bürger, 1985). However, this mode of selection is only of limited importance in multilocus systems since it becomes more and more difficult to maintain the necessary level of linkage disequilibrium (Wagner, in prep, and see below).
The model of constructional selection assumes that modularity evolves by preferential duplication of genes with fewer pleiotropic effects (Altenberg, 1994). This mode of evolution is indeed feasible as shown by simulation studies. It assumes that the effects of a gene are inherited by the duplicate copies of the gene, and that the spectrum of pleiotropic effects determines the probability of a gene duplication becoming fixed in the population. This is a highly interesting proposal that needs to be followed up to assess its biological plausibility.
The third mode of selection that needs to be discussed here is stabilizing selection. It is the mode of selection that a population is likely to experience most of the time (Endler, 1986). Stabilizing selection in itself is unlikely to produce modularity since it selects against the total mutational variance of all characters. Since modularity is the differential elimination of some but not all mutational effects on a group of characters, stabilizing selection is not a candidate for explaining the evolution of modularity (Wagner, submitted). It is nevertheless important to consider stabilizing selection since it may be a counter force against the maintenance of modularity. However, simultaneous stabilizing selection against a number of characters favors the reduction of the overall mutational effects on these characters irrespective of the strength of stabilizing selection (Wagner, submitted). Stabilizing selection is thus "blind" to the modular structure of the genotype phenotype mapping function and does not "wash out" any modular structure that may have evolved before. Modularity is stable against simultaneous stabilizing selection on all characters.
Adaptive evolution is most likely taking place by a combination of directional and stabilizing selection forces (Wagner, 1988). This conclusion can be inferred from the observation that during most adaptive processes only a limited number of characters actually change. For instance, the evolutionary increase in body size during the evolution of modern horses occurred under the preservation of most of the shape characters. Body size evolution generally occurs under preservation of the relative brain size, a trend that is not explainable as a correlated selection response (Lande, 1979) but is perhaps caused by stabilizing selection. Darwin's finches are mostly adapting with their beak shape but conserving other body proportions (Grant, 1986). At a more abstract level one can argue that any model assuming a fitness optimum for more than one character leads to a combination of directional and stabilizing selection on a population that is approaching the optimum (Fig. 4). It is thus suggested that a combination of directional and stabilizing selection is a common mode of selection.
Figure 4:
This diagram illustrates that a population which approaches an optimum in an at least two dimensional phenotype space is necessarily experiencing a combination of directional (dark arrow) and stabilizing selection (dashed arrows). The concentric circles are contour lines of fitness.
A simple fitness landscape that combines directional and stabilizing selection is the corridor model (Wagner, 1984, 1988; Bürger, 1986). It assumes that one direction of the phenotype space is under sustained directional selection while all the others are under stabilizing selection. Taken literally this model is highly unrealistic, since it assumes that fitness increases indefinitely in one direction. However, this is not an important part of the interpretation. What counts is the fact that the corridor model can be seen as a local approximation of the fitness landscape far from the optimum, such that the peak of the fitness landscape is not yet in the reach of the population. One can also think of the corridor as a surrogate for a moving optimum model, where the optimum is shifting in one direction and the population has to evolve to keep up with the optimum.
A simulation study on the rate of evolution in the corridor with pleiotropic effects has shown that the rate of evolution along a corridor is strongly influenced by the strength of stabilizing selection on the pleiotropic effects, confirming Bonner's intuition that pleiotropic effects interfere with adaptation (Baatz and Wagner, in prep.). The question now is whether genetic variation that decreases the magnitude of pleiotropic effects will become selected. This question was considered in another simulation study (Wagner, in prep.) in which a "modifier gene" was introduced to suppress pleiotropic effects. Table 1 lists the selection coefficients estimated from the average fixation time. It can be seen that the selection coefficient of the modifier is mainly determined by the strength of directional selection and not so much by the intensity of stabilizing selection. The selection coefficients range from 0.08 to 0.35, which is quite high (note that the selection coefficient is a dimension less value).
Table 1:
The selection coefficient s(b) of an allele which suppresses the pleiotropic
effects of 50 genes while the populations evolves along a ridge of fitness
(corridor model). The selection coefficient was estimated from the average time to
fixation. The estimates are base on 100 simulations per parameter combination. The size
of the parental population was 100. The parameter s measures the intensity of directional
selection on the first character and k measures the strength of stabilizing selection
on the second character. Stabilizing selection on the second character induces selection
against the pleiotropic effects. Note that the selection coefficient is mainly influenced
by the intensity of directional selection s.
The magnitude of the selection coefficients is primarily determined by stabilizing selection against the variance caused by pleiotropic effects. Since it is assumed that each gene with an effect on the adaptive character (i.e. the one under directional selection) also has pleiotropic effects on the character under stabilizing selection, each gene substitution is associated with a transient peak of genetic variance in the character under stabilizing selection. This transient signal of genetic variance is under direct stabilizing selection and any decrease of this signal will be favored by selection. A study in which the causal components of the selection coefficient were measured shows that about 90 to 95% of the selection coefficient is caused by this direct stabilizing selection on the variance caused by pleiotropic effects. The rest is due to selection for adaptation rate, or, more technically, by linkage disequilibrium among genotypes with different genotype phenotype mapping (Wagner, in prep).
These results suggest that a combination of directional and stabilizing selection induces a strong selection force differentially eliminating pleiotropic effects and maintaining the mutational effects on the other characters. It is effective under fairly general conditions and is thus likely to shape the structure of the genotype-phenotype mapping function.