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. 2013 Apr;193(4):1209-20.
doi: 10.1534/genetics.112.148627. Epub 2013 Jan 18.

Compensatory evolution and the origins of innovations

Etienne Rajon  1 , Joanna Masel
Affiliations

Compensatory evolution and the origins of innovations

Etienne Rajon et al. Genetics. 2013 Apr.

Abstract

Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to adaptation when co-opted--e.g., following a mutation increasing expression from a low, attenuated baseline. This view is described, for example, by the metaphor of the spread of a population across a neutral network in genotype space. As an alternative view, consider the fact that most phenotypic traits are affected by multiple sequences, including cryptic ones. Even in a strictly clonal population, the co-option of cryptic sequences at different loci may have different phenotypic effects and offer the population multiple adaptive possibilities. Here, we model the evolution of quantitative phenotypic characters encoded by cryptic sequences and compare the relative contributions of genetic diversity and of variation across sites to the phenotypic potential of a population. We show that most of the phenotypic variation accessible through co-option would exist even in populations with no polymorphism. This is made possible by a history of compensatory evolution, whereby the phenotypic effect of a cryptic mutation at one site was balanced by mutations elsewhere in the genome, leading to a diversity of cryptic effect sizes across sites rather than across individuals. Cryptic sequences might accelerate adaptation and facilitate large phenotypic changes even in the absence of genetic diversity, as traditionally defined in terms of alternative alleles.

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Figures

Figure 1
Figure 1
A schematic genotype network in which a clonal and a genetically diverse population can access similar sets of phenotypes through mutation. Nodes represent genotypes, which may yield different phenotypes represented by different colors (including white, which is optimal in the current environment). Connections between nodes represent possible mutations. The genotypes present in the two example populations are represented by gray areas. The population on the left is clonal, so its phenotypic potential (the distribution of new phenotypes accessible through mutations) corresponds to the neighborhood richness of the unique genotype. The population on the right is diverse, but each genotype has relatively poor neighborhood richness (genotypes can access one to two new phenotypes through one mutation). In this population, the phenotypic potential depends on neighborhood richness and on genetic diversity.
Figure 2
Figure 2
Both genetic diversity (A) and neighborhood richness (B) can contribute to phenotypic potential. Here phenotype is represented as a color scale (higher numbers encode darker color), which is selected against if it is too different from the background. (A) Consider one cryptic sequence (1). The upsidedown T represents its crypticity. Genetic diversity of cryptic sequences can be maintained, as sequences with different effects correspond to phenotypes only slightly different from the background (1). Despite being cryptic, sequences with too large an effect (e.g., +4) are likely eliminated by selection. The co-option of a cryptic sequence (2) usually leads to a large phenotypic change, so the corresponding variant is eliminated by selection. However, if co-option happens around the time of environmental change (3), this variant might be favored by selection. Represented as a genotype network (4), a polymorphic population (inside the red square) can access different phenotypes through co-option (dashed mutations). (B) When several cryptic sequences contribute to the phenotype (5), the co-option of different sequences can lead to different phenotypes (7, 8). This neighborhood richness can favor adaptation, even in a clonal population (6).
Figure 3
Figure 3
The standard deviation of the phenotypic effects, SD(βjlc), increases as ρ decreases and sequences become more cryptic. Variation across sites accumulates through compensatory evolution, which occurs at a speed that depends on the strength of selection. Accordingly, when selection is strong (ρ is high, crypticity is low) SD(βjlc) remains low regardless of the simulation time t and is unlikely to reach high values at evolutionarily relevant timescales. On the other hand, for highly cryptic sequences where selection is very weak, SD(βjlc) quickly reaches high values close to the expected value in a neutral model, calculated according to Rajon and Masel’s (2011) Equation S3 (dashed line). Only at intermediate levels of crypticity does the variation across sites increase noticeably with evolutionary time. The average of SD(βjlc) was calculated across traits in a given individual and then across individuals and across independently evolved populations.
Figure 4
Figure 4
Neighborhood richness dG explains most of the phenotypic potential of a population dP when sequences are strongly cryptic. Top: When L = 10, both the ratio dG/dP and dP increase when ρ decreases and sequences are more cryptic. Crypticity needs to be more complete to drive dP up when L = 1, a situation in which dG always equals 0 because an increase of neighborhood richness via intragenomic diversity is impossible. dP remains low when L = 1, even when the effective mutation rate is increased 10-fold (“high μ,” blue diamonds), such that the mutation rate per genome equals that for L = 10. Middle: The large ratio dG/dP cannot be explained by a lack of genetic diversity in the population. Pairwise diversity was quantified as the probability that two individuals have different genotypes, calculated as 1−∑ifi2, with fi the frequency of genotype i. Bottom: κ is a metric of compensatory evolution (see text), calculated as the normalized difference between the mean variance in ∑lβjlc expected if loci had evolved independently, and the mean variance observed in simulations. Positive values of κ indicate compensatory evolution. Parameter values: N = 105, μ = 10−7, C = 3. Results are averaged over 200 (L = 1) or 49 (L = 10) simulations. The bars in the top and middle represent the 0.25 and 0.75 quantiles in the distribution of dG/dP across replicate simulations.
Figure 5
Figure 5
The compensatory evolution of multilocus characters increases neighborhood richness. A mutation in a sequence controling color (see Figure 2) likely moves the phenotype away from the environmental optimum (1). Before this variant is eliminated, a backward mutation (2, unlikely) or a compensatory mutation (3) may occur and cancel its phenotypic effect. After the compensatory pair has fixed, a greater diversity of phenotypes can be accessed through co-option.
Figure 6
Figure 6
The mean proportion of variation due to neighborhood richness (dG/dP) decreases with the population size N and when weakly cryptic sequences encode a large number of characters. (A) dG/dP decreases when the product ρN exceeds a threshold. (B) dG/dP and dP decrease with C when ρ = 10−1 but not when ρ = 10−2. The blue dashed lines represent the absolute values of dP. Parameter values: L = 10, C = 3 (A), N = 105 (B). Results are averaged over 49 or 34 simulations (the latter when N > 105 in A and C > 5 in B). The bars represent the 0.25 and 0.75 quantiles in the distribution of dG/dP across replicate simulations.
Figure 7
Figure 7
Co-option increases the potential for adaptation to large environmental changes only. (A) Waiting time for an adaptive fixation scaled according to the number of mutations trialed before one fixes—the median number of trials is represented. A short waiting time (i.e., a small number of trials) indicates high evolvability. Mutations in noncryptic sequences yield a fixation event more rapidly, although the calculations do not include the fact that only co-option mutations have been prescreened for strong, unconditionally deleterious effects (Masel 2006; Rajon and Masel 2011). (B) Distance to the new optimum, following a fixation event. For larger environmental changes, one fixed co-option mutation yields a greater advantage than a regular mutation in either a cryptic or a noncryptic sequence. Parameter values: Ν = 105, μ = 10−7, C = 3, and ρ = 10−2 for cryptic sequences (ρ = 1 otherwise). The bars represent the 0.25 and 0.75 quantiles in the distribution of the number of trials until fixation (A) or of the distance to the new optimum (B).
Figure 8
Figure 8
Higher crypticity leads to higher evolvability through co-option. (A) The evolvability of co-option mutations, measured as the median of the (small) number of mutants that need to be trialed before one fixes, mirrors the results of Figure 4A. This means that high evolvability tracks high neighborhood richness driven by compensatory evolution in cryptic sequences. Regular mutations in cryptic sequences are shown for comparison. (B) Not only do co-option mutants fix more readily when they reveal more cryptic sequences; they also reach phenotypes much closer to the new optimum. Large adaptive phenotypic changes are possible through single co-option mutations in the 10-loci case when sufficient variation across cryptic sequences has accumulated through compensatory evolution (i.e., when dP and dG/dP are high in Figure 4A). Same parameter values as in Figure 4; the distance from the old to the new optimum d equals 4. The bars represent the 0.25 and 0.75 quantiles in the distribution of the number of trials until fixation (A) and of the distance to the new optimum (B).
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