Evolution of adaptive phenotypic variation patterns by direct selection for evolvability

Abstract

A basic assumption of the Darwinian theory of evolution is that heritable variation arises randomly. In this context, randomness means that mutations arise irrespective of the current adaptive needs imposed by the environment. It is broadly accepted, however, that phenotypic variation is not uniformly distributed among phenotypic traits, some traits tend to covary, while others vary independently, and again others barely vary at all. Furthermore, it is well established that patterns of trait variation differ among species. Specifically, traits that serve different functions tend to be less correlated, as for instance forelimbs and hind limbs in bats and humans, compared with the limbs of quadrupedal mammals. Recently, a novel class of genetic elements has been identified in mouse gene-mapping studies that modify correlations among quantitative traits. These loci are called relationship loci, or relationship Quantitative Trait Loci (rQTL), and affect trait correlations by changing the expression of the existing genetic variation through gene interaction. Here, we present a population genetic model of how natural selection acts on rQTL. Contrary to the usual neo-Darwinian theory, in this model, new heritable phenotypic variation is produced along the selected dimension in response to directional selection. The results predict that selection on rQTL leads to higher correlations among traits that are simultaneously under directional selection. On the other hand, traits that are not simultaneously under directional selection are predicted to evolve lower correlations. These results and the previously demonstrated existence of rQTL variation, show a mechanism by which natural selection can directly enhance the evolvability of complex organisms along lines of adaptive change.

Figure 1.

(a) Owing to different effects of the allele substitution on the trait z₂ at different values of the trait z₁, the regression slope between the two traits differs between genotypes. This variation is used in QTL mapping in experimental crosses to identify loci that affect the statistical relationship between the traits. These loci are called relationship loci, rQTL, because they affect the statistical relationship among phenotypic traits. (b) The type of rQTL that is used in the model. Note that the covariance between the two traits differs in two genotypes, although variances and means are constant. (c) Scheme of the result of selection on rQTL. In the presence of genetic variation in pleiotropy, the additive genetic variance aligns with the direction of selection. The bivariate distribution of additive genetic variance is represented here by an ellipse aligning with the direction of selection.

Figure 2.

rQTL variation and the evolution of genetic correlation owing to rQTL selection. (a–c) The evolution of genetic correlation between traits z₁ and z₂ during 400 generations of selection. The four lines in each plot represent different levels of linkage (L = 0.75 (light grey), 0.8 (black), 0.9 (dark grey) and 1.0 (dotted line)). Plot (a) shows the effect on genetic correlation of co-selection on both traits. Both traits are simultaneously selected for increased trait values (a₁ = a₂ = 0.05), starting with a population that contains 1% of an allele with high correlation between traits (r_i = 0.9), and 99% of an allele causing zero correlation. Selection leads to an increase in genetic correlation between the two traits until the allele causing high correlation is fixed. (b) A scenario in which selection is acting on the traits in opposite directions, i.e. antagonistic selection, causing increase in one and decrease in another trait (a₁ = 0.05, a₂ = −0.05). At the beginning, the most frequent allele is the one that causes zero genetic correlation, and the alternative allele causes a correlation of −0.9. Antagonistic selection favours the allele causing negative correlation. (c) Evolution of genetic correlation in a corridor model, i.e. directional selection on one trait, while the other trait is under stabilizing selection. The initially most frequent allele causes a positive correlation of 0.9, and the alternative allele leads to zero correlation. The genetic correlation decreases as the allele causing the lower correlation between traits is selected (r₁ = 0, r₂ = 0.9, directional selection coefficient = 0.001, stabilizing selection coefficient = 0.0025). Note that rQTL selection in the corridor model is much more effective than with directional selection alone. The strength of directional selection in this simulation is only 0.001, while in plots (b) and (c) it is 0.05 in order to reach the same level of correlation change in the similar amount of time.

Figure 3.

Evolution of genetic correlations under fluctuating selection. Four periods of co-selection were applied, each 100 generations long. In each epoch, the traits are simultaneously selected for higher mean values or lower mean values, respectively. All plots show three lines for simulations with different degrees of linkage (L = 0.75 (light grey), 0.8 (black), 0.9 (dark grey)). (a) In this scenario, the linkage equilibrium between the rQTL and the rest of the genome is restored between each epoch of directional selection. This is equivalent to the assumption that between each epoch there is a period of stabilizing selection during which linkage equilibrium is restored (not simulated, but linkage equilibrium is enforced by averaging genotypic values). The rate of evolution of genetic correlations is similar to the scenario of sustained directional selection, only slightly delayed at the beginning of each epoch. The reasons for these delays are two. First, at the beginning of each epoch, LD has to be rebuilt that fuels the selection of the rQTL allele (see the plot of the rQTL allele frequency in the electronic supplementary material, figure S1a, which does not show a drop in frequency but only a slowdown in increase). Second, the relaxation of LD between epochs leads to a decrease of the population-level genetic correlation, which explains the instantaneous drop of correlation visible in the L = 0.9 curve at generation 100 and somewhat less so in the other curves and epochs. (b) Same scenario as in (a) except that the LD is not relaxed between epochs of directional selection. This scenario leads to a pronounced sawtooth pattern at the beginning of each new epoch. The reason is that initially, at the switch from one epoch to the next, the favoured rQTL allele is associated with genotypic values of the traits that cause lower fitness in the new selection regime. This ‘wrong’ LD is dissipated over a few generations and then selection for the favoured rQTL allele resumes. Overall, these effects do not significantly delay the evolution of the favoured form of genetic correlation. (c) Fluctuating selection in the corridor model, with equilibration between the epochs. The direction of the directional selection changes, while the stabilizing selection is constant. There is no effect of linkage relaxation in this model (not shown).