The genetic architecture underlying a trait depends on the strength of selection on the trait, in a population-genetic model. Traits subject to intermediate selection (intermediate values of σf) evolve genetic architectures with the greatest number of controlling loci. Dots denote the mean number of loci in the architecture underlying a trait, among 500 replicate Wright–Fisher simulations, for each value of the selection pressure σf. The rectangular areas represent the distribution of the number of loci in the architecture. The neutral expectations for the equilibrium number of loci (see Methods) are represented as grey lines, when recruitment events are neutral (top line) or not (bottom line). Parameters are set to their default values (see electronic supplementary material, table S2).
The consequences of gene duplications, recruitments and deletions in a population-genetic model. Populations were initially evolved with a fixed number of controlling loci L (a), and we then measured the effects of recruitments, deletions and duplications on the trait value (b) and on fitness (c). From the latter, we calculated the rate at which deletions, recruitment and duplications enter and fix in the population (d), and the resulting rate of change in the number of loci contributing to the trait (e). (a) For L > 1, the variation in direct effects (αi) and indirect effects among controlling loci increases as selection on the trait is relaxed. (b) As a consequence of this variation among loci, the average change in the trait value following a duplication or a deletion also increases as selection on the trait is relaxed. (c) Changes in the trait value are not directly proportional to fitness costs, because the same change in x has milder fitness consequences when selection is weaker (larger σf). As a result, the average fitness detriment of duplications and deletions is highest for traits under intermediate selection. (d) Consequently, the fixation rates of duplications and deletions are smallest under intermediate selection. (e) The equilibrium number of loci controlling a trait under a given strength of selection is determined by that value of L for which duplications and recruitments on one side, and deletions on the other, enter and fix in the population at the same rate. For example, when σf = 10–1.5, these rates are equal when L is close to 12 (black arrow), so that the equilibrium genetic architecture contains ≈12 loci on average (compare electronic supplementary material, figure S3, black arrow). (Online version in colour.)
The number of genetic loci controlling a trait inferred (a) from real S. cerevisiae populations and (b) from simulated populations has a non-monotonic relationship with the strength of selection on the trait. (a) In the yeast data of Brem et al. , the largest number of eQTLs were detected for those transcripts (i.e. traits) under intermediate levels of selection (intermediate CAI), whereas fewer eQTLs were detected for transcripts under either weak or strong selection. Transcripts were binned according to their log (CAI) values. Squares represent the distribution of the number of one-way eQTLs identified from the study of Brem et al. , for traits within each bin of CAI. Grey scale indicates the number of transcripts in each bin. Mean numbers of detected eQTLs are represented by circles. (b) For the simulated experiment, we evolved 100 populations of genetic architectures, using the parameters corresponding to the electronic supplementary material, figure S3. From each such population, we then evolved two lines independently for 25 000 generations in the absence of deletions, duplications and recruitment, to mimic the divergent strains used in the yeast cross in . From these two divergent genotypes, we then created 112 recombinant lines following the genetic map of Brem et al. . We then analysed the resulting simulated data with R/qtl in the same way as we had analysed the yeast data (see electronic supplementary material S2). The distribution of QTLs detected and their means are represented as in figure 1, for each value of selection strength σf.