Highly expressed genes appear to evolve under stronger purifying selection than low-expressed genes (although the mechanistic basis of this pattern is still debated; 24252627). Consequently, gene expression level is a good predictor of the average fitness effect of deleterious mutations. Experimental gene knockouts have also identified suites of genes that are essential for survival, while many others are nonessential. To the extent that whole gene knockout phenotypes reflect the fitness effects of individual mutations, mutations in essential genes are predicted to have larger fitness effects than mutations in nonessential genes 25282930. Lastly, proteins have variable numbers of interaction partners (protein-protein interactions per gene – PPI – range up to nearly 300 PPI in yeast; Connallon & Knowles unpub.), which indicate the level of constraint due to pleiotropy 25. Because individual mutations are likely to disrupt more cellular processes in genes with many PPI compared to those with few PPI, purifying selection is expected to be stronger in genes with many PPI 31.

Previous inferences of the strength of purifying selection acting on different gene categories are based on an observed elevated rate of nonsynonymous substitution in low-expressed nonessential genes with few PPI 25, which assumes that elevated rates of substitution are caused by genetic drift. An alternative possibility is that rapidly evolving genes undergo frequent bouts of positive selection. To test this assumption, we analyzed available polymorphism data from S. cerevisiae genes (see Methods and Additional file 1). Under a neutral/nearly-neutral model, patterns of within species polymorphism are expected to mirror patterns of interspecific substitution (i.e. genes with high substitutions rates also exhibit high levels of polymorphism 32). Positive selection decouples patterns of polymorphism and divergence and is expected to increase the number of substitutions relative to polymorphisms 33.

Low-expressed genes harbor more nonsynonymous polymorphisms (represented by the P_n/P_s ratio; P_n and P_s refer to nonsynonymous to synonymous polymorphisms, respectively) and substitutions (D_n/D_s), than highly expressed genes, consistent with the neutral/nearly-neutral model (Fig. 2; see Additional file 1). Low-expressed genes also harbor higher levels of moderate- to high-frequency polymorphism (i.e. "non-singleton" polymorphism). High frequency polymorphisms are not expected to be strongly deleterious (see 34), but rather, will consist of neutral and slightly deleterious mutations – mutations that can potentially become fixed via genetic drift. D_n/D_s ratios are significantly lower than P_n/P_s ratios for all gene expression categories (G test; singletons included: P < 0.0001; singletons excluded: P < 0.005, except for upper 25% expressed genes: P > 0.1), indicating that the predominant pattern of selection on yeast genes is purifying. Similar results are reached by partitioning the data into gene essentiality categories (see Additional file 1; a meaningful statistical analysis based on PPI was not possible due to small sample size). The results strongly support previous inferences of selection intensity based on divergence data, and suggest that nonessential genes with low expression are relatively likely to evolve under a nearly-neutral process.

Analysis of 4786 genes in the yeast species Saccharomyces cerevisiae and S. paradoxus shows that nonsynonymous divergence is weakly negatively correlated with recombination rate (partial r = -0.052, P < 0.01 after Bonferroni correction; as previously reported by Pal et al. 14). This negative relationship is markedly stronger for low-expressed genes, particularly nonessential genes with few PPI (Fig. 3). In contrast, the divergence of highly expressed genes tends to correlate positively with recombination rate, though all such associations are weak. For both classes of nonessential genes as well as for the entire dataset, the relationship between recombination and divergence in low-expressed genes is more negative than that of highly expressed genes (Upper vs. lower 25% expression quartiles: all genes, n_low = 1197, n_high = 1197, P = 0.041; nonessential PPI = 1, n_low = 246, n_high = 218, P < 0.0001; nonessential PPI > 1, n_low = 222, n_high = 142, P = 0.041. Upper vs. lower 50% expression quantiles: all genes, n_low = 2393, n_high = 2393, P = 0.148; nonessential PPI = 1, n_low = 424, n_high = 411, P = 0.046; nonessential PPI > 1, n_low = 435, n_high = 327, P = 0.005).

These results clearly show that recombination can influence the rate of protein evolution at a genome wide scale and that the impact of recombination rate variation is strongest for low-expressed, nonessential genes with few PPI. Associations between recombination and divergence rate cannot be explained by covariation between recombination rate and several variables that independently affect protein evolution (the effects were controlled for; see Methods). Estimates of the relative recombination rate between genes are coarse and limited by the quality of the S. cerevisiae recombination map, and there are potential evolutionary changes in recombination between S. cerevisiae and S. paradoxus. However, both of these factors will decrease the strength of associations between divergence and recombination, and will cause our test to be conservative.

Mutation bias is also unlikely to account for the effect of recombination on protein evolution. We present associations between recombination and divergence at nonsynonymous sites (dN) rather than between recombination and dN/dS ratios because synonymous sites are under selection in yeast [e.g. 35]. Indeed, codon usage bias (F_op) is positively correlated with recombination (as previously reported 35), most strongly for highly expressed genes, which presumably have stronger selection for optimal codons (highest 50% expression partial r_rec-Fop = 0.214 vs. lowest 50% r_rec-Fop = 0.100; highest 25% expression partial r_rec-Fop = 0.249 vs. lowest 25% r_rec-Fop = 0.089; P < 0.0001 for both comparisons). As a consequence, dS is negatively correlated with recombination (highest 50% expression partial r_rec-Fop = -0.131 vs. lowest 50% r_rec-Fop = -0.077, P = 0.031; highest 25% expression partial r_rec-Fop = -0.122 vs. lowest 25% r_rec-Fop = -0.075, P = 0.123). Furthermore, direct estimates indicate higher mutation rates in regions of high recombination 3637, which should make our tests conservative. Despite these caveats with respect to using dS to estimate underlying mutational dynamics across the genome, dN/dS produces nearly-identical patterns of covariation with recombination (see Additional file 1, Fig. S3).

The results are consistent with evolutionary theory suggesting that recombination enhances the efficacy of selection [e.g. 612]. Mutations with weak fitness effects respond to selection when the effective population size (N_e) is large, but evolve via genetic drift when N_e is small. By increasing N_e, recombination enhances the power of selection and minimizes genetic drift. Furthermore, the adaptive consequences of recombination may be extreme in yeast since most genes in the yeast genome can be defined by weak purifying selection (~75% of genes are nonessential; ~50% have one PPI; TC & LLK unpub.). Such genes also tend to reside in genomic regions with relatively low recombination frequencies (see Additional file 1, Fig. S4). The correlations revealed by the data are particularly striking when one considers the method by which the genes are partitioned. Functional genomic data permits classification of genes according to their relative opportunities for slightly deleterious evolution. However, multiple types of substitutions (i.e. slightly deleterious, neutral, and beneficial) are likely to contribute to each gene's total genetic divergence between species. This plurality should dampen patterns predicted by any single processes, and will cause the conclusions presented here to be conservative.

Why does highly-expressed gene divergence show no correlation with recombination rate? There are two major possibilities. If genes under stronger selection tend to experience fewer beneficial mutations, their overall divergence rate might be relatively unaffected by local recombination. This might occur because strongly-selected genes are closer to perfection than weakly-selected genes and therefore have less opportunity for improvement, or because tradeoffs via pleiotropy (as indicated by high PPI 31) limit the opportunity for beneficial mutations 383940. Secondly, selection for beneficial mutations might be very strong. The adaptive impact of varying recombination rate (and thus N_e) is expected to decrease with the strength of selection (i.e. s; 341). If beneficial mutations tend to be strongly advantageous, they will tend to become fixed in low or in high recombinational environments.

Publically available polymorphism data was obtained via 43 and 44. Genes with at least four samples from S. cerevisiae and at least one polymorphic site were included in the analysis, resulting in a dataset of 35 genes (lower 25% expression, n = 11; lower 50% expression, n = 12; upper 50% expression, n = 23; upper 25% expression, n = 17; essential genes, n = 7; nonessential genes, n = 28), comprising 34443 nonsynonymous, and 9975 synonymous nucleotide sites. The mean number of samples per gene was n¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGafmOBa4Mbaebaaaa@2D50@ = 22. Orthologous sequences from S. paradoxus were obtained via BLAST search at 45.

Per gene recombination rates for S. cerevisiae are those reported by Gerton et al. 8 [data available at 46]. These estimates refer to recombination rates per sexual generation. The total, per generation recombination rate during the evolutionary history of each gene is the product of the rate under sexual reproduction (R_sex) and the frequency of outcrossing (O_c); R_TOT = R_sexO_c (modified from 47). Because the exact value of O_c will be the same for all genes in the genome, R_sex per gene i, relative to R_sex for other genes, will be the same as R_TOT per gene i, relative to R_TOT for other genes (i.e.RTOT(i)RTOT(max⁡)=Rsex(i)OcRsex(max⁡)Oc=Rsex(i)Rsex(max⁡)) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@7585@, and R_sex should accurately capture relative rates of total recombination for each gene. Furthermore, because 0 <O_c < 1 47, the critical transition between R_TOT ≈ 0 to R_TOT > 0, predicted to most strongly impact the efficacy of selection 48, will be represented with yeast genes.

Protein divergence data for S. cerevisiae and S. paradoxus orthologous genes were kindly provided by D. Allan Drummond (see 24 for details). Gene expression values for S. cerevisiae were calculated from seven time period estimates during the diauxic shift by DeRisi et al. 49 [data available at 50]. Average and maximum expression levels for the seven time periods were calculated using the method of Kliman et al. 35. Results for average gene expression (E_avg) across the time periods are presented here; results do not differ when maximum expression values (E_max) are used. Essential genes were identified through the GeneMerge database 51. Gene length, dispensability, protein-protein interactions and genome map positions were obtained from the Saccharomyces Genome Database. Genes with no known interaction partner were excluded from analyses involving PPI as a variable. Space between genes (SBG) was calculated by the method of Hey & Kliman 9. Recombination, expression, length, SBG and divergence estimates were available for 4786 genes in total, including essential genes with two or more PPI (n = 329), essential genes with 1 PPI (n = 195), nonessential genes with two or more PPI (n = 762), and nonessential genes with 1 PPI (n = 835). Our dataset is available upon request.

Population samples for each gene were aligned with ClustalW 52, available online, and manually adjusted. P_n, P_s, D_n, and D_s values were calculated with DnaSP, Version 4.10 53. Watterson's estimate of silent nucleotide diversity (theta) was calculated by hand (as described in 54). The complete polymorphism dataset is provided in Additional file 1.

Genes were classified into low and high expression level categories, based on quantile partitions. These correspond with ranges of lower 25%: 2.25 to 3.15 (n = 1197); lower 50%: 2.25 to 3.31 (n = 2393); upper 50%: 3.31 to 3.53 (n = 2393); and upper 25%: 3.53 to 4.54 (n = 1197) log mRNA abundance.

All divergence estimates were log₁₀ transformed to facilitate linear comparisons, which are presented (values of dN = 0 were converted to dN = 0.0001 prior to log transformation); the results are robust and also obtained with nonparametric comparisons (TC & LLK unpub.). Partial correlation analysis was used to compare recombination rate with dN (the rate of nonsynonymous substitutions); the same results were obtained for the comparison between recombination rate and dN/dS. The partial r statistic reported here reflects the association between recombination rate and protein divergence after associations between gene expression, gene length, and SBG were removed. These factors are known to influence patterns of protein evolution [25; TC & LLK unpub.], are all correlated with one another (i.e. recombination is positively correlated with expression and gene density, but negatively correlated with length), and can therefore give rise to spurious correlations between the variables of interest. All statistical analyses were carried out with JMP (SAS Institute). Statistical comparisons between r for different gene categories were carried out with software available online http://department.obg.cuhk.edu.hk/researchsupport/Correlation.asp. Bonferroni corrections for multiple comparisons (α/5; because of the 5 categories explored in Figure 2) were used to adjust P values of statistical significance.