Previous simulation results have shown that, in outcrossing species, weak selection on codon usage is expected to be significantly reduced in genomic regions with low rates of crossing over because of wHR effects 213637. We modified the model of 21 by adding one additional parameter, the selfing rate S (see Materials and methods). The results for S = 0%, 50% and 99% for several values of the population recombination rate 4N_er (where N_e is effective population size and r is the per base rate of recombination) and two values of the strength of selection 4N_es (where s is the selection coefficient) are presented in Figure 1. The effect of crossing over on the efficacy of selection on codon usage decreases strongly with S. For S = 99%, which is probably close to the true value for A. thaliana 2930, virtually no effect of crossing over is observed. This result reflects the strong reduction in the range of effective rates of recombination present in a selfing genome; high levels of homozygosity dramatically reduce the effective rate of recombination 31, and therefore a given difference in r between two genomic regions will produce much greater differences in effective recombination rates in an outcrosser than in a selfer. Therefore, the theory predicts very weak or no associations between selection on codon usage and the rate of crossing over in A. thaliana. Results with intermediate selfing rates of 50% show a similar effect of recombination to that with complete outcrossing, suggesting the presence of a threshold level of inbreeding that leads to uncoupling of recombination from codon bias evolution.

In A. thaliana, selection on codon usage seems to be relatively weak 34. Thus, it is quite hard to identify the so-called 'optimal' codons, which are preferentially retained by translational selection. In other species such as Drosophila and C. elegans, optimal codons have been shown to correspond to the most abundant tRNAs in cells 3839. Using tRNA gene number as a proxy for tRNA expression, we redefined the list of optimal codons in A. thaliana as those corresponding to major tRNAs (S.I.W, C.B.K.Yau, M. Looseley, and B. Meyers, unpublished data). The frequency of these newly defined optimal codons (hereafter denoted F_op) is more strongly correlated with the level of gene expression than was the case in previous work (Spearman rank coefficient R_s = 0.26 with p < 10^-4). This is consistent with the idea that this new index better captures translational selection on codon bias than do previous ones.

We then compared selection on codon usage measured by F_op with the rate of crossing over estimated from the comparison of genetic and physical maps for each chromosome arm (see Materials and methods). Figure 2 shows that there is no relationship between these parameters, with F_op being equal to approximately 0.49 throughout the genome. R_s = -0.02 with p < 10^-4. Although the p value is highly significant, the correlation coefficient implies that only 0.04% of the variability in F_op is explained by the rate of crossing over, and the p value reflects the large number of genes used in the analysis. There is thus virtually no genome-wide correlation between F_op and the rate of crossing over. It has been noted previously for other species that the genome-wide correlation between codon bias and recombination is weak, although large differences can be observed among chromosomes or chromosomal regions with very different rates of crossing over 7. This effect may result from poor map-based point estimates of recombination for any given locus, while global averages are much more reliable, as well as other causes 722. In A. thaliana, as in many species, crossovers are suppressed near centromeres 40. If we compare the centromeric regions with the remainder of the genome, we find at most a 1% difference: in centromeric regions, F_op = 0.477 (n = 2005), and in the other regions, F_op = 0.486 (n = 13,243). In contrast, comparisons of centromeric regions with other genomic regions in Drosophila show striking differences, which are larger than 20% 6. Taken together, these observations suggest that selection on codon usage does not vary with the rate of crossing over in A. thaliana, in agreement with the theory.

BGC can be seen as a sort of meiotic drive, in which GC gametes are favored over AT gametes 41. As high levels of inbreeding are associated with a strong decrease in heterozygosity, the strength of BGC should be dramatically reduced in inbreeders, because BGC can occur only in heterozygotes. The expected change in GC content due to BGC in the case of inbreeding can be derived straightforwardly from population genetics theory (see Materials and methods for details). By using standard diffusion equations modifed for inbreeding one can obtain the GC content at equilibrium under BGC, mutation, drift and inbreeding (see Materials and methods for details). The GC content at equilibrium (p*) depends on the effective population size (N_e), the mutational bias (α = u/v, where u is the mutation rate from GC→AT and v the reverse mutation rate), the coefficient of BGC (ω), and the selfing rate (S) (see Materials and methods).

In Figure 3, we plot the expected values of p* according to the scaled measure of the strength of BGC (4N_eω with different mutational biases (α) and selfing rates (S)). In Figure 3a, we show that BGC has little effect on expected GC content in highly selfing populations (S = 0.99) compared to outcrossing populations (S = 0), regardless of the strength of BGC. This means that, in a highly selfing population, genomic regions with high recombination and thus high BGC (high ω) are expected to have a very similar GC content to genomic regions with low recombination and thus little or no BGC (low or null ω). Figure 3b shows that a slight difference between such genomic regions can be observed in a partial selfer, with S = 50%, for example. In A. thaliana, where S has been estimated to be approximately 0.99 2930, the average GC contents for introns, 5' flanking regions and 3' flanking regions are 32.1%, 32.7% and 32.5%, respectively, with an overall mean of approximately 32%. Thus, a mutational bias of 2 (that is, u/v = 2) describes well the average GC content of noncoding DNA (see Materials and methods for details). This suggests that the results obtained with S ~1 and α = 2, are probably the closest to reality in A. thaliana. With these parameters, Figure 3 shows that no effect of BGC on GC content is expected.

In Figure 4, we plot the GC content for third codon positions of coding DNA (GC₃) and intron DNA (GC₃) against the rate of crossing over in A. thaliana. No significant correlations between GC₃ and GC_i with recombination is observed. The correlation coefficients are very weak for both GC₃ (R_s = -0.03 with p = 0.0002) and GC_i (R_s = -0.04 with p = 0.01). In both cases, less than 0.2% of the variability in GC content is explained by recombination. Again, we checked for a difference between centromeric regions and the remainder of the genome. In centromeric regions, GC₃ = 41.4% and GC_i = 32.3%, and in the other regions GC₃ = 43.3% and GC_i = 32.8%. Thus, we observe a 2% difference for GC₃ and a 0.5% difference for GC_i. Again these differences have a p value lower than 0.05 (with a nonparametric Kolmogorov test) but these minor differences may have no biological meaning. In contrast, the corresponding difference in GC content in Drosophila is as large as 20% for coding and 5% for noncoding DNA 6. Our results from the genome analysis thus seem to be in agreement with theory.

Our genome analysis suggests that recombination has little effect on base composition in A. thaliana. Neither codon usage bias nor GC content are correlated with the local rate of crossing over. Our theoretical work suggests that, first, selection on codon usage is not expected to vary with crossing over in highly inbred species and, second, that BGC is inefficient in highly inbred species. We also expect the global efficacy of selection on codon usage to be lower in inbred than in outbred species (see Figure 1). Interestingly, the level of codon usage is low in A. thaliana and high in Drosophila 34, in agreement with the respective levels of outcrossing in these species. Subsequent comparisons of selfing versus outcrossing Arabidopsis species have, however, shown a less clear pattern 35.

The budding yeast Saccharomyces cerevisiae is thought to have a high level of inbreeding in natural populations 42, and recent high estimates of the inbreeding coefficient from a population of the close relative S. paradoxus 43 suggest that long-term rates of selfing may be high. One might therefore expect a similar pattern in the genome of S. cerevisiae to that observed in A. thaliana. Although there is no evidence for a strong effect of recombination on the rate of protein evolution once gene expression is controlled for 44, recombination rates are strongly correlated with GC content in yeast 8. However, in contrast to A. thaliana, yeast has exceptionally high rates of recombination, approximately 100-fold higher than the multicellular model systems Arabidopsis, Drosophila and C. elegans 7. This may counteract the reduction in effective recombination rates caused by inbreeding, to such a degree that the strength of BGC may be significant. Indeed, a study of nucleotide variation at a prion-like gene in S. cerevisiae estimated a similar effective rate of recombination to that in Drosophila 45, despite possibly high rates of inbreeding in budding yeast.

In C. elegans, the level of codon bias is intermediate between that of A. thaliana and Drosophila 34, and there is also a significant correlation between crossing over and GC content in this species 6. This is puzzling, in view of the low levels of genetic diversity (suggesting a low effective population size) 4647 and the high levels of linkage disequilibrium (suggesting very restricted recombination due to inbreeding) 46. There are three possible explanations for this pattern: first, C. elegans is in fact a fairly outcrossing species, and has recently suffered a population bottleneck that reduced its levels of genetic variability; second, it has only become a self-fertilizing hemaphrodite relatively recently (this possibility cannot be excluded, since we lack knowledge of its close relatives) 48; and third, our models of the evolution of base composition are in error. Further information on the evolutionary biology of C. elegans and its relatives is needed to solve this problem.

Base composition is fairly variable across the A. thaliana genome, both for codon bias and GC content (see Figure 5). Recombination does not seem to be a determinant of this variation in A. thaliana. What could be the other possible determinants? It is well known that codon bias has multiple determinants: gene expression and protein length, for instance 34. Here, we find that a total of approximately 20% of the variability in F_op is explained by gene expression (measured by expressed sequence tag (EST) or massively parallel signature sequencing (MPSS) data) and protein length (S.I.W., C.B.K. Yau, M. Looseley, and B. Meyers, unpublished data), leaving 80% to be explained. The rate of nonsynonymous substitutions per site (d_N) seems to be another strong determinant of codon bias in Drosophila 16. However, no large-scale dataset of orthologous pairs between A. thaliana and its close relatives (required to estimate d_N) is currently available, so we cannot assess the contribution of d_N to variability in F_op. Both the GC content at synonymous sites and at introns are likely to be influenced by genetic drift 49. The cumulative effects of mutation, selection (in the case of synonymous sites) and drift should generate random variation in GC content across the genome. This can be explored by looking whether the distribution of GC content over genes (see Figure 5) follows a binomial distribution. However, the differences between the expected values (estimated using the mean GC content) and the observed values were statistically significant for both GC₃ and GC_i (data not shown). Variation in GC content does not seem to be fully explained by the effects of genetic drift.

This suggests that other factors, such as local differences in level of mutational bias, may contribute to the patterns of base composition in A. thaliana. If there are strong local effects driving the variation in GC, we would expect a strong positive correlation between GC₃ and GC_i across genes, as observed in humans 2650 and Drosophila 51. In contrast, we find a weak but significant negative correlation between GC₃ and GC_i (R_s = -0.115; p < 10^-4); this is the case even when the correlation between GC₃ and codon bias is factored out (R_s = -0.115; p < 10^-4). This suggests that local heterogeneity in mutational bias does not explain the variation in GC, and provides further evidence against a major effect of BGC in local GC variation in this species. The uncoupling of GC₃ and GC_i, and the residual variation in GC content, may result from the action of selective constraint on some intron sequences, and differences in the mutational context of introns and synonymous sites.

One important assumption of our analysis is that A. thaliana has been self-fertilizing for a sufficiently long time to remove any historical effects of recombination on base composition. This is questionable, given the fact that its closest known relatives are all obligate outcrosssers, including A. lyrata 52. The most extreme case is complete cessation of outcrossing and complete relaxation of selection or BGC since the divergence of A. thaliana from A. lyrata. Under this assumption, Equation (4) given in Materials and methods implies that the present-day deviation of GC content of a genomic region of A. thaliana from the completely neutral value is equal to the initial deviation multiplied by exp(-(u + v)t), where t is the time since divergence. This can be related to the expected DNA sequence divergence at completely unconstrained sites (after a Poisson correction for multiple hits), which is equal to 4αvt/(1 + α) 49. From the base composition of A. thaliana centromeric DNA (see Results), we can estimate α as 2.12, assuming that this reflects mutational equilibrium. Given that the maximum silent-site divergence between the two species is about 0.2 35, this implies that (u + v)t = 0.23, so that the current deviation of A. thaliana GC content from the mutational equilibrium value is expected to be at least 80% of the value in A. lyrata. Conversely, this means that the maximal departure of GC content in a genomic region of A. lyrata from mutational equilibrium is at most a factor of exp((u + v)t) times that for the corresponding region of A. thaliana, that is, about 25% greater. If A. thaliana has only been highly selfing for a proportion of the time since divergence, the value will be proportionately lower. This suggests that regional variation in GC content in A. lyrata should be relatively modest, a prediction which can be tested when more genomic information on A. lyrata is available.

Our theoretical model of drift, selection and mutation considered only a single population, but it is known that A. thaliana has strong population structure 2953. In addition, within-population silent nucleotide site diversity is very low compared with A. lyrata, but the diversity when pooled over samples from different localities is similar for the two species 53. This indicates that the effective population sizes of local populations are very low in A. thaliana, that migration among populations is limited, and that the effective population size determining the diversity among alleles randomly chosen from the species as a whole is not greatly reduced. The relatively high total diversity also suggests that local extinction and recolonization of populations does not play a major part in controlling genetic diversity 54.

This raises the question of what measure of effective population size is appropriate for determining the base composition under BGC or weak selection. In addition to mutational bias, theory shows that base composition is controlled by the relative fixation probabilities of new mutations from GC to AT and vice versa 2155. If migration is conservative (that is, the number of migrants entering each population equals the number leaving), with selection of the form of Equation (1) in Materials and methods, these fixation probabilities are controlled by the same N_e as is appropriate for the mean level of neutral diversity within demes, which is the same as for a population lacking any subdivision 565758. With nonconservative migration, rigorous theoretical results are not available, but heuristic models and computer simulations suggest that fixation probabilities will be usually be lower than with conservative migration 596061. These considerations imply that our conclusion, that fixation probabilities in A. thaliana will be closer to the neutral values than in A. lyrata for sites affected by BGC or weak selection, is either unaffected by population structure, or is a conservative one.