DISCUSSION

The panicoid grass crops provide an opportunity for efficient identification of genetic variation underlying common phenotypes of agronomic interest. Correspondence of QTL locations (Patersonet al. 1995) suggests that many such traits may have been subjected to convergent selection in different grasses, so the identification of the underlying gene in one taxon may often account for variation in other related taxa. The suitability of each species for various higher-resolution strategies such as LD mapping, association studies, and screens for targets of selection will depend on its particular level of genetic variation and extent of LD, both of which are affected by mating system. Among the panicoid grasses, these population genetic parameters have previously been estimated only in maize (Remingtonet al. 2001; Tenaillonet al. 2001). To provide a similar framework for studies in sorghum, we have surveyed genome-wide sequence variation in a diverse panel of germplasm.

Sequence diversity: This study shows that sorghum has about one-fourth the total variation of maize, from which sorghum is thought to have diverged ∼16.5 million years ago (Gaut and Doebley 1997). On the basis of synonymous sites alone, the fraction drops almost to one-fifth. The small discrepancy between total and synonymous variation may result from the different proportions of coding and noncoding sequences included in the sequences used to estimate “total” variation. In addition, levels of total variation may be affected by different patterns of nearly neutral evolution in the two species (see below).

The lower level of variation in sorghum may be due to a number of factors. First, there was a bias away from sequences with higher mutation rates, since 27 loci (21% of the 129 loci tested) that could not be amplified in S. propinquum were dropped from the study. Another possibility is that genome-wide mutation rates in sorghum are lower than those in maize. Considering replication errors alone, the fairly recent common ancestry of maize and sorghum makes this hypothesis implausible. However, the presence of duplicated genes in maize may allow for relaxed constraint and divergent evolution in paralogues, which may increase the neutral mutation rate (Ohta 1993; Clegget al. 1997; Kondrashovet al. 2002) although it has no effect on the underlying mutational process.

Since variation is a function of both neutral mutation rate and effective population size, it is likely that sorghum has an effective population size (N_e) considerably smaller than that of maize. To what extent this simply reflects differences in census population size is difficult to say. However, because there is seldom a very good correspondence between census size and effective size, other factors must be considered. A domestication “bottleneck” may have been more severe in sorghum than in maize, which has retained ∼70% of the variation present in ancestral teosinte (Eyre-Walkeret al. 1998; White and Doebley 1999). Our sampling is not adequate to address this question, but other studies that measured allozyme or RFLP variation in larger numbers of accessions estimated that cultivated sorghum retains 60–70% of the variation in its wild relatives (Aldrichet al. 1992; Cuiet al. 1995), similar to the estimate for maize. On the other hand, the average Tajima's D in cultivated sorghum (0.299) is considerably higher than that in maize, where it is close to zero (Tenaillonet al. 2001), possibly indicating a greater effect of a bottleneck. Population structure may also contribute to the higher D statistic.

The effects of self-pollination on population genetics: Another factor affecting the difference in sequence variation between sorghum and maize may be their respective mating systems, specifically, that maize is primarily an outcrosser and sorghum is primarily self-pollinated. There is considerable theoretical work on the effects of self-pollination on population genetics. In a completely self-pollinating species, effective population size, and hence polymorphism, is reduced by half (Pollak 1987). Furthermore, the effective rate of recombination is reduced because most individuals are homozygous at most loci. Background selection caused by the elimination of deleterious alleles therefore has a very important effect (Charlesworthet al. 1993), reducing variation as much as 10-fold, depending on the deleterious mutation rate. Hitchhiking effects of directional selection will also be stronger in a self-pollinating species. (All these effects would be intermediate in a partially selfing organism.) Indirectly, mating system may also affect population structure, since selfing species are more likely to be colonizers and may have a more fragmented distribution. The effects of a fragmented population structure are complicated, but can result in smaller effective population size in some situations (Whitlock and Barton 1997; Wakeley and Aliacar 2001).

Several empirical studies have compared patterns of sequence variation in selfing species to those in closely related outcrossing species. In the genus Lycopersicon, Baudry et al. (2001) found that two self-compatible tomato species were 4- to 40-fold less variable than the least variable of three self-incompatible species, a far greater difference than could be accounted for by mating system alone. In Leavenworthia (Liuet al. 1999), sequence variation at PgiC was also greatly reduced in the self-pollinating species. However, at the Adh locus in Arabidopsis lyrata and A. thaliana (Savolainenet al. 2000), the results were less clear and depended critically on whether the species were compared on the basis of within-population or across-population variation. In all three of these studies, each sample was composed of individuals from a single location. Theoretical models that predict reduced N_e in self-pollinators are also based on single population samples. Savolainen et al. (2000), who surveyed more than one such population, showed that variation within individual selfing A. thaliana populations is low compared to that in outcrossing A. lyrata populations, but that across-population variation is similar in the two species. A larger study by Wright et al. (2003) found that within-population variation in A. lyrata was 10-fold higher than that in A. thaliana, but that species-wide variation in A. thaliana was intermediate between that of A. lyrata petraea and A. lyrata lyrata. Their results suggested that (a) factors other than mating system contribute to the observed differences in variation and that (b) the effects of population subdivision and demographic history make it difficult to infer population genetic parameters from levels and patterns of sequence variation.

The analyses of Wright et al. (2003) were based on analyses of variation both within and between populations, so our data are not directly comparable. However, their results suggest that, because our sample includes individuals from many disparate populations, mating system may not be the primary explanation for the lower level of variation in sorghum relative to maize. And while it is reasonable to conclude that a fivefold reduction in synonymous site variation reflects a smaller effective population size, it is not possible to make a quantitative statement about that difference.

While one might expect comparisons to other self-pollinating species to provide some insight on the effect of mating system on levels of sequence variation, the comparisons to wild barley and Arabidopsis, which show severalfold higher levels of species-wide variation, are likely to be confounded by other factors. There are deeply diverged lineages at many loci in both these species, as well as strong geographic structure in barley, suggesting that the population histories of these species are quite different from that of cultivated sorghum. The comparison to maize is more easily interpreted, in that the two species are closely related and both have been domesticated and dispersed by humans within the last 10,000 years.

Linkage disequilibrium: The extent to which linked sites will have a correlated evolutionary history is a function of both effective population size and recombination rate, both of which are affected by mating system (Nordborg 2000), although sorghum's lower N_e may largely be due to other factors. Consistent with the predicted effects of self-pollination and reduced effective population size, sorghum has a greater extent of LD than does maize. Our sequencing strategy did not allow us to plot the decay of LD with physical distance, but short-range intralocus associations are much stronger than those in maize, and significant interlocus associations are severalfold more common. On the other hand, the vast majority of interlocus associations are not significant, and the relationship between polymorphism and divergence changes dramatically at fairly short genetic distances (e.g., Figure 1), suggesting that recombination has decoupled the evolutionary histories of most loci that are not tightly linked. We are currently surveying variation that spans tens of kilobases, and preliminary results suggest that LD dissipates within 10 kb or less (M. T. Hamblin, unpublished data). Thus it appears that the high, but partial, rate of self-pollination in sorghum produces a pattern of LD that is intermediate between that of maize and Arabidopsis (Nordborget al. 2002). It is worth noting, however, that comparison with wild barley also reveals that mating system is not a simple predictor of levels of LD or sequence variation: barley is highly self-pollinating but is more similar in diversity and LD to maize than to sorghum (Morrellet al. 2003).

Excess amino acid polymorphism: Effective population size not only determines levels of neutral variation, but also affects patterns of nearly neutral variation, although this process is still not well understood (Ohta 2002). We have found evidence for an excess of amino acid polymorphism in sorghum, a pattern that has also been observed in Arabidopsis (Bustamanteet al. 2002) and humans (Sunyaevet al. 2000; Fayet al. 2001). This pattern is thought to be due to the presence of variants that are subject to selection coefficients on the order of the reciprocal of N_e and may explain the difference in ratios of synonymous to nonsynonymous variation in species of different effective size. This ratio is smaller in sorghum than in maize, consistent with this theory. Also consistent is the fact that amino acid polymorphisms in sorghum have a lower average frequency than synonymous polymorphisms: while π for synonymous sites is >θ_W, there is essentially no difference between π and θ_W for nonsynonymous sites.

An alternative explanation is that, in this diverse group of accessions, human selection and/or local adaptation have favored different protein alleles in different environments (see below). Africa, where sorghum diversification occurred, has a particularly wide range of habitats ranging from humid tropics to desert (Kimber 2000), a situation that could produce strong diversifying selection. Association studies with nonsynonymous SNPs could address this interesting possibility. (Note that the racial groups analyzed in Table 6 do not correspond to geographical subpopulations; the durra sample, for example, consists of accessions from India, Ethiopia, and Botswana.)

The effects of selection on sequence variation: Candidate genes for association studies are typically identified through integration of QTL mapping, molecular genetics, and bioinformatics approaches. Population genetic analyses can complement this strategy by identifying regions that have been subject to selection (Vigourouxet al. 2002). This approach is likely to be particularly fruitful in crop species, where recent human selection is known to be responsible for much of the useful phenotypic variation.

Selection by humans to improve the agronomic properties of crops is expected to produce characteristic signatures of selection at loci underlying those traits (see, e.g., Wanget al. 1999). Genes underlying “domestication traits,” such as the retention of seeds, should show a signature of directional selection, namely a deficiency of variation relative to divergence. We observed several loci in our study that have this signature (Table 3), suggesting that genes in these regions may have been targets of selection. The genomic region affected by a selective event may be relatively larger in sorghum than in maize or other largely outcrossing taxa, due to the reduced effective rate of recombination.

In contrast to targets of directional selection, loci that have responded to selection from local conditions may show an elevated level of diversity in a species-wide sample such as ours, although they might show reduced variation within a local population. Six of the most unusual loci in our HKA tests (Table 3) departed in the direction of excess polymorphism. Of these six, loci 1056, 1218, and 1249 have five, seven, and one nonsynonymous polymorphism(s), respectively, while coding sites were not identified in the other three loci. Interestingly, theoretical work (Nordborget al. 1996) has shown that high rates of selfing increase the signalto-noise ratio for diversifying selection, making it easier to detect than in outcrossing species.

Our power to detect strong evidence of selection at particular loci in this study is impaired because detection of selection was not the major motivation of the study and the amount of data at any one locus is quite small. None of the departures that we identify in Table 3 is significant; they simply identify candidate regions for further investigation. Conversely, there are regions not highlighted in Table 3 for which independent evidence suggests that they may be associated with phenotypes under selection. On LG D, for example, π at loci 747 (57 cM) and 161 (59 cM) is eightfold less than average, while divergence is more than three times the average (see arrow in Figure 1). These loci are within the likelihood intervals for QTL affecting tillering, regrowth (Patersonet al. 1995), and leaf morphology (R. Ming and A. H. Paterson, unpublished results), traits likely to have been under strong directional selection during sorghum domestication.

Conclusions: On the basis of a survey of almost 30,000 sites throughout the genome of S. bicolor, we find a frequency of SNPs about one-fourth of that observed in a comparable sample of maize accessions. There is no evidence of a skew to rare alleles; thus many of these SNPs are found in the frequency range useful for LD mapping and association studies. While the high level of intralocus LD in sorghum may prevent phenotypic differences from being attributed to individual sequence variants, interlocus LD does not appear to be so high as to reduce the utility of genome scans. Comparisons of polymorphism and divergence suggest that both directional and diversifying selection have played important roles in the evolutionary history of sorghum and that identification of the targets of that selection may provide important insights into the genetic basis of agronomically important phenotypes in the grasses and grains.