BACKGROUND
linkage disequilibrium  is non-random association between alleles at different loci and helps us to reconstruct the genetic history of human populations and to improve our understanding of the biological processes of recombination and natural selection  <cit> .
ld also helps association studies to identify haplotypes that are linked to disease-causing variations.
early studies of ld focused on small sets of genes, such as the hla genes  <cit>  or the growth hormone gene cluster  <cit> .
recently, large-scale genotyping studies  <cit>  have investigated the genomic patterns of ld in the human genome and have found considerable variation in its values, even for snp pairs that are separated by identical physical distances.
some studies have tried to associate this variation with sequence features existing in the genome and found that genic or exonic regions are associated with strong ld in human populations.
for example, extended ld regions are significantly overpopulated with snps located in genic or coding regions  <cit> , and ld is stronger between exonic variants within a gene compared with intronic or intergenic snps  <cit> .
the recent international hapmap project also revealed an excess number of genes with strong ld on a genomic scale  <cit> .
these findings can be explained by the previous hypothesis that purifying selection leads to an increase of ld  <cit> .
this basic hypothesis in turn suggests that ld might be stronger in regions conserved among species than in non-conserved regions, since regions exposed to purifying selection tend to be conserved over evolutionary time.
in the present study, using the complete human/mouse sequences and polymorphic data from the hapmap project, we unexpectedly observed that ld was significantly weaker in conserved regions than in non-conserved regions.
a similar tendency was recently reported in a companion paper of the hapmap project  <cit> .
to investigate this inconsistency between the predicted and observed tendencies, we examined the possibility that the relationship between ld and conserved regions is distorted by other sequence features, such as physical distance, genic content, gc/cpg frequency, or chromosomal location.
however, these features were independent of the weaker ld tendency in conserved regions.
finally, we found that ld patterns carried by interspersed repeats were associated with this discrepancy.
to precisely understand the relationship between ld and sequence conservation, we removed the effect of repetitive elements from the ld patterns, and found that although the previous hypothesis is partly correct, the reality is more complex than expected.
that is, sequence conservation itself is not well associated with the degree of ld; however, on conserved coding regions only, it is related to a strong degree of ld.
the results of our detailed analysis of the ld tendency in conserved regions imply that selective force produces a more complicated tendency in polymorphic patterns that varies according to the long-range or short-range functionality of dna sequences.
RESULTS
ld within conserved regions
we calculated pairwise r <dig> and |d'| values within conserved and non-conserved regions across the human genome and found that conserved regions contained lower proportions of snp pairs that were in complete or nearly complete ld  when calculated as a function of physical distance .
a permutation test confirmed the significance of this observation .
we confirmed that allele frequencies had no effect on this result .
since all results described here and below had the same tendencies for both r <dig> and |d'|, we show only the r <dig> results.
we further checked the result by fine-scale recombination rates from the hapmap data  <cit>  and found a higher recombination rate  in conserved regions than that  in non-conserved regions.
this result is consistent with the ld results, since, in general, lower ld values are widely known to be related to higher recombination rates  <cit> .
the finding of lower ld in conserved regions is inconsistent with the hypothesis that purifying selection increases the extent of ld  <cit> .
therefore, we first considered the possibility that the unexpected decrease of ld in conserved regions  was distorted by the presence of genes, since genic regions had previously been shown to exhibit increased ld  <cit> .
for that purpose, we took intersected regions of conserved/non-conserved regions with genic/non-genic regions, and generated datasets for four classes of regions: conserved genic, conserved non-genic, non-conserved genic, and non-conserved non-genic.
figure 1b  shows that conserved regions still possessed lower proportions of snp pairs in strong ld compared to non-conserved regions for both genic and non-genic classes.
thus, gene content does not account for this effect.
next, since centromeric regions show stronger ld than telomeric regions  <cit> , we also checked the possible involvement of chromosomal location by intersecting conserved and non-conserved regions with telomeric, centromeric, and other residual regions .
figure 1c  shows the same tendency for all centromeric, telomeric, and residual regions.
this result suggested that the weak ld in conserved regions was independent of chromosomal location.
in view of these results, we considered whether other factors, such as gc-content or cpg dinucleotides, may have been involved in the weak ld in conserved regions, because it was recently found that gc-content is associated with weak ld on a genomic scale  <cit> .
however, gc-content and cpg dinucleotides are unlikely to account for the observed ld differences, since the proportions of their bases in conserved regions were almost equal to those in non-conserved ones .
to verify this, we executed permutation tests , and found that even when the effect of these sequence features was subtracted from ld, the adjusted ld in conserved regions was still significantly weaker than that in non-conserved ones .
the influence of repetitive elements
next, we considered whether the weak ld tendency in conserved regions might be related to a lack of interspersed repeats in these regions, since interspersed repeats were recently reported to be related to strong ld on a genomic scale  <cit> .
we found that the proportion of the total number of bases in repeats within conserved regions was half of the proportion found within non-conserved ones , as previously observed  <cit> ; this was probably because local rates of neutral variation may be low in conserved regions  <cit>  or because selective pressure working around conserved regions may have excluded repetitive elements that would cause deleterious changes in the genome, such as changes in a gene's structure  <cit> .
indeed, our permutation tests showed that, after subtracting the effect of repeats from ld by regression, we no longer observed any significant difference in ld between conserved and non-conserved regions .
we confirmed these results by partial correlation analysis .
these findings suggest that the lack of repetitive elements accounts for weak ld in conserved regions.
among the several types of repeats, line/l1s had the largest regression coefficient in the regression analysis between ld and the proportion of bases contained in repeats , the smallest proportion of bases in conserved regions compared to non-conserved ones , and the largest total number of bases in the human genome .
therefore, l1s appeared to mostly account for the weak ld in conserved regions.
since we found that repetitive elements are strongly associated with weaker ld in conserved regions, we adjusted for the base-pair proportion of repeats as well as gc-content; the latter due to outliers of ld related to extreme gc-content after the repeat adjustment.
we then compared the ld levels in highly conserved regions with those in less highly conserved regions.
we expected that highly conserved regions would have stronger ld because the selective pressure on these regions was considered to be stronger.
however, unexpectedly, we found no enhancement of the strong ld fraction within highly conserved regions compared to less highly conserved regions .
we then classified these regions into two groups, those enriched with coding sequences and those enriched with non-coding sequences.
as a result, we found that regions enriched with highly conserved coding sequences had stronger ld than regions enriched with less highly conserved coding sequences.
meanwhile, no difference in ld was found between highly conserved non-coding regions and less highly conserved non-coding regions.
to further confirm these results, we used fine-scale recombination rates from the hapmap data  <cit>  and calculated average recombination rates for the same regions .
this method revealed a similar tendency, with a somewhat smaller recombination rate shown in highly conserved non-coding regions than in less highly conserved non-coding regions, while the difference was far greater between highly and less highly conserved coding rich-regions .
these results suggest that purifying selection that works on evolutionarily conserved regions surely increases the ld level in a series of coding sequences; however, it does not do so in non-coding sequences, as discussed below.
discussion
throughout the evolutionary history of a population, a variety of factors influence the ld level, such as recombination, mutation, genetic drift, natural selection, and demographic events  <cit> .
among these factors, natural selection is considered to generally increase the degree of ld, though there are stochastic fluctuations in individual cases.
there are two primary routes for selection to increase ld  <cit> .
the first is a hitchhiking effect , in which an entire haplotype with an advantageous variant is rapidly selected to high frequency or even fixation  <cit> , leading to a high degree of ld carried by the selected haplotype.
this occurs in the process of positive  selection.
purifying  selection against deleterious variants can also increase ld, as the deleterious haplotypes are swept from the population  <cit> .
the second route is epistatic selection for combinations of alleles at multiple loci  <cit> , in which natural selection may favor or may not favor certain combinations of alleles that work synergistically.
recent studies  <cit>  on ld patterns by large-scale genotyping datasets have demonstrated that ld in genic regions is strong at sizes roughly up to  <dig> to  <dig> kb.
because most genes are exposed to purifying  selection, these studies illustrate that the overall effect of purifying selection is to increase the degree of ld.
this in turn suggests that the degree of ld may be strong in regions that are evolutionarily conserved between distantly related species, e.g., humans and mice, because it is evolutionarily conserved regions that remain unchanged by purifying selection  <cit> .
however, a recent hapmap companion paper  <cit>  reported that, although base-pairs in regions conserved between the human and mouse genomes were associated with low ld when sequence features were analyzed individually, the sequence conservation was not identified as an important predictor of ld in a multiple linear regression analysis.
consistent with these findings, although we initially found that conserved regions showed low ld levels, after consideration of sequence features one-by-one, we eventually determined that this relationship between ld and conserved regions was distorted by the lack of repetitive elements in such regions.
thus, we excluded the effect of repetitive elements  in order to determine the relationship between ld and conserved regions.
however, the result was not as simple as expected.
we did not see a strong association between the level of ld and the degree of conservation in overall conserved regions but observed that strong ld was related to strong conservation in conserved coding regions.
in addition, the ld level was not strongly related to sequence conservation in conserved non-coding regions.
because it has been demonstrated that even in non-coding regions, conserved regions include more functionally important segments, such as regulatory elements, than non-conserved regions  <cit> , conservation thus seems to indicate selective constraint even in non-coding regions.
taking this into account, one interpretation of our results is that selective force works differentially between coding and non-coding regions.
purifying selection works on the function of exons' final protein products and may not allow frequent recombination between sequential series of coding sequences, which leads to strong ld in these sequences.
meanwhile, the similar ld levels in highly and less highly conserved non-coding regions may be explained by the independence of functional units, such as regulatory elements, present in those non-coding regions.
that is, just individual alleles in conserved non-coding regions may be exposed to selective pressure; therefore, they may more often accept recombination between them.
alternatively, our results may suggest that conservation does not indicate selective constraint only for non-coding regions since non-coding regions might include too much noise unlike coding-regions, which are by definition functional.
CONCLUSIONS
following the previous hypothesis that purifying selection increases the extent of ld, we examined whether ld was actually lower in evolutionarily conserved regions and attempted, by considering one potential factor at a time, to determine if a third factor may distort ld in conserved regions.
we found that this tendency was associated with a lack of repetitive elements in those regions.
we then showed that after correcting for the effect of repeat abundance, the degree of conservation itself was not strongly associated with the extent of ld in non-coding regions, but it was associated with ld in coding regions, which suggested that the effect of purifying selection on ld was more complex than expected from the previous hypothesis.
this can be explained by the idea that natural selection works on the function of conserved exons' final protein products, while it works independently on the constituent alleles of conserved functional units in non-coding regions.
in summary, purifying selection may prominently increase the extent of ld only when regions between alleles contain sequentially meaningful segments, such as segments translated into proteins.
as we demonstrated, in-depth analyses are needed to elucidate the relationship between ld and sequence features.
by means of such analyses, the ld patterns of the human genome may help to clarify the biological processes of recombination, mutation, and natural selection during the evolutionary history of human populations.

 linkage disequilibrium is non-random association between alleles at different loci and helps us to reconstruct the genetic history of human populations and to improve our understanding of the biological processes of recombination and natural selection. ld also helps association studies to identify haplotypes that are linked to disease-causing variations. early studies of ld focused on small sets of genes, such as the hla genes or the growth hormone gene cluster. recently, large-scale genotyping studies have investigated the genomic patterns of ld in the human genome and have found considerable variation in its values, even for snp pairs that are separated by identical physical distances. some studies have tried to associate this variation with sequence features existing in the genome and found that genic or exonic regions are associated with strong ld in human populations. for example, extended ld regions are significantly overpopulated with snps located in genic or coding regions, and ld is stronger between exonic variants within a gene compared with intronic or intergenic snps. the recent international hapmap project also revealed an excess number of genes with strong ld on a genomic scale. these findings can be explained by the previous hypothesis that purifying selection leads to an increase of ld. this basic hypothesis in turn suggests that ld might be stronger in regions conserved among species than in non-conserved regions, since regions exposed to purifying selection tend to be conserved over evolutionary time. in the present study, using the complete human/mouse sequences and polymorphic data from the hapmap project, we unexpectedly observed that ld was significantly weaker in conserved regions than in non-conserved regions. a similar tendency was recently reported in a companion paper of the hapmap project. to investigate this inconsistency between the predicted and observed tendencies, we examined the possibility that the relationship between ld and conserved regions is distorted by other sequence features, such as physical distance, genic content, gc/cpg frequency, or chromosomal location. however, these features were independent of the weaker ld tendency in conserved regions. finally, we found that ld patterns carried by interspersed repeats were associated with this discrepancy. to precisely understand the relationship between ld and sequence conservation, we removed the effect of repetitive elements from the ld patterns, and found that although the previous hypothesis is partly correct, the reality is more complex than expected. that is, sequence conservation itself is not well associated with the degree of ld; however, on conserved coding regions only, it is related to a strong degree of ld. the results of our detailed analysis of the ld tendency in conserved regions imply that selective force produces a more complicated tendency in polymorphic patterns that varies according to the long-range or short-range functionality of dna sequences.  ld within conserved regions we calculated pairwise r and |d'| values within conserved and non-conserved regions across the human genome and found that conserved regions contained lower proportions of snp pairs that were in complete or nearly complete ld when calculated as a function of physical distance. a permutation test confirmed the significance of this observation. we confirmed that allele frequencies had no effect on this result. since all results described here and below had the same tendencies for both r and |d'|, we show only the r results. we further checked the result by fine-scale recombination rates from the hapmap data and found a higher recombination rate in conserved regions than that in non-conserved regions. this result is consistent with the ld results, since, in general, lower ld values are widely known to be related to higher recombination rates. the finding of lower ld in conserved regions is inconsistent with the hypothesis that purifying selection increases the extent of ld. therefore, we first considered the possibility that the unexpected decrease of ld in conserved regions was distorted by the presence of genes, since genic regions had previously been shown to exhibit increased ld. for that purpose, we took intersected regions of conserved/non-conserved regions with genic/non-genic regions, and generated datasets for four classes of regions: conserved genic, conserved non-genic, non-conserved genic, and non-conserved non-genic. figure 1b shows that conserved regions still possessed lower proportions of snp pairs in strong ld compared to non-conserved regions for both genic and non-genic classes. thus, gene content does not account for this effect. next, since centromeric regions show stronger ld than telomeric regions, we also checked the possible involvement of chromosomal location by intersecting conserved and non-conserved regions with telomeric, centromeric, and other residual regions. figure 1c shows the same tendency for all centromeric, telomeric, and residual regions. this result suggested that the weak ld in conserved regions was independent of chromosomal location. in view of these results, we considered whether other factors, such as gc-content or cpg dinucleotides, may have been involved in the weak ld in conserved regions, because it was recently found that gc-content is associated with weak ld on a genomic scale. however, gc-content and cpg dinucleotides are unlikely to account for the observed ld differences, since the proportions of their bases in conserved regions were almost equal to those in non-conserved ones. to verify this, we executed permutation tests, and found that even when the effect of these sequence features was subtracted from ld, the adjusted ld in conserved regions was still significantly weaker than that in non-conserved ones. the influence of repetitive elements next, we considered whether the weak ld tendency in conserved regions might be related to a lack of interspersed repeats in these regions, since interspersed repeats were recently reported to be related to strong ld on a genomic scale. we found that the proportion of the total number of bases in repeats within conserved regions was half of the proportion found within non-conserved ones, as previously observed; this was probably because local rates of neutral variation may be low in conserved regions or because selective pressure working around conserved regions may have excluded repetitive elements that would cause deleterious changes in the genome, such as changes in a gene's structure. indeed, our permutation tests showed that, after subtracting the effect of repeats from ld by regression, we no longer observed any significant difference in ld between conserved and non-conserved regions. we confirmed these results by partial correlation analysis. these findings suggest that the lack of repetitive elements accounts for weak ld in conserved regions. among the several types of repeats, line/l1s had the largest regression coefficient in the regression analysis between ld and the proportion of bases contained in repeats, the smallest proportion of bases in conserved regions compared to non-conserved ones, and the largest total number of bases in the human genome. therefore, l1s appeared to mostly account for the weak ld in conserved regions. since we found that repetitive elements are strongly associated with weaker ld in conserved regions, we adjusted for the base-pair proportion of repeats as well as gc-content; the latter due to outliers of ld related to extreme gc-content after the repeat adjustment. we then compared the ld levels in highly conserved regions with those in less highly conserved regions. we expected that highly conserved regions would have stronger ld because the selective pressure on these regions was considered to be stronger. however, unexpectedly, we found no enhancement of the strong ld fraction within highly conserved regions compared to less highly conserved regions. we then classified these regions into two groups, those enriched with coding sequences and those enriched with non-coding sequences. as a result, we found that regions enriched with highly conserved coding sequences had stronger ld than regions enriched with less highly conserved coding sequences. meanwhile, no difference in ld was found between highly conserved non-coding regions and less highly conserved non-coding regions. to further confirm these results, we used fine-scale recombination rates from the hapmap data and calculated average recombination rates for the same regions. this method revealed a similar tendency, with a somewhat smaller recombination rate shown in highly conserved non-coding regions than in less highly conserved non-coding regions, while the difference was far greater between highly and less highly conserved coding rich-regions. these results suggest that purifying selection that works on evolutionarily conserved regions surely increases the ld level in a series of coding sequences; however, it does not do so in non-coding sequences, as discussed below. discussion throughout the evolutionary history of a population, a variety of factors influence the ld level, such as recombination, mutation, genetic drift, natural selection, and demographic events. among these factors, natural selection is considered to generally increase the degree of ld, though there are stochastic fluctuations in individual cases. there are two primary routes for selection to increase ld. the first is a hitchhiking effect, in which an entire haplotype with an advantageous variant is rapidly selected to high frequency or even fixation, leading to a high degree of ld carried by the selected haplotype. this occurs in the process of positive selection. purifying selection against deleterious variants can also increase ld, as the deleterious haplotypes are swept from the population. the second route is epistatic selection for combinations of alleles at multiple loci, in which natural selection may favor or may not favor certain combinations of alleles that work synergistically. recent studies on ld patterns by large-scale genotyping datasets have demonstrated that ld in genic regions is strong at sizes roughly up to to kb. because most genes are exposed to purifying selection, these studies illustrate that the overall effect of purifying selection is to increase the degree of ld. this in turn suggests that the degree of ld may be strong in regions that are evolutionarily conserved between distantly related species, e.g., humans and mice, because it is evolutionarily conserved regions that remain unchanged by purifying selection. however, a recent hapmap companion paper reported that, although base-pairs in regions conserved between the human and mouse genomes were associated with low ld when sequence features were analyzed individually, the sequence conservation was not identified as an important predictor of ld in a multiple linear regression analysis. consistent with these findings, although we initially found that conserved regions showed low ld levels, after consideration of sequence features one-by-one, we eventually determined that this relationship between ld and conserved regions was distorted by the lack of repetitive elements in such regions. thus, we excluded the effect of repetitive elements in order to determine the relationship between ld and conserved regions. however, the result was not as simple as expected. we did not see a strong association between the level of ld and the degree of conservation in overall conserved regions but observed that strong ld was related to strong conservation in conserved coding regions. in addition, the ld level was not strongly related to sequence conservation in conserved non-coding regions. because it has been demonstrated that even in non-coding regions, conserved regions include more functionally important segments, such as regulatory elements, than non-conserved regions, conservation thus seems to indicate selective constraint even in non-coding regions. taking this into account, one interpretation of our results is that selective force works differentially between coding and non-coding regions. purifying selection works on the function of exons' final protein products and may not allow frequent recombination between sequential series of coding sequences, which leads to strong ld in these sequences. meanwhile, the similar ld levels in highly and less highly conserved non-coding regions may be explained by the independence of functional units, such as regulatory elements, present in those non-coding regions. that is, just individual alleles in conserved non-coding regions may be exposed to selective pressure; therefore, they may more often accept recombination between them. alternatively, our results may suggest that conservation does not indicate selective constraint only for non-coding regions since non-coding regions might include too much noise unlike coding-regions, which are by definition functional.  following the previous hypothesis that purifying selection increases the extent of ld, we examined whether ld was actually lower in evolutionarily conserved regions and attempted, by considering one potential factor at a time, to determine if a third factor may distort ld in conserved regions. we found that this tendency was associated with a lack of repetitive elements in those regions. we then showed that after correcting for the effect of repeat abundance, the degree of conservation itself was not strongly associated with the extent of ld in non-coding regions, but it was associated with ld in coding regions, which suggested that the effect of purifying selection on ld was more complex than expected from the previous hypothesis. this can be explained by the idea that natural selection works on the function of conserved exons' final protein products, while it works independently on the constituent alleles of conserved functional units in non-coding regions. in summary, purifying selection may prominently increase the extent of ld only when regions between alleles contain sequentially meaningful segments, such as segments translated into proteins. as we demonstrated, in-depth analyses are needed to elucidate the relationship between ld and sequence features. by means of such analyses, the ld patterns of the human genome may help to clarify the biological processes of recombination, mutation, and natural selection during the evolutionary history of human populations. 
the strong linkage disequilibrium recently found in genic or exonic regions of the human genome demonstrated that ld can be increased by evolutionary mechanisms that select for functionally important loci. to assess this hypothesis, we used genome-wide polymorphism data from the hapmap project and investigated ld within dna sequences conserved between the human and mouse genomes. rather, it implies that purifying selection changes the polymorphic patterns of coding sequences but has little influence on the patterns of functional units such as regulatory elements present in non-coding regions, since the former are generally restricted by the constraint of maintaining a functional protein product across multiple exons while the latter may exist more as individually isolated units. to appropriately understand the relationship between ld and conserved regions, we removed the effect of repetitive elements and found that the high degree of sequence conservation was strongly associated with strong ld in coding regions but not with that in non-coding regions. our work demonstrates that the degree of sequence conservation does not simply increase ld as predicted by the hypothesis. we found that interspersed repeats, and not other sequence features, were associated with the weak ld tendency in conserved regions. this suggests that ld might be stronger in regions conserved among species than in non-conserved regions, since regions exposed to natural selection tend to be conserved.
 the strong linkage disequilibrium recently found in genic or exonic regions of the human genome demonstrated that ld can be increased by evolutionary mechanisms that select for functionally important loci. this suggests that ld might be stronger in regions conserved among species than in non-conserved regions, since regions exposed to natural selection tend to be conserved. to assess this hypothesis, we used genome-wide polymorphism data from the hapmap project and investigated ld within dna sequences conserved between the human and mouse genomes.  unexpectedly, we observed that ld was significantly weaker in conserved regions than in non-conserved regions. to investigate why, we examined sequence features that may distort the relationship between ld and conserved regions. we found that interspersed repeats, and not other sequence features, were associated with the weak ld tendency in conserved regions. to appropriately understand the relationship between ld and conserved regions, we removed the effect of repetitive elements and found that the high degree of sequence conservation was strongly associated with strong ld in coding regions but not with that in non-coding regions.  our work demonstrates that the degree of sequence conservation does not simply increase ld as predicted by the hypothesis. rather, it implies that purifying selection changes the polymorphic patterns of coding sequences but has little influence on the patterns of functional units such as regulatory elements present in non-coding regions, since the former are generally restricted by the constraint of maintaining a functional protein product across multiple exons while the latter may exist more as individually isolated units. 