BACKGROUND
the historical pattern of recombination in the population of genomes of a species or breed contain an enormous amount of information on history of population size, including expansions and contractions, gene flow between other breeds, and selection  <cit> .
it has also been demonstrated that rate of recombination is not uniform across a chromosomal segment, rather recombination events tend to occur in recombination hotspots  <cit> .
the pattern of linkage disequilibrium  in the current generation of a species reflects all of these processes.
while the pattern of ld therefore contains much information, deciphering the relative contribution of each process to the current pattern of ld is challenging  <cit> .
some additional insight into the relative contribution of each process can be gained from comparing historical patterns of recombination inferred from ld to recent patterns of recombination inferred from genetic maps.
one hypothesis would be that in genome regions where large discrepancies are observed between map distances inferred from ld and genetic map distances, strong selection is occurring.
norwegian red cattle  was developed mainly through crosses of old norwegian breeds with other scandinavian breeds like swedish red and white, black and white swedish and finnish ayrshire.
pedigree data has been recorded since formation of nrf, and the breed has been under strong artificial selection for traits such as milk and meat production, fertility and health.
a further attraction of using nrf for this type of study is the extensive pedigree data available, assisting determination of frequency of recombination events between adjacent markers.
the extent of ld in cattle has been investigated in a number of studies  <cit> .
relative to humans cattle display elevated ld, which is likely due to small recent effective population size generally observed in livestock populations  <cit> .
previous studies have shown some variation between cattle breeds in rate of decline in ld with increasing distance between genetic markers  <cit> , which is also at least partly attributable to population history.
another application for recombination rate estimates is within validation of positioning and assembly of genome contigs by linkage analysis.
the bovine genome has recently been sequenced by a combined bacterial artificial chromosome and whole-genome shotgun approach  <cit> .
the resulting btau_ <dig>  assembly has contig and scaffold n <dig> sizes of  <dig>  kb and  <dig>  mb respectively, and represents 95% of the total genome sequence placed on the  <dig> autosomes and the x chromosome.
construction of genetic maps in nrf was used to assess quality of the btau_ <dig>  assembly and indicated a positional error rate of less than  <dig> %  <cit> .
the sequencing and assembly of larger genomes is a complex task with many challenges, and will usually result in imperfect assemblies.
the desire to build a complete assembly is often at odds with the application of stringent merging criteria, and a compromise strategy resulting in longer scaffolds containing some assembly errors is usually the end result  <cit> .
aim of this study was to provide maps of historic and recent recombination rate in nrf, and then to attempt to use these to infer aspects of population history.
recombination rate information was also used to assess quality of the btau_ <dig>  assembly.
RESULTS
a total of  <dig>  paternal half-sib nrf sires and  <dig> founding nrf sires were genotyped using the affymetrix  <dig> k mip array.
the final male genetic map contained  <dig>  snps distributed on the  <dig> bos taurus chromosomes   <cit> , and distributions of spacing between adjacent snps and minor-allele frequency  for the snps are presented in additional files  <dig> and  <dig>  in order to examine the relationships between nrf and cattle breeds that have contributed to the development of nrf,  <dig> holstein,  <dig> finnish ayrshire,  <dig> sided troender and nordland cattle and  <dig> icelandic bulls were also genotyped.
icelandic cattle are believed to have been derived from old norwegian breeds approximately  <dig> years ago.
genetic distances between breeds were investigated using a principal component analysis of the genomic relationship matrix among individuals of different and the same breed  <cit> .
principal component  <dig> , pc <dig> and pc <dig> are plotted in figure  <dig>  for pc <dig> and pc <dig>  the finnish ayrshires and nrf animals group together, likely reflecting the high level of contribution of finnish ayrshire to nrf.
icelandic cattle appear genetically distinct, perhaps reflecting the  <dig> years of genetic isolation of this breed from the other breeds.
pc <dig> separates holsteins from the other breeds.
the principal component analysis also clearly demonstrates heterogeneity in composition among nrf.
for example, some nrf animals have higher than average levels of relationship to finnish ayrshires, while other nrf animals have high levels of relationship with holsteins.
the extent of ld in each breed was assessed by average r <dig> for pairs of markers binned by distance between them .
at short distances  icelandic cattle had highest ld, likely reflecting small effective population size.
nrf had lower levels of ld at comparable distances, especially distance greater than  <dig> kb, than any of the other breeds.
the low levels of ld observed in nrf relative to the other breeds is likely due to elevated heterogeneity in nrf from historic admixture, recent attempts to control inbreeding and gene flow through import of sires from other nordic countries  <cit> .
for nrf the highest and lowest chromosomal mean values for r <dig> were found on bta <dig> and bta <dig>  and highest and lowest mean values of r <dig> for inter marker distances less than  <dig> mb were found for bta <dig> and bta <dig>  chromosomal mean values for nrf for r <dig>  and for r <dig> for inter marker distances less than  <dig> mb, for all chromosomes are presented in additional file  <dig>
at very short inter-marker distances, the level of ld in nrf was high .
a mean r <dig> of  <dig>  or more was observed for snps positioned less than  <dig> kb apart while a mean r <dig> of  <dig>  or more was observed for snps positioned less than  <dig> kb apart.
the results suggest that to obtain an expected r <dig> between markers and a causal polymorphism of at least  <dig>  for genome-wide association studies, approximately one snp every  <dig> kb or a total of  <dig>  snps would be required for the  <dig>  gb genome.
a report of decline in r <dig> with increasing distance between snps in australian holstein-friesian cattle  <cit>  describes quite similar results as for nrf at these short distances.
reports from other breeds have described similar or more rapid decline in r <dig> at short distances than what was found in nrf  <cit> .
however, long range ld  is lower in nrf than in these other breeds.
whole-genome mean r <dig> for bins of short inter-marker distances  between syntenic snps in norwegian red cattle.
to investigate recombination patterns across genomic regions, maps describing historic ld levels were constructed for each chromosome based on population recombination rate in the nrf data.
by the method presented by auton and mcvean  <cit> , estimates of scaled population recombination rate   <cit>  were found for each interval between adjacent snps for all  <dig> btas with the ldhat software  <cit> .
following pritchard and przeworski  <cit> , historical scaled recombination rate ) was compared with recent scaled recombination rate ) calculated from the genetic map by plotting their cumulative values against physical position .
correlation between total cumulative ρ and ρ over all chromosomes was found to be  <dig> .
a reduced ρ relative to ρ for a genomic region could be an indication that animals in the observed pedigree have been under strong artificial selection for traits affected by polymorphisms in that particular region.
regions where ρ was most strikingly reduced relative to ρ were in the middle of bta <dig> and in the middle of bta <dig>  reduced ρ relative to ρ was also found on btas  <dig>   <dig> ,  <dig>   <dig>   <dig>   <dig> and  <dig>  while elevated ρ relative to ρ was found on btas  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  and  <dig>
on bta <dig> several qtls affecting milk production traits have been reported  <cit> , and a meta-analysis reported by khatkar et al.
<cit>  indicated presence of three qtls for milk yield on this chromosome.
the bta <dig> region centres around a mutation reported to affect protein percentage in the ghr gene  <cit> .
hayes et al.
<cit>  reported evidence for strong selection in this region in a study of divergence between dairy cattle and beef cattle.
on bta <dig> two qtls affecting milk production traits have been reported in nrf  <cit>  and signatures of strong selection have been detected  <cit> .
elevated population recombination rate may be due to population expansion or gene conversion, while reduced recombination rate may be due to directional selection, genetic drift, gene flow, population substructure or low effective population size  <cit> .
regions under strong selection in both historic and recent generations might not show differences between ρ and ρ.
it was also investigated whether recombination rates per physical distance were related to chromosomal region or chromosome size.
telomeres showed significantly higher values for both recent and historic recombination rate per physical distance than the genome average .
a negative correlation between recombination rate and chromosome length is expected  <cit> , and for ρ and ρ correlations of - <dig>  and - <dig>  was found between length of genetic map and physical chromosome length.
identification of chromosomes with unexpectedly elevated or reduced recombination rate could be identified by looking at outliers deviating from the expected linear relationship between recombination rate and chromosome length.
in figure  <dig> total cumulative values of recombination rate for ρ and ρ are plotted against physical chromosome length for each bovine chromosome.
expected recombination map lengths relative to chromosome lengths with 95% confidence intervals  are also indicated in the figure.
it can be seen that ρ is elevated for btas  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig> and  <dig>  while ρ is elevated for btas  <dig>   <dig>   <dig>   <dig> and  <dig>  further, reduced ρis observed for btas  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig> and  <dig>  while ρis reduced for btas  <dig> and  <dig>  consistently elevated ρ and ρ are found for btas  <dig>   <dig> and  <dig> and consistently reduced ρ and ρ are found for bta <dig>  in accordance with results described above, ρ is significantly reduced relative to ρ for bta <dig>  bta <dig> and bta <dig>
in addition to chromosome region and chromosome size, sex-specific differences in recombination rates have been reported  <cit> .
in this study male genetic maps for nrf were used, which might differ from female genetic maps.
the patterns of recombination described here might also be sex-specific.
moreover, rate of recombination is not uniform across a chromosomal segment and recombination events tend to occur in recombination hotspots  <cit> .
it has been estimated that these hotspots occur on average every  <dig> -  <dig> kb in the human genome  <cit> .
although the procedure applied here for estimation of ρ incorporates a model accounting for variable recombination rates across chromosomes  <cit> , a snp density higher than obtained in this study would be required in order to detect such fine-scale recombination hotspots in the bovine genome.
quality assessment of btau_ <dig>
approximately 5% of the genomic sequence is expected to be missing in btau_ <dig>   <cit> , and positioning of previously un-positioned contigs could aid completion of the assembly by pointing towards regions of special interest for re-sequencing efforts.
here a comparative analysis of the btau_ <dig>  assembly with the human genome build  <dig> allowed  <dig>  previously un-positioned bovine contigs to be given putative genome positions.
determining recombination events between adjacent markers in an extensive pedigree can be used to construct dense genetic maps, and sufficient information was available from our nrf linkage analysis to validate the positions of  <dig> of these contigs  <cit> .
comparative analysis and linkage analysis identified  <dig> new contig positions as being less than  <dig> mb apart .
even though large synteny blocks exist between species comparative analysis will yield spurious positions.
here 40% of positions identified by comparative analysis were validated by linkage analysis.
to further assess assembly accuracy, population recombination rates between adjacent snps were assessed.
regions of putative problematic assembly were identified as extreme values of scaled population recombination rate  relative to inter-marker distance between adjacent snp pairs.
extreme values of ρ would be expected for intervals where assembled inter-marker distance was shorter than actual inter-marker distance.
in figure  <dig> ρ is plotted for btas  <dig>   <dig>   <dig> and  <dig>  contig positions predicted by comparative analysis are indicated in light grey, contig positions predicted by linkage analysis are indicated in dark grey and contig positions validated by similar positions from both comparative analysis and linkage analysis are indicated in light blue.
plots for all chromosomes are given in additional file  <dig>  from figure  <dig> it can be seen that several ρ peaks were located near validated positions for previously un-positioned contigs, which further highlights these regions as erroneous in the original assembly.
examples are the three ρ peak regions on bta <dig> around  <dig> mb,  <dig> mb and  <dig> mb, the ρ peak region on bta <dig> around  <dig> mb, the ρ peak region on bta <dig> around  <dig> mb and the ρ peak region on bta <dig> around  <dig> mb.
of the putative contig positions found by comparative analysis 24% lay within  <dig> mb of an extreme value for population recombination rate  and of positions found by linkage analysis 27% lay within  <dig> mb of an extreme value for population recombination rate.
for the  <dig> contigs given similar positions by comparative analysis and linkage analysis 28% of validated positions lay within  <dig> mb of an extreme value for population recombination rate.
putative contig positions not coinciding with elevated ρ may be due to failure to detect regions with elevated recombination rate, incorrect positioning of un-positioned contigs or un-positioned contigs containing sequence overlap with already assembled contigs.
inability to detect regions with elevated recombination rate could result from surrounding snps not containing enough information or from un-positioned contigs being too short to detectably affect ρ. incorrect positioning of un-positioned contigs could be due to repeat sequence mapping to similar but not equal genomic sequence or random mapping to the wrong position by linkage analysis.
incorrect positioning of un-positioned contigs could also explain why not all of positions found by linkage analysis for the  <dig> contigs validated positions found by comparative analysis.
an alternative bos taurus genome assembly  was reported by zimin et al.
<cit> .
this assembly had 95% identity with the btau_ <dig>  assembly but had more genomic sequence placed on the bovine chromosomes.
regions differing between umd <dig> and btau_ <dig>  were identified by sequence alignments  <cit>  and some of these regions coincide with regions identified as problematic here.
some examples are the region around  <dig> mb on bta <dig>  the region around  <dig> mb on bta <dig>  the region around  <dig> mb on bta <dig>  the region around  <dig> mb on bta <dig> and the proximal ends of bta <dig>  bta <dig> and bta <dig> .
genotyping of snps positioned on un-positioned contigs in a large pedigree and consequent linkage analyses as described here provide useful information for improving the current bovine genome assembly .
the approach will gain even higher power and more accurate predictions as denser genetic maps become available.
likewise comparative sequence analysis would be a good supplement for correct contig or scaffold positioning.
CONCLUSIONS
low levels of ld were observed in nrf relative to some of the breeds from which this breed originates.
this is likely due to elevated heterogeneity in nrf from historic admixture, recent attempts to maintain a large effective population size through control of inbreeding and gene flow through import of sires from other nordic countries.
reports from breeds other than those assessed in this study have described more rapid decline in r <dig> at short distances  <cit>  than was found in nrf.
the results suggested that to obtain an expected r <dig> between markers and a causal polymorphism of at least  <dig>  for genome-wide association studies in nrf, approximately one snp every  <dig> kb or a total of  <dig>  snps would be required for the  <dig>  gb genome.
for well known qtl regions for milk production on bta <dig>  bta <dig> and bta <dig>  map length based on historic recombination was greater than map length based on recent recombination in nrf.
selective sweeps have previously been identified for the qtl regions on bta <dig>  <cit>  and bta <dig>  <cit> .
reduced ρ relative to ρ was also found on btas  <dig> ,  <dig>   <dig>   <dig>   <dig> and  <dig>  while elevated ρ relative to ρ was found on btas  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  and  <dig>
while over 95% of the total genome sequence is included in bovine genomic assembly btau_ <dig> , problematic regions exists and should be identified to facilitate assembly completion.
here such regions were identified by combining comparative sequence analysis, linkage analyses and detection of regions with extreme values of population recombination rate.

 the historical pattern of recombination in the population of genomes of a species or breed contain an enormous amount of information on history of population size, including expansions and contractions, gene flow between other breeds, and selection. it has also been demonstrated that rate of recombination is not uniform across a chromosomal segment, rather recombination events tend to occur in recombination hotspots. the pattern of linkage disequilibrium in the current generation of a species reflects all of these processes. while the pattern of ld therefore contains much information, deciphering the relative contribution of each process to the current pattern of ld is challenging. some additional insight into the relative contribution of each process can be gained from comparing historical patterns of recombination inferred from ld to recent patterns of recombination inferred from genetic maps. one hypothesis would be that in genome regions where large discrepancies are observed between map distances inferred from ld and genetic map distances, strong selection is occurring. norwegian red cattle was developed mainly through crosses of old norwegian breeds with other scandinavian breeds like swedish red and white, black and white swedish and finnish ayrshire. pedigree data has been recorded since formation of nrf, and the breed has been under strong artificial selection for traits such as milk and meat production, fertility and health. a further attraction of using nrf for this type of study is the extensive pedigree data available, assisting determination of frequency of recombination events between adjacent markers. the extent of ld in cattle has been investigated in a number of studies. relative to humans cattle display elevated ld, which is likely due to small recent effective population size generally observed in livestock populations. previous studies have shown some variation between cattle breeds in rate of decline in ld with increasing distance between genetic markers, which is also at least partly attributable to population history. another application for recombination rate estimates is within validation of positioning and assembly of genome contigs by linkage analysis. the bovine genome has recently been sequenced by a combined bacterial artificial chromosome and whole-genome shotgun approach. the resulting btau_ assembly has contig and scaffold n sizes of kb and mb respectively, and represents 95% of the total genome sequence placed on the autosomes and the x chromosome. construction of genetic maps in nrf was used to assess quality of the btau_ assembly and indicated a positional error rate of less than %. the sequencing and assembly of larger genomes is a complex task with many challenges, and will usually result in imperfect assemblies. the desire to build a complete assembly is often at odds with the application of stringent merging criteria, and a compromise strategy resulting in longer scaffolds containing some assembly errors is usually the end result. aim of this study was to provide maps of historic and recent recombination rate in nrf, and then to attempt to use these to infer aspects of population history. recombination rate information was also used to assess quality of the btau_ assembly.  a total of paternal half-sib nrf sires and founding nrf sires were genotyped using the affymetrix k mip array. the final male genetic map contained snps distributed on the bos taurus chromosomes, and distributions of spacing between adjacent snps and minor-allele frequency for the snps are presented in additional files and in order to examine the relationships between nrf and cattle breeds that have contributed to the development of nrf, holstein, finnish ayrshire, sided troender and nordland cattle and icelandic bulls were also genotyped. icelandic cattle are believed to have been derived from old norwegian breeds approximately years ago. genetic distances between breeds were investigated using a principal component analysis of the genomic relationship matrix among individuals of different and the same breed. principal component, pc and pc are plotted in figure for pc and pc the finnish ayrshires and nrf animals group together, likely reflecting the high level of contribution of finnish ayrshire to nrf. icelandic cattle appear genetically distinct, perhaps reflecting the years of genetic isolation of this breed from the other breeds. pc separates holsteins from the other breeds. the principal component analysis also clearly demonstrates heterogeneity in composition among nrf. for example, some nrf animals have higher than average levels of relationship to finnish ayrshires, while other nrf animals have high levels of relationship with holsteins. the extent of ld in each breed was assessed by average r for pairs of markers binned by distance between them. at short distances icelandic cattle had highest ld, likely reflecting small effective population size. nrf had lower levels of ld at comparable distances, especially distance greater than kb, than any of the other breeds. the low levels of ld observed in nrf relative to the other breeds is likely due to elevated heterogeneity in nrf from historic admixture, recent attempts to control inbreeding and gene flow through import of sires from other nordic countries. for nrf the highest and lowest chromosomal mean values for r were found on bta and bta and highest and lowest mean values of r for inter marker distances less than mb were found for bta and bta chromosomal mean values for nrf for r and for r for inter marker distances less than mb, for all chromosomes are presented in additional file at very short inter-marker distances, the level of ld in nrf was high. a mean r of or more was observed for snps positioned less than kb apart while a mean r of or more was observed for snps positioned less than kb apart. the results suggest that to obtain an expected r between markers and a causal polymorphism of at least for genome-wide association studies, approximately one snp every kb or a total of snps would be required for the gb genome. a report of decline in r with increasing distance between snps in australian holstein-friesian cattle describes quite similar results as for nrf at these short distances. reports from other breeds have described similar or more rapid decline in r at short distances than what was found in nrf. however, long range ld is lower in nrf than in these other breeds. whole-genome mean r for bins of short inter-marker distances between syntenic snps in norwegian red cattle. to investigate recombination patterns across genomic regions, maps describing historic ld levels were constructed for each chromosome based on population recombination rate in the nrf data. by the method presented by auton and mcvean, estimates of scaled population recombination rate were found for each interval between adjacent snps for all btas with the ldhat software. following pritchard and przeworski, historical scaled recombination rate ) was compared with recent scaled recombination rate ) calculated from the genetic map by plotting their cumulative values against physical position. correlation between total cumulative ρ and ρ over all chromosomes was found to be. a reduced ρ relative to ρ for a genomic region could be an indication that animals in the observed pedigree have been under strong artificial selection for traits affected by polymorphisms in that particular region. regions where ρ was most strikingly reduced relative to ρ were in the middle of bta and in the middle of bta reduced ρ relative to ρ was also found on btas, and while elevated ρ relative to ρ was found on btas and on bta several qtls affecting milk production traits have been reported, and a meta-analysis reported by khatkar et al. indicated presence of three qtls for milk yield on this chromosome. the bta region centres around a mutation reported to affect protein percentage in the ghr gene. hayes et al. reported evidence for strong selection in this region in a study of divergence between dairy cattle and beef cattle. on bta two qtls affecting milk production traits have been reported in nrf and signatures of strong selection have been detected. elevated population recombination rate may be due to population expansion or gene conversion, while reduced recombination rate may be due to directional selection, genetic drift, gene flow, population substructure or low effective population size. regions under strong selection in both historic and recent generations might not show differences between ρ and ρ. it was also investigated whether recombination rates per physical distance were related to chromosomal region or chromosome size. telomeres showed significantly higher values for both recent and historic recombination rate per physical distance than the genome average. a negative correlation between recombination rate and chromosome length is expected, and for ρ and ρ correlations of - and - was found between length of genetic map and physical chromosome length. identification of chromosomes with unexpectedly elevated or reduced recombination rate could be identified by looking at outliers deviating from the expected linear relationship between recombination rate and chromosome length. in figure total cumulative values of recombination rate for ρ and ρ are plotted against physical chromosome length for each bovine chromosome. expected recombination map lengths relative to chromosome lengths with 95% confidence intervals are also indicated in the figure. it can be seen that ρ is elevated for btas and while ρ is elevated for btas and further, reduced ρis observed for btas and while ρis reduced for btas and consistently elevated ρ and ρ are found for btas and and consistently reduced ρ and ρ are found for bta in accordance with results described above, ρ is significantly reduced relative to ρ for bta bta and bta in addition to chromosome region and chromosome size, sex-specific differences in recombination rates have been reported. in this study male genetic maps for nrf were used, which might differ from female genetic maps. the patterns of recombination described here might also be sex-specific. moreover, rate of recombination is not uniform across a chromosomal segment and recombination events tend to occur in recombination hotspots. it has been estimated that these hotspots occur on average every - kb in the human genome. although the procedure applied here for estimation of ρ incorporates a model accounting for variable recombination rates across chromosomes, a snp density higher than obtained in this study would be required in order to detect such fine-scale recombination hotspots in the bovine genome. quality assessment of btau_ approximately 5% of the genomic sequence is expected to be missing in btau_, and positioning of previously un-positioned contigs could aid completion of the assembly by pointing towards regions of special interest for re-sequencing efforts. here a comparative analysis of the btau_ assembly with the human genome build allowed previously un-positioned bovine contigs to be given putative genome positions. determining recombination events between adjacent markers in an extensive pedigree can be used to construct dense genetic maps, and sufficient information was available from our nrf linkage analysis to validate the positions of of these contigs. comparative analysis and linkage analysis identified new contig positions as being less than mb apart. even though large synteny blocks exist between species comparative analysis will yield spurious positions. here 40% of positions identified by comparative analysis were validated by linkage analysis. to further assess assembly accuracy, population recombination rates between adjacent snps were assessed. regions of putative problematic assembly were identified as extreme values of scaled population recombination rate relative to inter-marker distance between adjacent snp pairs. extreme values of ρ would be expected for intervals where assembled inter-marker distance was shorter than actual inter-marker distance. in figure ρ is plotted for btas and contig positions predicted by comparative analysis are indicated in light grey, contig positions predicted by linkage analysis are indicated in dark grey and contig positions validated by similar positions from both comparative analysis and linkage analysis are indicated in light blue. plots for all chromosomes are given in additional file from figure it can be seen that several ρ peaks were located near validated positions for previously un-positioned contigs, which further highlights these regions as erroneous in the original assembly. examples are the three ρ peak regions on bta around mb, mb and mb, the ρ peak region on bta around mb, the ρ peak region on bta around mb and the ρ peak region on bta around mb. of the putative contig positions found by comparative analysis 24% lay within mb of an extreme value for population recombination rate and of positions found by linkage analysis 27% lay within mb of an extreme value for population recombination rate. for the contigs given similar positions by comparative analysis and linkage analysis 28% of validated positions lay within mb of an extreme value for population recombination rate. putative contig positions not coinciding with elevated ρ may be due to failure to detect regions with elevated recombination rate, incorrect positioning of un-positioned contigs or un-positioned contigs containing sequence overlap with already assembled contigs. inability to detect regions with elevated recombination rate could result from surrounding snps not containing enough information or from un-positioned contigs being too short to detectably affect ρ. incorrect positioning of un-positioned contigs could be due to repeat sequence mapping to similar but not equal genomic sequence or random mapping to the wrong position by linkage analysis. incorrect positioning of un-positioned contigs could also explain why not all of positions found by linkage analysis for the contigs validated positions found by comparative analysis. an alternative bos taurus genome assembly was reported by zimin et al.. this assembly had 95% identity with the btau_ assembly but had more genomic sequence placed on the bovine chromosomes. regions differing between umd and btau_ were identified by sequence alignments and some of these regions coincide with regions identified as problematic here. some examples are the region around mb on bta the region around mb on bta the region around mb on bta the region around mb on bta and the proximal ends of bta bta and bta. genotyping of snps positioned on un-positioned contigs in a large pedigree and consequent linkage analyses as described here provide useful information for improving the current bovine genome assembly. the approach will gain even higher power and more accurate predictions as denser genetic maps become available. likewise comparative sequence analysis would be a good supplement for correct contig or scaffold positioning.  low levels of ld were observed in nrf relative to some of the breeds from which this breed originates. this is likely due to elevated heterogeneity in nrf from historic admixture, recent attempts to maintain a large effective population size through control of inbreeding and gene flow through import of sires from other nordic countries. reports from breeds other than those assessed in this study have described more rapid decline in r at short distances than was found in nrf. the results suggested that to obtain an expected r between markers and a causal polymorphism of at least for genome-wide association studies in nrf, approximately one snp every kb or a total of snps would be required for the gb genome. for well known qtl regions for milk production on bta bta and bta map length based on historic recombination was greater than map length based on recent recombination in nrf. selective sweeps have previously been identified for the qtl regions on bta and bta. reduced ρ relative to ρ was also found on btas, and while elevated ρ relative to ρ was found on btas and while over 95% of the total genome sequence is included in bovine genomic assembly btau_, problematic regions exists and should be identified to facilitate assembly completion. here such regions were identified by combining comparative sequence analysis, linkage analyses and detection of regions with extreme values of population recombination rate. 
although low ld measured by r was observed in nrf relative to some of the breeds from which this breed originates, reports from breeds other than those assessed in this study have described more rapid decline in r at short distances than what was found in nrf. while ld is reduced in nrf compared to some of the breeds from which this admixed breed originated, it is elevated over short distances compared to some other cattle breeds. further, positions for previously unpositioned contigs from assembly of the bovine genome sequence found using comparative sequence analysis were validated by linkage analysis, and 28% of these positions corresponded to extreme values of population recombination rate. linkage analysis in combination with comparative sequence analysis and detection of regions with extreme values of population recombination rate proved to be valuable for detecting problematic regions in the btau_ genome assembly. for well known quantitative trait loci for milk production traits on bos taurus chromosomes and map length based on historic recombination was greater than map length based on recent recombination in nrf. genomic regions in nrf where map length based on historic recombination was greater than map length based on recent recombination coincided with some well known qtl regions for milk production traits. norwegian red cattle make an interesting case study for investigating these patterns as it is an admixed breed with an extensively recorded pedigree. comparison of recent patterns of recombination derived from linkage maps to historical patterns of recombination from linkage disequilibrium could help identify genomic regions affected by strong artificial selection, appearing as reduced recent recombination. rate of decline in r for nrf suggested that to obtain an expected r between markers and a causal polymorphism of at least for genome-wide association studies, approximately one snp every kb or a total of snps would be required. nrf have been under strong artificial selection for traits such as milk and meat production, fertility and health. while measures of ld is also crucial for determining the number of markers required for association mapping studies, estimates of recombination rate can be used to assess quality of genomic assemblies. a dataset containing more than genome-wide distributed snps and animals was used to assess recombination rates and ld in nrf.
 comparison of recent patterns of recombination derived from linkage maps to historical patterns of recombination from linkage disequilibrium could help identify genomic regions affected by strong artificial selection, appearing as reduced recent recombination. norwegian red cattle make an interesting case study for investigating these patterns as it is an admixed breed with an extensively recorded pedigree. nrf have been under strong artificial selection for traits such as milk and meat production, fertility and health. while measures of ld is also crucial for determining the number of markers required for association mapping studies, estimates of recombination rate can be used to assess quality of genomic assemblies.  a dataset containing more than genome-wide distributed snps and animals was used to assess recombination rates and ld in nrf. although low ld measured by r was observed in nrf relative to some of the breeds from which this breed originates, reports from breeds other than those assessed in this study have described more rapid decline in r at short distances than what was found in nrf. rate of decline in r for nrf suggested that to obtain an expected r between markers and a causal polymorphism of at least for genome-wide association studies, approximately one snp every kb or a total of snps would be required. for well known quantitative trait loci for milk production traits on bos taurus chromosomes and map length based on historic recombination was greater than map length based on recent recombination in nrf. further, positions for previously unpositioned contigs from assembly of the bovine genome sequence found using comparative sequence analysis were validated by linkage analysis, and 28% of these positions corresponded to extreme values of population recombination rate.  while ld is reduced in nrf compared to some of the breeds from which this admixed breed originated, it is elevated over short distances compared to some other cattle breeds. genomic regions in nrf where map length based on historic recombination was greater than map length based on recent recombination coincided with some well known qtl regions for milk production traits. linkage analysis in combination with comparative sequence analysis and detection of regions with extreme values of population recombination rate proved to be valuable for detecting problematic regions in the btau_ genome assembly. 