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* INRA, UR337 Station de Génétique Quantitative et Appliquée, F-78350 Jouy-en-Josas, France, INRA, Union Nationale des Coopératives Agricoles d'Elevage et d'Insémination Animale, F-75595 Paris, France, INRA, UR339 Laboratoire de Génétique Biochimique et Cytogénétique, F-78350 Jouy-en-Josas, France, Institut de l'Élevage, F-75595 Paris, France and ** CEA/Institut de Génomique—Centre National de Génotypage, F-91057 Evry, France
1 Corresponding author: Laboratoire de Génétique Biochimique et de Cytogénétique, Département de Génétique Animale, INRA, Domaine de Vilvert, 78352 Jouy-en-Josas, France.
E-mail: mathieu.gautier{at}jouy.inra.fr
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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In some cases, fine-mapping studies were carried out to reduce these confidence intervals (MEUWISSEN et al. 2002; OLSEN et al. 2005; GAUTIER et al. 2006), leading in some instances to the identification of the underlying causal mutation (GRISART et al. 2002; BLOTT et al. 2003; COHEN-ZINDER et al. 2005). These fine-mapping studies were mostly based on addition of new sire families, additional markers, and the use of statistical methods combining linkage analysis (LA) and linkage-disequilibrium (LD) analysis (LDLA). In general, the marker density was slightly increased by the addition of a few tens of new markers (microsatellite markers or SNPs) identified within the QTL region or in some candidate genes.
High-throughput SNP analysis and SNP microarrays now give one the opportunity to genotype many animals for hundreds of SNPs per chromosome (KHATKAR et al. 2006, 2007; GAUTIER et al. 2007). Due to these techniques, marker density is no longer a limiting factor in QTL fine-mapping studies, which can be speeded up or even performed without prior knowledge of segregating QTL. However, these dense marker maps require efficient statistical methods that work fast and efficiently with large numbers of markers.
In France, fine mapping of QTL related to female fertility is of utmost importance. Fertility has been decreasing in the Holstein breed despite its economical importance. The heritability of this trait is particularly low and the efficiency of traditional selection remains limited. Therefore identification of genetic variants involved in the fertility decline of Holstein cows might be particularly beneficial to improve selection through marker assistance. As a consequence, it was decided to evaluate the efficiency of dense SNP maps for QTL fine mapping considering a QTL underlying nonreturn rate estimated 90 days after artificial insemination (NRR90) previously identified on bovine chromosome 3 (BTA03) and segregating in the French Holstein population using a sparse 16-microsatellite map as a model (GUILLAUME et al. 2007).
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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Phenotypes were equivalent to twice the daughter yield deviation (DYD) (VANRADEN and WIGGANS 1991) estimated on NRR90 as described previously (GUILLAUME et al. 2007). These represent the average performance of the daughters of a sire, corrected for the environmental effects and the genetic value of the mates.
Genotypic data:
The methods for SNP detection, selection, and genotyping were presented previously (GAUTIER et al. 2007). Briefly, SNPs were detected in silico on the basis of the sequences available in public databases. In total, 1373 SNPs were chosen to cover the whole BTA03 on the basis of comparative mapping results and included in a 1536-SNP GoldenGate assay provided by Illumina (http://www.illumina.com; Illumina, San Diego) to be genotyped at the Centre National de Génotypage (Evry, France). A dense linkage map of BTA03 containing 460 SNPs could then be constructed using available pedigrees and comparative mapping information after rejecting uninformative SNPs (GAUTIER et al. 2007). The BTA03 genetic map was estimated to span 125 Mb (and 127 cM) with an average marker spacing of 280 kb (from <500 bp to 3 Mb). For this study, 437 SNPs belonging to this dense BTA03 map and with a minor allele frequency (MAF) >0.05 in the Holstein breed were considered for further fine-mapping analysis. Genotypes for these 437 chosen SNPs were available for the 926 sons of the Holstein GDD, with few missing data or inconsistency with familial information. On average each son was genotyped for 99.7% of the SNPs (from 79.4 to 100%).
Haplotype reconstruction:
A program was developed for rapid haplotype reconstruction working with dense marker maps. The most likely genotypes of the different sires were first determined. For each SNP, the likelihood of each of the three possible sire genotypes (all SNPs in the study being biallelic) was equal to the product of the contribution of all its sons. The contribution of each son corresponded to its genotype probability given the sire genotype considered and the probability of inheriting the observed maternal allele estimated by its population frequency. A probability of genotyping error was set to 0.001 in the computation of the likelihood.
Paternally and maternally inherited haplotypes for the different animals were then calculated using the following algorithm:
(WINDIG and MEUWISSEN 2004), where y (x) is the number of offspring with a marker phase in agreement (disagreement) with the tested sire haplotype configuration and 
l is the recombination rate between the tested marker and the closest informative marker for offspring l. Similarly, 
is computed with the closest informative markers downstream. If 
, then the probability that the first marker allele of the sire belongs to the haplotype k is 
(WINDIG and MEUWISSEN 2004). 
> 0.95, the corresponding marker allele is assigned to the sire haplotype k. Thus, the other sire allele is then assigned to the sire haplotype 3 – k.
QTL mapping method:
First, half-sib linear regression (KNOTT et al. 1996) was performed,
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, where 
is the residual variance in sire family i and RELij is the reliability of the proof of son j of sire i based on progeny information only. The model was tested for each marker interval. Marker informativity for each interval was computed as the mean 
. Chromosomewide significance thresholds were estimated with 30,000 within-family permutations (CHURCHILL and DOERGE 1994). At the location of the maximum likelihood-ratio test (LRT), heterozygous status of the sires was estimated with a t-test on the basis of the value of the substitution effect, residual variance in the sire family, and the number of sons. A 90% confidence interval was estimated using the Lod drop-off approach and corresponds to the positions around the peak (with a LRT value of LRTp) for which the LA curve is >(LRTp – 3.84).
In addition to the half-sib regression analysis, a variance component (VC)-based linkage analysis (GEORGE et al. 2000) was performed with the model
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The (co)variance structure was
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is the polygenic variance. Gv is the relationship matrix among QTL allelic effects estimated due to relationships and marker information (FERNANDO and GROSSMAN 1989) and 
is the gametic variance. As in PONG-WONG et al. (2001), the method for calculating the gametic matrix used the closest informative bracket (as defined in 3.1 above) instead of estimating probabilities-of-descent of a gamete (PDQ) from parent to offspring by integration over all possible haplotypes. Rules to compute the PDQ using the closest informative bracket can be found in Table 1 in PONG-WONG et al. (2001). In summary, the probability to receive the QTL allele from the first haplotype of the sire is equal to 
, 
, 
, or 
if both, only the first, only the second, or none of the marker alleles of the closest informative markers are equal in the paternal haplotype of the offspring and the first haplotype of the sire (where , 1, and 2 are the recombination rates between the two closest informative markers, between the first informative marker and the QTL location, and between the second informative marker and the QTL location, respectively). The variances of paternal and maternal alleles were assumed to be equal and a single parameter was estimated () as previously described (GRIGNOLA et al. 1996a). Then, variance associated with the QTL (QTL allelic variance) was twice . The proportion of total genetic variance due to the QTL was
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) divided by the weight of the corresponding DYD for NRR90. These weights were daughter equivalent and were corrected for the number of inseminations and cows in each herd (VANRADEN and WIGGANS 1991).
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p) were estimated among each pair of base haplotypes conditionally on the identity-by-state (IBS) status of the neighboring markers using windows of 10 flanking markers (MEUWISSEN and GODDARD 2001). p) as a distance measure. Base haplotypes were grouped if p > 0.50 (YTOURNEL et al. 2007). PCs were also grouped within the clusters if (i) the two SCs of a sire are grouped in the same cluster (the PCs of all his sons are then grouped in this cluster) or (ii) a PC can be associated with a base haplotype with a probability >0.95 (it is grouped to the corresponding cluster).
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In addition, a similar model with the following new rules was applied: (1) all chromosomes, even PCs, were considered as base haplotypes; (2) smaller marker windows were used (three markers); and (3) haplotype groups were no longer constructed on the basis of IBD probabilities but on the basis of IBS status (if haplotypes were IBS for all markers they were grouped together). This method searches if an effect can be associated with a small haplotype covering a small region. Small marker windows were preferred to obtain a small number of groups. HAP3 is used to refer to this model.
For the three different models (VC linkage analysis, IBD10, and HAP3), genetic parameters were estimated after maximizing likelihoods with an average information–restricted maximum-likelihood (AI–REML) approach (JENSEN et al. 1996). The BLUPF90 software (MISZTAL et al. 2002) was modified to incorporate relationship matrices among QTL allelic effects.
The likelihood-ratio test statistic considered variance components as parameters and was used to confirm whether there was a QTL present at the studied position,
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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5% (data not shown). As a consequence, for these two sire families, informativity dropped to 0.35 and 0.40. Although this might affect power of LA, in the case that the corresponding sires are found heterozygous at the QTL, assuming the two sire haplotypes are IBD at the corresponding (large) homozygous positions and the causal mutation(s) are relatively old, the QTL could be excluded from this part of the chromosome. The LDLA approach uses to a broader extent this kind of IBD information. The QTL was confirmed by both regression and the VC linkage analysis (Figure 1). The maximum LRT location was found in neighboring intervals with both methods (positions 19.03 and 18.98 cM with the regression analysis and the VC approach, respectively). With the regression analysis the QTL was significant (P < 0.001) while with the VC approach, the likelihood-ratio test (–2(ln(H0) – ln(H1)) = 9.92 (P < 0.01). The confidence interval spanned 9 cM on the map: from position 15.85 to 24.82 cM.
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Linkage disequilibrium and linkage analysis:
These analyses were performed on the 150 first marker intervals (until position 34.96 cM) corresponding to a region larger than the 90% QTL confidence interval as determined by the Lod drop off (Figure 1).
The LRT curves presented five and six peaks >6.0 with models IBD10 and HAP3, respectively (Figure 2 and Table 2). For most of the described peaks, the LRT curve obtained with LDLA models exceeded clearly the LA LRT curve while outside these regions it was below it and often reduced to zero. As shown in Table 2, only peaks 1, 2, and 4 were significant for both LDLA models. For both models, the maximum was located in the second peak (at position 16.9 cM on the map). The first peak (at position 11.7 cM on the map) also presented particularly high LRT values with both models.
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In addition to N20, the haplotypes of the six heterozygous sires (P < 0.10) were studied. As expected, for all the positions, more base haplotypes were grouped with model HAP3 than with the IBD10 model. However, this was also true for haplotypes with opposite effects. At the first and fifth peaks, all the positive haplotypes of the heterozygous sires were identical for three markers and were grouped together with the HAP3 model (Table 3). The HAP3 model grouped at least five haplotypes of six in one cluster at peaks 1, 2, 4, 5, and 6 (see haplotypes of sires in Table 3). The peaks 3, 7, and 8 were locations where base haplotype clusters contained less than four haplotypes of heterozygous sires together.
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With the IBD10 model, four haplotypes with positive effects were grouped in one cluster and the two remaining haplotypes were grouped in another cluster at the first position. At other positions, three or fewer haplotypes of heterozygous sires were clustered together with the IBD10 model.
At peaks 5 and 7, LRT is high with IBD10 while low with HAP3. For these positions, there is little grouping with the IBD10 model (the haplotypes of the heterozygous sires are not grouped together) while there is more grouping with the HAP3 model. However, haplotypes with opposite effects are also grouped together with the HAP3 model. Therefore, the LRT curve dropped with model HAP3 for these positions.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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p between haplotypes 1 and 3, this probability will be high since all the nine remaining alleles are identical alleles. The same high p will be computed between haplotypes 2 and 3, which is inconsistent with the first p estimated. To avoid these problems, minimal p were used in this study: if a marker allele was missing in a haplotype, it was supposed different from another haplotype one for p computation. This has consequences on the LDLA since not all the LD information is used and haplotypes containing missing markers will have low p with other base haplotypes and will not be clustered. Therefore, it is very important to reconstruct as much as possible the base haplotypes. For SCs, the haplotype reconstruction program leaves few missing markers but for MCs, there are still some missing markers for ungenotyped markers, in low-informativity regions and in regions displaying high recombination rates. The haplotype reconstruction program can still be improved to reduce the number of missing alleles by using the LD between markers.
Linkage analysis:
The QTL was confirmed with respect to the previously published study (GUILLAUME et al. 2007) based on a larger half-sib design comprising 26 families. The LRT peak was within the 95% confidence interval of this latter one and the obtained significance was higher with fewer families. The use of a high-density marker map resulted in almost optimal genetic information along the whole chromosome. In consequence, a sharper and higher LRT curve was obtained. With this density of markers, QTL transmission is followed more precisely and locations of recombinations are determined within smaller intervals, allowing an almost perfect achievement of the pedigree linkage-mapping resolution. Four sires were heterozygous (P < 0.05), which represents <25% of the tested families. This proportion is close to the one previously obtained (GUILLAUME et al. 2007), where 6 of 26 sires (23%) were determined as heterozygous. This corresponds approximately to allelic frequencies of 0.15 and 0.85 for the two alternate QTL alleles, assuming a biallelic QTL and that QTL genotypes are distributed according to Hardy–Weinberg proportions in the sire population. The average allelic substitution effect was 4.6% of NRR90 and represents 0.7 standard genetic deviation, which is higher than the effect (3% corresponding to 0.45 standard genetic deviation) previously reported (GUILLAUME et al. 2007). Nevertheless, these estimated effects have a rather large impact on the fertility and would represent a large part of the genetic variation. Indeed, the variance explained by the QTL can be approximated as 2pq
2 (where p and q are the allelic frequencies and is the average allelic substitution effect) and this would result in 12% of the genetic variance in our study. However, these are rough approximations since both average substitution effects and allelic frequencies are estimated approximately. For instance, some old sire families had low reliabilities (because recording of fertility traits started when their daughters were already old) while younger ones might also get more records in the coming years.
With the VC approach, the location of the peak was nearly identical to the one found with the regression method although different hypotheses and information were used (complex pedigree, numerous QTL alleles). The significance of the QTL was also high (P < 0.01). The variance associated with the QTL represented 14% of the genetic variance. This value is close to the variance approximated through the average allelic substitution effect and the allelic frequencies. The part of variance associated with this QTL and the allelic substitution effect are rather large and the use of this QTL in selection would help breeders to improve fertility of dairy cows, which is dramatically decreasing.
Linkage disequilibrium and linkage analysis:
The method used for LDLA was based on LDLA methods proposed recently (MEUWISSEN and GODDARD 2000; KIM and GEORGES 2002; BLOTT et al. 2003). MEUWISSEN et al. (2002) proposed to use p between base haplotypes, which generates a very dense relationship matrix among haplotypes that is often nonpositive and requires bending strategies, reducing IBD relationships between base haplotypes. In addition, inversion of this dense matrix might be computationally demanding. Due to the clustering approach, the method by KIM and GEORGES (2002) uses a diagonal matrix associated with the random base haplotype effects since base haplotypes are assigned to a given cluster according to LD information and there is no relationship between different clusters. The model and the results are easier to interpret since pairs of base haplotypes can be described as equal or as different.
KIM and GEORGES (2002) and BLOTT et al. (2003) tested all possible distances from 0 to 1 to cluster the base haplotypes. In this study, only one grouping was tested at each position to reduce computational time and because multiplication of the test might lead to large amounts of results that are difficult to interpret. At the chosen 0.5 maximum distance, it was shown in a simulation study (YTOURNEL et al. 2007) that most of the base haplotype pairs were actually IBD while in 75% of the cases where two QTL alleles were non-IBD, the probability was <0.10. The distance was also chosen to obtain a small number of groups with many base haplotypes. Indeed, if there is little grouping, the groups are correct but little LD information (only from common ancestors from recent generations) is used whereas if there is too much grouping, the grouping is incorrect.
From 58 to 99% of the base haplotypes were grouped within 20 clusters. All the LD information was not used since some base haplotypes were not grouped. This is due to haplotypes containing missing alleles. However, already a large part of LD is used since generally 75% or more of the base haplotypes are grouped and information of SCs is used. Indeed, these haplotypes are known with more precision and are therefore more important. Fortunately, these haplotypes are also reconstructed with more precision and therefore contain only a few missing markers. Most PCs were grouped directly in the clusters because with the marker density the probability of transmission of the paternal allele was >0.95 at most locations. These probabilities were <0.95 if there was a recombination or if the sire was noninformative in that region. In the latter case, the sire was homozygous for all the markers in the region and therefore, both SCs were grouped in the same cluster. In consequence, the corresponding PC was also grouped in that cluster.
Despite the fact that the LDLA did not result in a single peak, it improved strongly the information on the QTL location with respect to the LA. Indeed, many regions were discarded according to the LDLA because QTL alleles of opposite effects were grouped in the same cluster. The LDLA discarded regions where heterozygous sires did not share common haplotypes. As a consequence, the possible location of the QTL is confined to a few small intervals.
Additional information at the peaks such as grouping of haplotypes of sires estimated to be heterozygous helps discard some peaks. This information is similar to that used in haplotype-sharing methods (RIQUET et al. 1999; NEZER et al. 2003): positive or negative alleles of heterozygous sires should be surrounded by small identical haplotypes. Peaks 1, 2, 4, 5, and 8 were the positions where the four heterozygous sires (P < 0.05) shared a common haplotype of three markers for their favorable or unfavorable haplotypes. At peak 2, the only negative haplotype not grouped with the others was the haplotype of sire 41 that had the less significant t-test (P < 0.10). Peaks 1 and 2 seem to be the most interesting since at other peaks, the common haplotype is also associated with several haplotypes of opposite effect. These three-marker haplotypes cover regions of 0.1 and 2.04 cM for peaks 1 and 2, respectively. Flanking markers are at a distance of –0.05 and +2.04 cM and –0.70 and +0.15 cM, respectively.
In contrast, there was little grouping at some positions even with the HAP3 model: haplotypes with favorable (or unfavorable) effects do not share a common three-marker haplotype. This was found at peaks 3, 6, and 7. Therefore, confidence in these peaks is lower than in the first two peaks.
In addition, peaks where some heterozygous sires at the QTL appear homozygous at the markers are less likely to contain the QTL. For instance, for sire 633, with the strongest t-test, p between his two haplotypes was 0.84 at peak 1. Similarly, when favorable and unfavorable haplotypes of heterozygous sires are grouped together, there is less probability that the QTL is located at that peak. The negative haplotype of sire 633 is identical to the positive haplotypes of sire 307 and 311 for a region spanning from marker 83 to marker 101. Therefore, p for these haplotypes is >0.90 at peak 5. At peak 6, this is still true for the haplotypes of sires 633 and 307. Similarly, peaks 4 and 8 are less likely to contain the QTL because several haplotypes with opposite effects have high p and are clustered together.
In summary, the first two peaks appear to be the most likely intervals for the QTL location because LRT values are high with both methods, and most heterozygous sires share a common haplotype, while at other peaks there is little grouping of haplotypes of heterozygous sires or haplotypes with opposite effects are grouped together.
These conclusions are based on a model assuming a single QTL with two alleles. This is the most parsimonious model and it appears to be in agreement with the data since studies in linkage analysis did not show evidence for multiple QTL, the same sires are heterozygous at different positions, and heterozygous sires have a common haplotype (Table 3). For several peaks, the grouping of the sire haplotypes is relatively similar, indicating that these peaks are likely to reflect the same QTL. In this context, the multiple-peak profile would then be explained by the heterogeneous LD structure within the QTL region. This might be increased by possible local inconsistencies in the map order, which was based on draft assembly or on comparative map information. Moreover, the method and the data structure might not allow the discarding of some regions even though they do not harbor the QTL. In addition, NRR90 is a complex biological trait resulting from several distinct unobserved events such as fertilization or embryo survival (GUILLAUME et al. 2007). More discriminating phenotypes would then enhance accuracy of the QTL fine mapping. However, such phenotypes are difficult and costly to obtain. Hence, several (possibly linked) genes might thus be expected to underlie the genetic variability of different biological related events of such a broad trait. Nevertheless the method should be relatively robust if there are several QTL alleles, each possibly embodied in a different cluster, since the model does not assume only two alleles. Alternatively, if several QTL located between positions 10 and 35 cM on our map are affecting NRR90, fine mapping of these linked QTL would require a more complex method such as multi-QTL fine-mapping methods (MEUWISSEN and GODDARD 2004; OLSEN et al. 2005). Larger designs might be advised to clearly and correctly separate several QTL in a 25-cM region.
The models HAP3 and IBD10 have some complementary properties. First, HAP3 searches for small informative regions of three markers that have a quantitative effect. Therefore, these regions must be in LD with the QTL. Noninformative regions are not detected if all QTL alleles (favorable and unfavorable) are grouped together. If all (un)favorable alleles of a QTL are associated with one haplotype, the HAP3 method should detect that region unless the opposite allele is associated with the same haplotype (noninformative haplotype with very high frequency). The method automatically performs the search for haplotype sharing for a three-marker haplotype. It is expected that within the QTL region, the QTL will be detected but also that false positive results might be found. Indeed, by chance, four or six haplotypes of heterozygous sires might have a common haplotype over three markers, especially if these three markers have low MAF. For instance, according to the allelic frequencies, the probability for a haplotype to be CAA was 0.417 and to be ATG was 0.370 at peaks 1 and 2, respectively. Therefore, the probability to observe that the six positive haplotypes of heterozygous sires are CAA was 0.005 and the probability to observe that the five negative haplotypes of the five sires with the highest t-test are ATG was 0.007. Since 150 marker intervals were tested, it is possible to find by chance regions for which haplotypes of heterozygous sires are IBS and not IBD. The IBD10 method uses IBD probabilities and uses a large marker window. Therefore, it helps to discard regions that were identical for three markers by chance from regions where haplotypes were grouped because they have high p. However, IBD10 will be more sensitive to missing information or to genetic map inconsistencies. Finally, the LD information (haplotype sharing) must be confirmed by the LA information used by the method. Indeed, a tested region will present a high LRT value only if LD and LA information is high in that region.
Use of two distinct techniques, one based on the regression on a small number of markers and one based on p obtained from larger haplotypes, is in agreement with recent findings (GRAPES et al. 2006; ZHAO et al. 2007) showing that a method based on single-marker regression can be as efficient as the IBD method (MEUWISSEN and GODDARD 2000). In addition, according to one of these studies (GRAPES et al. 2006), 4 or 6 markers must be used in the latter method, which represents the optimal compromise between power (increasing with the number of markers) and discrimination between successive tested positions (decreasing with the number markers). In our study, a larger number of markers (namely 10) are used but our method is different since p's are used to cluster haplotypes together. Therefore, the number of effects considered in the model is smaller. Most of the haplotypes are grouped in 20 clusters, which corresponds more to the number of haplotypes obtained with 4–6 markers than with 10 markers. Finally, differences between likelihood values at successive tested positions indicate that the method discriminates sufficiently between these positions.
Conclusions:
The fertility QTL on BTA3 was highly significant (P < 0.001) and has large effects on insemination results. Indeed, the average allelic substitution effect was 0.7 genetic standard deviation and the QTL explained 14% of the genetic variance. The program implemented for this study successfully handled the large amount of data for haplotype construction, LA, and LDLA. The QTL was not fine mapped to a small single region. However, the analysis, combined with the analysis of haplotypes of heterozygous sires, refined the QTL position to a small set of narrow intervals out of which two intervals appeared to be the regions the most likely to harbor the QTL. However, additional information is required to find the causal mutations.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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LITERATURE CITED |
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).
), and LDLA curve with model HAP3 (----) are shown.