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1 Department of Animal and Aquacultural Sciences, Agricultural University of Norway, N-1432 Aas, Norway
2 Centre for Integrative Genetics and Department of Animal Science, Agricultural University of Norway
Corresponding author: H. G. Olsen; e-mail: hanne-gro.olsen{at}iha.nlh.no.
| ABSTRACT |
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Key Words: cattle fine mapping linkage disequilibrium milk
Abbreviation key: BTA = bovine (Bos taurus) chromosome, IBD = identical by descent, LA = linkage analysis, LD = linkage disequilibrium, logL = logarithm of the likelihood
| INTRODUCTION |
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Linkage disequilibrium (LD) mapping allows the utilization of all recombinations that occurred during the generations before marker genotyping started and is thus a powerful method for fine mapping. Meuwissen and Goddard (2000) postulated that a base population in linkage equilibrium undergoes a mutation at the QTL, creating a novel QTL-allele embedded in one specific marker haplotype. Due to recombinations in the following generations, the original haplotype will remain only for markers close to the QTL. Thus, in the current generations, these marker alleles will be in linkage disequilibrium with the QTL alleles. The LD can be detected by estimating the effects of the marker haplotypes on the quantitative trait. Haplotypes with identical marker alleles are expected to have a similar effect on the trait because the identical marker alleles imply that the chromosomal region is inherited in a manner that is identical by descent (IBD) from an ancient common ancestor, and the haplotypes are therefore expected to carry similar QTL alleles. However, as LD approaches are highly affected by factors such as population admixture causing spurious long-distance disequilibria, the extent of LD along the chromosome, and how correct the linkage phases are estimated, pure LD analysis may report a number of false positives (Perez-Enciso, 2003).
Linkage analysis and linkage disequilibrium analysis can be combined as proposed by Meuwissen et al. (2002). This approach allows the utilization of recombinations occurring both within and outside the pedigreed and genotyped generations (i.e., linkage analysis and linkage disequilibrium analysis, respectively) and also accounts for unknown background genes. Additionally, a combined approach prevents the false positives caused by accidental marker-phenotype associations from LA or the long-distance disequilibria found in cattle (Farnir et al., 2000) that may arise when the approaches are used separately.
In dairy cattle, much effort has been undertaken to detect QTL for milk production traits, and a number of chromosomes have been reported to harbor regions with significant effects. Several studies have reported the presence of one or more QTL on chromosome 6 (BTA6) (e.g., Georges et al., 1995; Spelman et al., 1996; Zhang et al., 1998; Velmala et al., 1999; Ron et al., 2001), but the results of the studies differ somewhat with respect to the number of QTL detected, their positions, and to which extent the milk traits are affected by the QTL. Several studies performed in a number of breeds have reported segregation of at least one QTL close to marker BM143 in the middle of BTA6 (e.g., Spelman et al., 1996; Kühn et al., 1999; Velmala et al., 1999; Nadesalingam et al., 2001; Ron et al., 2001). In a previous study in Norwegian Dairy Cattle, linkage analysis was utilized in a genome scan for QTL affecting 5 milk production traits (milk yield, fat percentage, fat yield, protein percentage, and protein yield) in 6 elite sire families with a total of 284 sons (Olsen et al., 2002). A highly significant QTL was detected on chromosome 6 close to marker FBN9, with its most likely position approximately 2 cM downstream of BM143. The 95% confidence interval for the QTL position was found to be 16 cM. Two of the elite sires, which were paternal half sibs, shared a common haplotype in the relevant area that seemed to cause a marked reduction in both fat and protein percentages and a weak increase of milk yield. No effect on fat and protein yield was found. The aim of the present study was to utilize the combined linkage and linkage disequilibrium method of Meuwissen et al. (2002) to refine the position of the detected QTL, and to investigate whether more than one QTL was segregating in this chromosomal segment.
| MATERIALS AND METHODS |
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Predicted transmitting abilities of the sons from the 35 families were used as performance information in the analyses. The PTA for the 5 milk production traits (milk yield, fat percentage, fat yield, protein percentage, and protein yield) were available from the national genetic evaluation in June 2000 carried out by GENO Breeding and AI Association and evaluated using BLUP with a single trait sire-maternal grandsire model.
Marker Map
Initially, 16 publicly available microsatellites in the region around the putative QTL on chromosome 6 were tested for genotyping difficulties, number of alleles, and degree of heterozygosity among the 35 elite sires. Of these, 10 markers (URB16, BM1329, BMS2508, FBN12, BMS1242, BM143, BMS690, DIK82, FBN13, and BMS470) were selected for genotyping in all sires and sons. The relative positions, number of alleles, and heterozygosity of these markers are shown in Table 1
. The markers spanned a region of approximately 31 cM around the putative QTL found in Olsen et al. (2002), thus covering approximately the peak of the test statistic curve of that study. Markers were genotyped using primers and PCR conditions as described by Ma et al. (1996) and Weikard et al. (1997) for URB16 and FBN markers, respectively, and at USMARC Genome Database (2003) for BM and BMS markers. Figure 1
shows the position of these markers as compared to the markers used in the previous genome scan (Olsen et al., 2002).
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Statistical Analyses
Single QTLsingle-trait analysis.
Each of the 5 milk traits was analyzed separately using the combined linkage and linkage disequilibrium method of Meuwissen et al. (2002). In short, the method consisted of the following steps: First, the linkage phases of all sires and sons were estimated based on marker information. In the second step, the midpoint of each marker bracket was regarded as a putative position for a QTL. For each putative QTL position (i.e., midpoint of marker bracket), the IBD probabilities of pairs of haplotypes were calculated from marker and/or pedigree information (for details, see Meuwissen and Goddard, 2001; and Meuwissen et al., 2002). Only the bracket midpoints were considered since, for a dense marker map, individual positions within the bracket would have similar probabilities. The IBD probability depended on the effective population size and the number of generations since the base populations, which were both assumed to be 100. For each bracket, a complete matrix of IBD probabilities between all haplotypes at the putative QTL position was obtained. This matrix is denoted Gi, where the subscript i reflected the fact that the probabilities depended on the ith position of the QTL. The last step was to calculate the likelihood of the data using restricted maximum likelihood. The model of the performance data was expressed as
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where y is a (nx1) vector of records (i.e., PTA for the milk trait in question), µ is the overall mean, 1 is a vector of 1s, h is a vector of random haplotype effects of dimension q x 1, where q is the number of different haplotypes, Z is a (nxq) incidence matrix relating observations and haplotype effects, u is a vector of random polygenic effects, and e is a vector of residuals. The variances of h, u, and e are
,
, and
, respectively, where Gi is the matrix of IBD probabilities among haplotypes, A is the additive genetic relationship matrix, and R is a diagonal matrix with
on the diagonals (nj is the number of daughters of bull j). For each marker bracket, the logarithm of the likelihood (logL) of a model containing a QTL, as well as background genes, was calculated by maximizing the likelihood with respect to the variance components using the ASREML package (Gilmour et al., 2000). The likelihood of the alternative hypothesis of no QTL was calculated based on a model containing only background genes and the test statistic formed as the difference in logL between the model with and without a QTL. The marker bracket with the highest logL difference was taken as the most likely QTL position. The significance level of the test statistic was determined from the chi-square distribution, as the logL ratio times 2 is chi-squared distributed with 1 degree of freedom (i.e., the number of degrees of freedom is equal to the difference in number of parameters fitted in the model with a QTL vs. the model with no QTL). Because the QTL were already found to be highly significant in the study of Olsen et al. (2002), no specific methods for determining the significance threshold were used. Therefore, a nominal P-value of 5% was considered to be significant.
Single QTL-multiple trait analysis.
The ASREML program was also used to perform the multiple-trait analysis using the same IBD matrix (Gi) as in the single-trait analysis. The multitrait analysis included the 3 yield traits only. The data were modeled as:
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where yi is a (3 x 1) vector of PTA of bull i for milk, fat, and protein yield, b is a vector of fixed effects, which includes the mean for each of the 3 traits, hi1 and hi2 are (3 x 1) vectors of effects of the paternally or maternally inherited haplotype of bull i on each of the 3 traits, respectively, and ui and ei are (3 x 1) vectors of random polygenic effects and residuals of bull i on each trait, respectively. Following Goddard (2001), it was assumed that all vectors of haplotype effects hij are along the same line, instead of pointing in all directions of their 3-dimensional space. This substantially reduces the number of parameters to be estimated, and the assumption is true when the QTL is bi-allelic (i.e., all haplotype effect vectors point to either the effect of QTL allele 1 or QTL allele 2 and thus lay along the line connecting these 2 points). The assumption is only approximately true when the QTL is multi-allelic, but 2 of the QTL alleles are much more frequent than the others. If the hij effects all lay along the same line, the variance-covariance matrix of hij can be modeled by:
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where v is the (3 x 1) direction vector of the line along which all hij are modeled. Thus, ASREML estimated only the 3 parameters of the direction vector v, instead of the 6 parameters contained by the full variance-covariance matrix H.
Multiple QTL-single-trait analysis.
All traits were analyzed with the multiple QTL single trait method proposed by Meuwissen and Goddard (2002). The data were modeled as:
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where y, 1, µ, Z, u, and e is as for the single QTL-single-trait analyses,
i denotes summation over all possible QTL positions (bracket midpoints), qi is a vector of haplotype effects, Xi is a known incidence matrix relating allelic effects with records, and Ii is an indicator variable, where Ii = 1 (Ii = 0) indicates (no) QTL at position i.
, where Gi is the IBD matrix between the haplotypes at the ith position. The variance components and haplotype effects were estimated using Gibbs sampling with 500,000 cycles, and Ii was sampled with a Metropolis-Hastings step (Meuwissen et al., 2001). As opposed to the paper of Meuwissen and Goddard (2002), the prior probability of having a QTL in bracket i (Ii = 1) depended on the length of the bracket. As a QTL previously had been mapped to the relevant area of BTA6 (Olsen et al., 2002), the total prior probability of detecting a QTL in the genotyped area of 31 cM was 100%. The prior of each bracket was then set equal to the relative length of that bracket. Flat priors were assumed for
and
, whereas the prior distribution of
was inverse-chi-squared with 4.2 degrees of freedom (Meuwissen and Goddard, 2002). After discarding the initial 10,000 cycles from the MCMC chain as burn-in, the fraction of cycles with Ii = 1 gave an estimate of the posterior probability of a QTL at position i. A significant QTL was present in a bracket if the posterior probability of that bracket exceeded 0.5.
Multiple QTL-multiple-trait analysis.
Multiple QTL-multiple-trait analysis was performed according to Meuwissen and Goddard (accepted). This method is an extension of the multiple QTL-single-trait method. The data were modeled as:
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where yi, Xib, ui, and ei are the same as for single QTL-multitrait analysis,
j denotes summation over all possible QTL positions, vj is the direction vector for the effects of the QTL alleles at position j, qij1 and qij2 are the sizes of the QTL effects for the paternal and maternal allele of animal i at position j along the direction vector vj. As in the single QTL multitrait analysis, the number of parameters was reduced by assuming that the effects of the QTL alleles on each of the traits were lying on the same line instead of pointing in all directions of their 3-dimensional space. This reduction of the number of parameters was more important in this analysis, since the effects of several QTL were estimated simultaneously. For details, see Meuwissen and Goddard (2003).
| RESULTS |
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| DISCUSSION |
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The milk traits are known to be highly correlated, with a positive correlation among the 3 yield traits as well as between the 2 percentage traits, and a negative correlation between yield and percentage traits. Thus, by using a composite hypothesis combining information from all traits simultaneously in multitrait analyses, the power to detect QTL and the accuracy of estimating QTL positions might be improved, as the QTL may have pleiotropic effects on all traits. Only the 3 yield traits were used for the multitrait analysis, as the percentage traits are functions of the yield traits and would contribute no extra information. The multitrait approach confirmed the QTL found in the single-trait approach but did not refine the QTL position as the shape of the logL ratio curves was similar for the 2 approaches (Figures 3
and 5
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The rather broad curve extending from brackets 2 to 5 could be due to the presence of 2 or more closely linked QTL affecting the trait in the same direction, which could cause a significant test statistic over a large chromosome segment. This was investigated by fitting 2 or more QTL simultaneously. The multipoint QTL analyses were performed for each of the 5 traits individually, as well as for a multitrait analysis including only the 3 yield traits (Figures 4
and 5
, respectively). The multi-QTL analysis did not clearly show the presence of more than one QTL in this area, but the fitting of multiple QTL gave a much sharper indication of bracket 3 as the QTL position than the single QTL models. This is probably because the multi-QTL mapping reduced the carryover effect of the QTL to adjacent putative QTL positions (Meuwissen and Goddard, accepted).
All analyses revealed small peaks around brackets 6 to 8. Although no significant test statistics were detected, the fact that the peak remains through all analyses could indicate a second QTL with minor effects in this area.
These results strongly suggested the interval between markers BMS2508 and FBN12 as the most likely position of the QTL. In a study of Israeli Holstein, Ron et al. (2001) detected a highly significant QTL for fat and protein percentages close to BM143, with a 95% confidence interval for the position of a QTL for protein percentage of only 4 cM in two families. The confidence interval for fat percentage was spanning approximately 10 cM in their study. The most likely QTL position in our study, i.e., the midpoint of the interval between markers BMS2508 and FBN12, was situated approximately 4 cM to the left of BM143 in our map. A QTL in the vicinity of BM143 has also been reported in a number of other Holstein populations (e.g., Spelman et al., 1996; Kühn et al., 1999; Nadesalingam et al., 2001) as well as Finnish Ayrshire (Velmala et al., 1999). Both in the study of Velmala et al. (1999) and of Ron et al. (2001), two families were segregating for protein percentage close to BM143. In both cases, however, the two sires had different alleles for BM143, so if they have had an IBD segment containing a common QTL allele, the IBD region is no longer including this marker. Thus, the QTL found in Norwegian Dairy Cattle seems to be the same as that found in these studies.
In a previous genome scan performed on a subset of the families utilized in the current study, the most likely QTL position was found close to marker FBN9 (Olsen et al., 2002). FBN9 is situated between markers DIK82 and FBN13, which was bracket 8 in the current study (Figure 1
). Although the QTL position found in the former study was somewhat to the right compared with marker bracket 3 of the present study, a 95% confidence interval for the QTL position found in the previous study spanned approximately brackets 2 to 9 here, and thus the results of the 2 studies are in agreement with each other. In the current study, some smaller, nonsignificant peaks were found around brackets 6 to 8, i.e., close to the most likely position from the genome scan. If these additional peaks are in fact real QTL with minor effects, their effects could have contributed to the shift to the right of the log likelihood peak in the former study.
The combined LA and LD approach narrowed the interval of the QTL from a 16 cM confidence interval in the genome scan (Olsen et al., 2002) to a marker bracket of 7.5 cM in this study. However, in order to identify the gene(s) affecting the traits or utilize QTL information efficiently in marker assisted selection, the QTL position needs to be narrowed down further to 1 to 2 cM. One of several approaches for refining this interval could be to repeat the analyses for individual cM within bracket 3, as only the bracket midpoints were considered with the methods outlined here. However, with a dense marker map, individual positions within a bracket would normally have very similar probabilities of harboring a QTL and would thus yield little new information.
In the present study, with some rather broad intervals and the QTL situated in the second largest bracket, one could argue that the utilization of the combined analysis did not improve the mapping resolution much as compared to a pure linkage analysis. To test the advantage of the combined approach over LA, the same data were analyzed for protein percentage with a model similar to that of the single-traitsingle-QTL model but including linkage information only. As shown in Figure 7
, the shape of the LogL curve was relatively similar to that of the combined analysis (uppermost curve of Figure 2
), although flatter and with a decreased difference in likelihood between the hypotheses of one versus no QTL. Confidence intervals of the QTL position were calculated for both models using the 1 LOD drop-off criteria (Lander and Botstein, 1989). The interval for the combined analysis contained brackets 3 and 4 only, whereas for the linkage analysis, all brackets, except 1 and 9, were included. Since the combined linkage-linkage disequilibrium mapping approach is especially suited to fine-mapping with a dense marker map, the best approach to refine the QTL position is to increase the marker density between BMS2508 and FBN12 and repeat the analysis on the improved marker map. As the numbers of microsatellites in the region are very limited, effort is now undertaken to generate and genotype a large number of single nucleotide polymorphisms in order to refine the QTL position.
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| CONCLUSIONS |
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| ACKNOWLEDGEMENTS |
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Received for publication April 28, 2003. Accepted for publication August 11, 2003.
| REFERENCES |
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