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,#,
* Research Institute for the Biology of Farm Animals Dummerstorf, D-18196 Departments of
Dairy Science and
Statistics, Virginia Polytechnic Institute and State University Blacksburg, VA-24061-0315
# Department of Animal Breeding and Genetics, Danish Institute of Agricultural Sciences Research Centre Tjele, DK-8830
Corresponding author:
Gertraude Freyer; e-mail:
freyer{at}fbn-dummerstorf.de.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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Key Words: milk yield traits • QTL mapping • multivariate analysis
Abbreviation key: AIREML = average information restricted maximum likelihood, CVC = covariance components, DYD = daughter yield deviations, IBD = identity by descent, LR = likelihood ratio, LS = least squares
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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To the best of our knowledge, results of QTL findings in dairy cattle have been reported on the basis of univariate analyses until now. Such results provide only partial information on the genetic architecture of milk production, and univariate analyses do not optimally use the available information.
The multivariate QTL mapping methods take advantage of the correlation structure of the traits. In this way, they achieve higher statistical power for detecting QTL and higher precision of parameter estimates compared to univariate QTL mapping methods (Jiang and Zeng, 1995; Sørensen, 2000). Using multitrait QTL mapping method enables researchers to detect pleiotropic QTL and to distinguish them from closely linked trait-specific QTL.
In this study, we used a multivariate QTL mapping based on the variance component model (e.g., Grignola et al., 1996; Sørensen, 2000). An "average information restricted maximum likelihood" (AIREML) method, developed by Jensen and Madsen (1994), was adapted for estimating the positions and variance contributions of QTL affecting one or several traits in addition to additive polygenic and residual variance components. This method is based on a random QTL model, where phenotypes, QTL effects, and polygenic effects are assumed to be normally distributed.
We also performed univariate single-family analyses based on the least squares (LS) method to investigate whether main deviations in the putative QTL positions between individual families exist and how these affect the result of the multitrait analysis.
The objective of our study was to obtain multivariate QTL mapping results for yield traits and to compare these results to previous findings from different univariate analyses. A significant QTL for fat yield and for protein yield was found, with very similar QTL positions for both traits (Kühn et al., 1999; Freyer et al., 2002). Thus, the main goal of the present paper was to determine whether there is a pleiotropic QTL on chromosome 6 affecting milk yield traits.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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). The pool of sons with complete phenotypic data for the milk yield traits (Table 2) was reduced to the genotyped animals. We used both the daughter yield deviations (DYD) and the estimated breeding values (EBV) in the QTL analysis. The correlation coefficients for DYD and EBV were 0.89 for milk yield, 0.91 for fat yield and 0.87 for protein yield. DYD is the actual deviation of sires’ daughter performances from contemporaries (VanRaden and Wiggans, 1991). The phenotypes of the daughters were adjusted for the fixed environmental effects, including effects of herd, year, and season of calving) and for genetic values of their dams. EBV is based on DYD and includes weighted information from all available relatives and is a regressed measure. The German method of estimating breeding values was described in the annual reports of the Computing Centre for Animal Breeding, VIT Verden (e.g., VIT, 2001). To ensure complete phenotypic information on the DYD data for the genotyped sons, we used the 1996 evaluation data. QTL analysis based on granddaughter design requires weighting of the trait values (e.g., Grignola et al., 1996; Zhang et al., 1998). The reliabilities of EBV were computed as squared correlations of sire’s predicted and true transmitting abilities, described by VanRaden and Wiggans (1991). The reliabilities can account for information on all relatives and had to be considered for weighting of EBV of son j of sire i in terms of zij = 1/RELij, and accordingly zij = 1/ndij for DYD, where nd is the number of daughters. Sons without complete genetic evaluations on traits or without genotypes for the markers, which were informative in the particular family, were excluded.
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LS Method.
Multimarker regression (e.g., Knott et al., 1994) was implemented in a computer program by Du and Hoeschele (1999). The probability of inheriting a particular sire QTL allele was calculated for each son in 1 cM steps along the chromosome, using the information on the closest informative flanking markers. The trait values were regressed on this conditional probability.
The model including n QTL, based on the granddaughter design, was
 | (1) |
where yij was the trait value of son j of (grand)sire i, (i = 1,..., 5), µ was the overall mean, si represented the fixed effect of (grand)sire i, bik was a regression coefficient for QTL q nested within (grand)sire i at position k of QTL q, and eij was the residual with variance approximately equal to zij 
e2. The specific use of weights zijfor DYD and EBV is described in the previous section. The number n of QTL fitted at a time was 1 for the single-family analyses discussed in this paper. Pijklwas the probability of son j inheriting QTL allele l of from (grand)sire i at position k of QTL q. The probabilities Pijklin equation [1] were calculated as described by Hoeschele (2001), with the most likely linkage phase for sire i treated as the true phase. An F-statistic for H0(no QTL) vs. HA (one QTL present) was calculated at 1 cM intervals. The computer program (Du and Hoeschele, 1999) performing the LS analysis provided 95% confidence intervals for QTL location by bootstrapping and a chromosomewide significance threshold by data permutation (Churchill and Doerge, 1994). We set the number of permutations to 100,000 and the number of bootstrap samples to 1000.
(Co)Variance Components (CVC) Method.
The data was analyzed by fitting the following multivariate "purely additive" mixed model with n QTL:
 | (2) |
whereywas a vector of t = 2 yield traits observed for each son of each grandsire. MatricesXandZwere known design matrices, associating the observations of each son to the fixed and random effects, ß was a vector of fixed effects (here containing the overall trait means),uwas the vector of random polygenic effects of the (grand)sires and their sons, ande represents the vector of random residual effects.Wq was a matrix relating each individuals record to its unknown additive QTL effect. The genotypic part was modeled by aq, the vector of random genotypic effects for QTL q. The QTL effects, the polygenic effects, and the residuals were assumed to be normally distributed with expectation and covariance matrices (0, Kt0 
Qk|M), (0, Gt0 A) and (0,zijEt0 I), respectively.
The dimension of the unknown t x t covariance matrix Kt0 depended on the number of traits t (here t = 1 or t = 2) affected by the QTL. Matrices Gt0 and Et0 were unknown t x t covariance matrices of additive genetic and residual effects, respectively. Also, A was the numerator relationship matrix, I was an identity matrix, and x denotes the direct product of matrices. Matrix Qk|M was the genotypic identity by descent (IBD) matrix at QTL position k. The IBD matrix is a function of marker data (M) and position (k) of the QTL q on the chromosome. The weighting zij was introduced in the Animals section.
Calculating IBD probabilities.
The genotypic IBD matrix for a QTL, Qk|M, was computed by first constructing the allelic or gametic relationship matrix with the method of Fernando and Grossman (1989), extended to flanking markers (Grignola et al., 1996), and with the most likely linkage phase of the sires treated as known. Subsequently, the genotypic IBD matrix was formed from the gametic IBD matrix as described by George et al. (2000). We computed the IBD probabilities for the QTL alleles in the sons conditional on the closest informative marker bracket inherited from a sire (Table 3). The genotypic IBD matrix Qk|M was computed, conditional on QTL position k, in 1 cM steps along the chromosome.
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). Specifically, the analyses were performed with the following models:
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| (MPLEI) | = | a pleiotropic model containing a single QTL q, affecting traits 1 and 2 with (co)variance matrix K0 and position k12;
| (MQ1) | = | a model containing a single QTL q, affecting trait 1 only, with QTL variance K0 = (2q1)and position k1;
| (MQ2) | = | a model containing a single QTL q, affecting trait 2 only, with QTL variance K0 = (2q2)and position k2;
| (MPOLY) | = | the fully reduced model without any QTL effects and
| (MQ1Q2) | = | a linkage model with two linked QTL affecting only trait 1 (q1_1) and only trait 2 (q2_2), respectively, with K10 = (2q1), and K20 = (2q2), and with positions k1_1unequal to k2_2, respectively.
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Accordingly, we also conducted a univariate CVC analysis, based on
| (UQ1) | = | a model containing one single QTL q, with QTL variance K0 = ( 2q) and position k and
| (UPOLY) | = | the simple polygenic model.
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Hypothesis tests were based on the asymptotic distribution of the likelihood ratio (LR) test statistic
 | (3) |
where Lreduced and Lfull are the logarithms of the maximized likelihoods under the reduced model and full model, respectively. The reduced model was either the no-QTL model (MPOLY) in testing the null hypothesis of no QTL for both traits, or either bivariate model with a QTL affecting only one trait (MQ1) or (MQ2), against (MPLEI) in the case of testing for a pleiotropic QTL effect (Table 4
). The number of degrees of freedom (df) was the difference in the number of free parameters between two models. We assumed that the existence of multiple QTL on chromosome 6 affecting several milk traits is known from the literature, including our own previous results (e.g., van Tassel et al., 2000; Ron et al., 2001; Mosig et al., 2001; Freyer et al., 2002, to mention only very recent publications). For this reason we used a chromosomewise significance threshold based on the nominal type I error probability of 
= 0.05 instead of a genomewise threshold.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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Single-Family Analysis
Single-family analyses based on the LS method (Table 5) revealed putative QTL positions for single traits, exceeding the significance threshold for fat yield at 68 cM and at 71 cM for protein yield in family S2. Significant QTL positions for milk yield were obtained from two different families, suggesting QTL locations at 49 (family S1) and at 64 cM (family S5), respectively. The latter position is located between markers BM143, which both Gomez-Raya et al. (1998) and Velmala et al. (1999) found to be associated with milk yield, and TGLA37. Ron et al. (2001) reported QTL for yield traits in the region between 51 and 58 cM in a single family. In our study, additional putative QTL for fat yield with positions at 61 and 91 cM were near the significance threshold in families S1 and S3. An illustration of the wide confidence intervals (Table 5) can be found in Figure 1 for milk yield. Family S1 showed two peaks in the test statistic profile. Thus, the confidence interval, 27 to 97 cM, includes both positions. Very similar results exist for family S5. Freyer et al. (2002) reported superiority of the single trait two-QTL model in several families. Here, however, our focus is on a putative pleiotropic QTL, where family S2 is of special interest, as it provides evidence for a single segregating QTL both for fat and protein yield.
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for comparison). The variance component estimates from the two-QTL model and the one-QTL model were similar for the QTL at 67 cM. In addition, a variance component of about 20% was estimated for the second QTL. The results of the two-QTL model are not shown in detail, because they were meaningless for the other yield traits. The putative QTL position for protein yield was in the same region as that for fat yield (Table 6). The significant result from the single-family analysis, suggesting a QTL at 71 cM in family S2, was confirmed (here 70 cM). This result agreed with reports of QTL findings for yield traits by Velmala et al. (1999) and Gomez-Raya et al. (1998). Significant QTL results for milk yield, as found by the within family LS analysis, could not be confirmed. The peak in the test statistic profile suggesting a QTL at 88 cM, with an estimated QTL variance contributing about 16% to the total variance, was fairly distant from the two significant single-family results (Figure 1). We noticed high errors of the variance estimates in this case. Other studies (e.g., Lien et al., 1995; Velmala et al., 1998) reported QTL in this area, within or around the casein locus, which is located at 95 cM on our map.
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). This QTL contributed about 23% and 25% to the total variance of fat yield and protein yield (Table 8), respectively. Both likelihood ratio (LR) tests (MPLEI:MQ1) and LR (MPLEI:MQ2) were significant, suggesting that this region harbors a pleiotropic QTL affecting both traits simultaneously.
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For milk and protein yield, the high LR (MPOLY:MPLEI) suggested a QTL at position 58 cM. But this was not in agreement with the single-trait analyses (Table 7). Ron et al. (2001) found a QTL for milk yield at exactly this position. The absence of a more conclusive result might be related to the partially significant family specific QTL positions for milk yield (Table 5). The position of a pleiotropic QTL for milk yield and protein yield was apparently biased by this fact. No evidence was found for a pleiotropic QTL affecting milk yield and fat yield simultaneously.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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The pleiotropic model (MPLEI) was compared to the close linkage model (MQ1Q2) for trait combination fat and protein yield in terms of the residual variances and the Akaike Information Criterion (AIC = -2 ln MLH + 2 number of parameters). But no significance test was performed, due to the nonnested nature of the two models. The results from the close linkage model were not shown in detail. The standard errors of the estimates, obtained in all related analyses under this model, were high. Lebreton et al. (1998) presented a nonparametric bootstrap method for testing close linkage vs. pleiotropy. Our significant QTL findings for fat yield and protein yield in family S2 and in the univariate across family analyses were at most 4 cM apart from each other. We did not conduct the empirical test of the pleiotropic model against the close linkage model, because we expected very limited power, given the small distance between these positions. Future finemapping analyses may provide more conclusive results. We will focus first on using additional informative markers for sire S2 being QTL heterozygous within an extended family structure. In a pre-finemapping analysis, such markers should be identified in the region between markers BM1329 (46 cM) and TGLA37 (66 cM) in order to avoid a bias, caused by an information gap in family S2.
Confidence intervals obtained by the bootstrapping method were quite large. If more than one single QTL was segregating on the chromosome, results obtained by this method might probably be incorrect. In addition, we estimated the confidence interval CI (95%) across the families according to a method, suggested for saturated marker maps (Darvasi and Soller, 1997), based on CI95M = 3000/(N 
2),when adapting this method to our design. Here, N is the number of genotyped animals, and is the substitution effect in units of residual standard deviation. For deriving the substitution effect from the QTL variance
, we assumed a biallelic QTL with equal allele frequencies. When treating the whole non-QTL variance as "residual variance", then the computed confidence intervals CI (95%) ranged from 8 to 13 cM for fat and protein. Here, we did not expect a comparable small CI (95%) of about 4 cM as reported by Ron et al. (2001) from a single-family analysis.
The QTL variance component, which is part of the polygenic component in the fully reduced QTL model (MPOLY), was not biased by partitioning of the total variance into polygenic and residual variance. estimates from a simple marker analysis (data not shown) confirmed a highly significant impact (P < 0.0036) of marker TGLA37 (at 66 cM) on fat yield, an effect of marker FBN13 (at 71 cM) on protein yield and milk yield, and supported the statement of conclusive results obtained by our study.
No previous results on multivariate QTL estimation in dairy cattle have been published to our knowledge. canonical transformation (e.g., adapted by van tassel et al., 2000) uncorrelates the traits and does not ensure that a QTL influences a single canonical trait separately (knott and haley, 2000). in breeding programs, we focus on several correlated traits. it is important to identify QTL influencing two or more traits of interest and traits of secondary importance and to distinguish pleiotropic from closely linked QTL.
Such knowledge is particularly of interest for use of QTL in marker-assisted selection. furthermore, such findings may contribute to our understanding of the background of genetic correlations and to our ability to manipulate these correlations for breeding purposes.
Our results suggest the presence of one QTL at 68 cM on BTA6, affecting both fat and protein yield. this finding of a pleiotropic QTL influencing two positively correlated traits was in agreement with the estimated putative QTL positions using different genetic models, statistical methods, and algorithms. we cannot exclude some bias in the estimated QTL position, because we did not fit multiple QTL in the multivariate analysis, except for model MQ1Q2, allowing for two QTL, each affecting one trait. however, given our results, e.g., from the single-family analyses (table 5) and from two QTL analyses of single traits (here briefly discussed for fat yield), an important bias on the pleiotropic QTL finding for fat and protein yield does not seem to be likely.
Despite our increasing knowledge about the inheritance of important quantitative traits, this type of investigation needs to be continued. The physiological evidence is still at the very beginning, in particular with regard to pleiotropic effects and quantitative traits (Harlizius and Lende, 2001). An integrated effort of several disciplines such as quantitative genetics and functional genomics will "establish linkages between predisposition and physiology, enhancing our understanding of how economically important traits in animal agriculture are controlled and regulated..." (Pomp et al., 2001).
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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Received for publication August 1, 2002. Accepted for publication October 1, 2002.
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References |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSReferences |
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