Mapping Quantitative Trait Loci for Milk Production and Health of Dairy Cattle in a Large Outbred Pedigree

Corresponding author: Ina Hoeschele, Department of Dairy Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060., inah{at}vt.edu (E-mail).

Communicating editor: P. D. KEIGHTLEY

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Quantitative trait loci (QTL) affecting milk production and health of dairy cattle were mapped in a very large Holstein granddaughter design. The analysis included 1794 sons of 14 sires and 206 genetic markers distributed across all 29 autosomes and flanking an estimated 2497 autosomal cM using KOSAMBI's mapping function. All families were analyzed jointly with least-squares (LS) and variance components (VC) methods. A total of 6 QTL exceeding approximate experiment-wise significance thresholds, 24 QTL exceeding suggestive thresholds, and 34 QTL exceeding chromosome-wise thresholds were identified. Significance thresholds were determined via data permutation (for LS analysis) and chi-square distribution (for VC analysis). The average bootstrap confidence interval for the experiment-wise significant QTL was 48 cM. Some chromosomes harbored QTL affecting several traits, and these were always in coupling phase, defined by consistency with genetic correlations among traits. Chromosome 17 likely harbors 2 QTL affecting milk yield, and some other chromosomes showed some evidence for 2 linked QTL affecting the same trait. In each of these cases, the 2 QTL were in repulsion phase in those families appearing to be heterozygous for both QTL, a finding which supports the build-up of linkage disequilibrium due to selection.

DAIRY cattle and other livestock species have undergone selection with the goal of improving economically important traits for a number of generations. Most traits of economic importance are of quantitative nature, i.e., are influenced by many genes and by environmental factors. Selection has solely relied upon the collection and utilization of phenotypic and pedigree data, and on statistical tools for partitioning the phenotypic performances of individuals into their additive genetic values plus environmental contributions. At present, major collaborative projects are underway to map genes affecting traits of economic importance in several livestock species, using moderate resolution genetic marker maps. The collaborations are producing genetic maps and genotypes on the one hand and suitable statistical methods for analysis of these data on the other hand. There have been substantial advances both in the map densities and in the development of statistical methods. The latter are needed for QTL (quantitative trait loci) mapping, for genetic parameter estimation (e.g., variance contributions at individual QTL), and for the estimation of additive genetic values by combining phenotypic, pedigree, and genetic marker information. The benefits resulting from the mapping collaborations include the gaining of basic scientific knowledge about the genetic basis of quantitative traits, the achievement of the necessary first step toward fine-mapping and function evaluation of important QTL, and, in the context of livestock improvement, an increase in the selection efficiency for production and health-related traits through marker-assisted selection (MAS).

The granddaughter design (GDD; GELDERMANN 1975 ; WELLER et al. 1990 ; GEORGES et al. 1995 ) is sufficiently powerful for the detection of moderate QTL, provided that it consists of multiple grandsire families with a total of several hundred sons in these families. GEORGES et al. 1995 have previously mapped QTL in a large granddaughter design for US Holstein dairy cattle. Since the completion of their work, the same granddaughter design has been expanded to include more progeny, with 276 additional sons in the same families, two additional phenotypic traits (somatic cell score, length of productive life), and genotypes for additional markers, with all markers covering nearly 2500 cM or 100% instead of 1645 cM or 66% of the estimated length of the male genome in cattle (LOGUE and HARVEY 1978 ; cited in GEORGES et al. 1995 ). While in the study of GEORGES et al. 1995 each of the fourteen families was analyzed separately by maximum likelihood, here we analyzed all families jointly using two approaches, least-squares (LS) and variance components (VC) analysis. An advantage of analyzing each family separately is that there is no need for assuming a particular genetic model specifying the number of alleles at a QTL, which may be incorrect. Maximum likelihood analysis across families has been based on the assumption of a biallelic QTL (e.g., WELLER 1986 ) although other models of QTL variation should be assumed (HOESCHELE et al. 1997 ). The VC analysis by residual maximum likelihood (GRIGNOLA et al. 1994 , GRIGNOLA et al. 1996A , GRIGNOLA et al. 1996B , GRIGNOLA et al. 1997 ; XU and ATCHLEY 1995 ) permits an analysis across families without the need for estimating allele or genotype frequencies. Hence, the VC analysis, where QTL allelic effects have a prior normal distribution, requires fewer parametric assumptions than standard maximum likelihood, where the effects at a biallelic QTL are treated as fixed. While the VC analysis has been tested with simulated data and shown to be robust to the number of alleles at a QTL (GRIGNOLA et al. 1994 , GRIGNOLA et al. 1996A , GRIGNOLA et al. 1996B , GRIGNOLA et al. 1997 ; XU and ATCHLEY 1995 ), in this study it is applied for the first time to real data in a large granddaughter design and its results are compared to those from least-squares analysis, which has been used previously to map QTL in actual data (e.g., SPELMAN et al. 1996 ; VILKKI et al. 1997 ).

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Experimental design:
The granddaughter design consisted of 14 paternal half-sib families with an average number of 128 and a range of 33 to 313 sons per sire, with sire denoting the male parent common to each half-sibship. The total number of genotyped sons was 1794. The sires have more sons than those included in the analysis because semen samples from many sons that were culled after the progeny test were discarded, and genotyping was not possible. GEORGES et al. 1995 showed that for production traits the average phenotype of all sons in one of the families was clearly lower than the average of those sons with marker information. Although pedigree information was available, i.e., there were (considerable) relationship ties among the 14 sires, these sires were assumed to be unrelated in the analyses for several reasons. First, previous simulation studies have shown that inclusion of relationships among sires has only minor effects on power of QTL detection and QTL parameter estimation in a GDD with similarly large numbers of sons per family (GRIGNOLA et al. 1996B ). Second, the marker genotypes in the original granddaughter design were coded within the sire family, and the original allele sizes were not available. Third, many common ancestors of the sires do not have any genotype information at this time.

Marker data:
Marker data were available on 246 microsatellite markers. Of these, 222 were assigned to the 29 autosomal chromosomes, while 24 markers were not assigned to a chromosome. Most likely orders of and recombination rates among markers were estimated with the CRI-MAP program (P. GREEN, unpublished results). Because on some chromosomes, 2 to 3 markers were located at the same position, the most informative of these markers within each family was chosen for the analysis, or these were treated as one locus. Hence, only 206 marker positions were actually used in the analyses. Using Kosambi's mapping function and summing over all linkage groups, we obtained a total of 2497 autosomal cM flanked by linked markers, which represents the estimated genetic length of the entire male genome of 2500 cM (LOGUE and HARVEY 1978 ; cited in GEORGES et al. 1995 ). Because we employed Haldane's function to map QTL relative to the markers, the map was reconstructed using this mapping function. The Haldane map was 3104 cM in length. The average length of the linkage groups was 107 (88) cM, with a range from 26 (23) cM on chromosome 25 to 179 (138) cM on chromosome 1 (values in parentheses are for the Kosambi function). The average length of the marker intervals was 17.8 (14.3) cM. Heterozygosity measured as the percentage of sires heterozygous at a marker was 46.1% on average across all 206 markers, compared with 45.8% for the markers used in the previous study (GEORGES et al. 1995 ). The average number of markers per chromosome was 7.83, with a range from 4 to 10. However, the average number of informative markers per chromosome and sire was only 2.81, with a range from 1.36 to 4.64 across chromosomes (averaged over sires). Table 1 contains for each chromosome the estimated genetic length, the number of markers used, and the number of informative markers within each sire family averaged across sires.

Phenotypic data:
Seven traits [MY, milk yield; FY, fat yield; PY, protein yield; F%, fat percentage; P%, protein percentage; PL, length of productive life (VANRADEN and KLAASKATE 1993 ); and SCS, somatic cell score (SCHUTZ 1994 )] were considered in the analysis. The phenotypic unit of measurement was daughter yield deviation (DYD; VANRADEN and WIGGANS 1991 ), which is the average of the phenotypes of the daughters of a son adjusted for systematic environmental effects and the additive genetic values of the daughters' dams. We analyzed DYDs, because a simulation study had shown that there is virtually no difference in the accuracy of estimation of QTL locations and variance contributions when analyzing DYD or phenotypes of individual daughters with the VC method (Q. ZHANG and I. HOESCHELE, unpublished results). Also available were the numbers of daughters per son and trait, and the reliabilities (REL) for the estimated additive genetic values of the sons and their sires and dams, with REL representing the squared correlation between true and predicted values. Average REL and number of daughters by trait were 0.85 and 1200 for MY, FY and F%, 0.83 and 1146 for PY and P%, 0.67 and 1048 for SCS, and 0.63 and 1058 for PL. All the phenotypic information was provided by the Animal Improvement Programs Laboratory of the Agricultural Research Service of the U.S. Department of Agriculture, Beltsville, MD.

Statistical methods:
The statistical methods employed for QTL mapping were least-squares (LS) analysis and variance components (VC) analysis. One chromosome was analyzed at a time, using all markers available on that chromosome and with the genetic variation contributed by all other chromosomes accounted for via polygenic effects in the VC analyses or included in the error in the LS analysis.

Least-squares analysis: This method is described in detail by KNOTT et al. 1994 , SPELMAN et al. 1996 , and UIMARI et al. 1996 . The model of analysis was

(1)

where µ is an overall mean, s_j is fixed effect of sire j, b_iki is the regression coefficient for QTL i nested within sire j at QTL position k_i, P_ik is the probability of inheriting a QTL allele from sire j for son l and for QTL i at position k_i, t (t = 1 or 2) is the number of QTL fitted, and e_jl is a residual with variance approximately equal to _e²/REL_jl, where REL_jl is reliability of son jl due to his daughters only, which can be computed as described by VANRADEN and WIGGANS 1991 and GEORGES et al. 1995 . A weighted LS analysis was conducted, with the weights equal to 1/REL_jl.

Using model (1) with t = 1, an "F" statistic for testing H₀ ("all b's are zero") versus H_A ("some b's are nonzero") was calculated using the standard type III sums of squares at QTL position intervals of 1 cM on a chromosome. The calculations were conditional on the most likely linkage phase of the sires (see below), and were computed using all markers on the chromosome simultaneously and by including not only offspring with known but also those with unknown marker allelic inheritance. The distribution of the test statistic was obtained empirically using data permutation as described below. It happened rarely that a sire did not have any informative markers for a particular chromosome. This sire family was then deleted for analyses of that chromosome.

For t = 2 (two-QTL model), a two-dimensional search was performed, i.e., all combinations of the positions of the two QTL (in 1-cM intervals) were evaluated. However, to ensure estimability of both QTL positions and regression coefficients (ZENG 1993 ; WHITTAKER et al. 1996 ), only those combinations of QTL positions that were separated by two markers were considered. For any combination, those sire families that did not have an informative, empty marker interval between the two QTL were discarded. Tests of one QTL versus two QTL were performed by computing the F statistic , where SSE (MSE) is the residual sum of squares (mean-square) at the two positions yielding the smallest MSE_full under the two-QTL model, and q is the number of sire families used for this set of QTL positions. In the reduced model, the regression coefficients for the first or the second QTL were set to zero, and both resulting test statistics were used in an intersection-union test (BERGER 1997 ; GRIGNOLA et al. 1997 ). Rejection of the null hypothesis of the one-QTL model required both test statistics to be significant.

To investigate a potential increase in power for detecting QTL, a few additional analyses were conducted, where a chromosome was searched for a single QTL while fitting a second QTL on another chromosome at the position with the highest significance among all experiment-wise significant (see below) QTL positions for the same trait, which were previously identified in the one-QTL analyses. In these analyses, sire families with no informative markers on either of the two chromosomes were discarded.

Variance components analysis: The VC analysis is described in detail by GRIGNOLA et al. 1996A , GRIGNOLA et al. 1996B for the single-QTL model and for the two-QTL model by GRIGNOLA et al. 1997 , who referred to it as an approximate Residual Maximum Likelihood (AREML) method. For analysis of the two-QTL model, a more efficient search strategy than the two-dimensional search in LS based on cyclic optimization of the QTL positions was employed. In cyclic optimization, the first QTL was fixed at its current most likely position while the position of the second QTL was optimized, subsequently the second QTL was fixed while the position of the first QTL was optimized, etc. Testing for linkage (one versus no QTL on the chromosome) was based on a likelihood ratio test as described in GRIGNOLA et al. 1996A , and testing for one vs. two QTL was performed as described by GRIGNOLA et al. 1997 and based on the intersection-union test as outlined for the LS analysis. The model for DYD in the VC analysis was

(2)

where u_jl is the polygenic effect of son j of sire l, and v^k_ijl is effect of allele k (k = 1, 2) at QTL i in son l of sire j. As pointed out by GRIGNOLA et al. 1996B , when DYD is analyzed with the weights 1/w_jl, it has an expected heritability of 0.5. Hence, there is the option of treating heritability as known.

Linkage phases: Probabilities of all possible linkage phases of the sires were computed as

(3)

where G_i is a particular multi-locus, phase-known marker genotype of sire i, M is the marker information for the sire and its sons, M_i is the marker information on the sire, H^s_ij is a multi-locus haplotype that son j inherited from sire i, H^d_ij is the haplotype inherited from the dam that is determined by the haplotype inherited from the sire (dam not genotyped), M_ij is the marker information on son j of sire i, and n_i is the number of sons of the sire. While the first term in the summation over H^s_ij in (3) depends on the recombination rates among loci, the second term is a function of the marker allelic frequencies, which were estimated within sire families as described in GEORGES et al. 1995 . All multi-locus genotypes and haplotypes include only those loci for which the sire is heterozygous.

Significance thresholds: QTL findings from the one-QTL model analyses across families are reported in three ways, by listing (1) all locations significant at the chromosome-wise _c = 0.05 type-I error level [with six (= 116 x 0.05) type-I errors expected by chance under the null hypothesis of no QTL segregating, see below], (2) all locations of suggestive significance (with one type-I error expected by chance), and (3) all locations of experiment-wise significance. For experiment-wise significance, the type-I error (_c) for each chromosome by trait combination was determined from the equation _exp = 1 - (1 - _c)ⁿ (WEIR 1990 ), where _exp represents the experiment-wise type-I error set equal to 0.05, and n is the number of independent tests in the entire experiment. Approximately, n_c = 0.05. A canonical transformation (WELLER et al. 1996 ), based on estimates of the genetic correlations taken from the literature (PEARSON et al. 1990 ; SCHUTZ et al. 1990 ; WEIGEL et al. 1997 ), produced four uncorrelated factors that accounted for 94% of the total variation. Hence, the number of independent subexperiments was equal to the number of chromosomes times the number of uncorrelated factors, or n = 29 x 4 = 116, resulting in _c = 0.0004421. A similar approach was used by SPELMAN et al. 1996 and UIMARI et al. 1996 . The type-I error for suggestive significance (LANDER and KRUGLYAK 1995 ) was determined similarly, but with _c calculated from the equation n_c = 1, which is the expected number of type-I errors in the experiment when the null hypotheses of no QTL segregating is true, yielding _c = 0.008621. Each subexperiment consisted of multiple dependent tests along a chromosome, with dependence among these tests accounted for via data permutation (see below).

For LS analysis, the significance thresholds were determined by the permutation method of CHURCHILL and DOERGE 1994 . A total of 100,000 permutations of the DYD and REL of the sons relative to their marker genotypes were performed within sire families for each chromosome by trait combination. From each permutation, the largest value of the test statistic within a chromosome by trait combination was retained. The threshold was then set equal to the (1 - _c) percentile of these 100,000 values. For VC analysis, performing 100,000 permutations for each chromosome by trait combination was too CPU-time-consuming. GRIGNOLA et al. 1996B showed that the distribution of the VC likelihood ratio statistic for zero versus one QTL linked is in between a 1- and a 2-d.f. chi-square distribution. Therefore, we are reporting QTL with test statistics exceeding the 2-d.f. chi-square threshold, as well as QTL with test statistics in between the 1- and 2-d.f. thresholds.

For the tests of one vs. two QTL, the significance thresholds in the LS analysis were obtained from the F distribution. For the VC analysis, a chi-square distribution with 1 d.f. was used, as GRIGNOLA et al. 1997 showed that using the 1-d.f. chi-square distribution made the empirical type-I error level under the null hypothesis of one QTL close to the nominal value, while using 2 or 3 d.f. made it too conservative. No adjustment for multiple testing was performed for these tests.

Confidence intervals: Confidence intervals (CIs) for the QTL position were calculated with the LOD drop-off method (LANDER and BOTSTEIN 1989 ) and with bootstrapping (VISSCHER et al. 1996 ). The LOD drop-off method finds the location at either side of the estimated QTL position that corresponds to a decrease of 0.83 units in the LOD score, yielding a 95% CI (VISSCHER et al. 1996 ). The LS and REML test statistics were transformed to LOD scores for this purpose. For REML, the test statistic is a likelihood ratio (LR), which can be directly transformed to a LOD score. For LS analysis, when errors are independent and normally distributed, the likelihood ratio statistic can be computed as (AITKIN et al. 1989 )

where n is the number of observations, and SSE_reduced and SSE_full are residual sums of squares of the reduced model (no QTL) and the full model (one QTL), respectively.

Bootstrap CIs were calculated for those QTL locations exceeding experiment-wise thresholds. For bootstrapping, estimates of QTL position from n samples (with replacement) were obtained and their 2.5th and 97.5th percentiles determined for an empirical 95% CI. Three bootstrapping methods were employed. In the first method, all samples were used and all families in the original data set were retained. In a second method, only those families showing evidence for segregation of the QTL were retained for sampling. In the third method, all families were used, but only those bootstrap samples where the QTL was significant were retained. Selective bootstrapping has recently been proposed by LEBRETON and VISSCHER 1997 .

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

LS analysis:
Single QTL analysis: Figure 1 and Figure 2 depict the test statistic profiles for all chromosome x trait (C x T) combinations with profiles exceeding or nearly exceeding the experiment-wise and suggestive significance thresholds, respectively, somewhere on the chromosome. The significance thresholds determined by permutation varied among traits, as observed by SPELMAN et al. 1996 , and also among chromosomes. Generally, the variation among traits was smaller than that among chromosomes. The profiles in Figure 1 provide strong evidence for the presence of at least one QTL on chromosome (C) 3 for P%, on C6 for MY, F% and P%, and on C20 for F% and P%. The C6 effects on F% and P% may be pleiotropic effects of the same QTL (same estimated map position) or may be due to closely linked QTL. The C6 effect on MY appears to have a different map position, although bootstrap CIs are wide and overlap (see Table 2). The QTL for F% and P% on C20 have nearly the same estimated map position, indicating the possibility of a pleiotropic effect. But unexpectedly the effect on the percentage traits was not accompanied by an effect on MY as opposed to the findings for C6. The segregation of additional QTL is suggested (Figure 2) for C4 and SCS, C9 and FY, C13 and SCS, C14 and SCS, C17 and MY, C26 and F% and SCS, and C28 and F% and P%. Maximum and mean values of the estimates of the within-sire QTL substitution effects (regression coefficients) are given in Table 3 for the QTL of experiment-wise significance.

View larger version (37K): In this window In a new window Download PPT slide   Figure 1. Test statistic profiles from LS analysis. The straight lines represent experiment-wise significance threshold levels from permutations.

View larger version (32K): In this window In a new window Download PPT slide   Figure 2. Test statistic profiles from LS analysis. The upper and lower straight lines represent experiment-wise and suggestive significance thresholds from permutations, respectively.

Two-QTL analyses: Test statistics and corresponding QTL map positions under the two-QTL model can be found in Table 4 for those C x T combinations with experiment-wise significance from the single-QTL analysis and for other combinations with both test statistics exceeding the 5% significance threshold for the two-QTL analyses (only C17 and MY). C17 probably harbors two QTL for MY located at the two opposite ends of the linkage group. C6 also showed some evidence for two QTL for F%, but the two QTL positions were very close to each other and the significance was not very strong. To investigate a potential increase in power for the suggestive QTL, these were reanalyzed by also fitting a second QTL on another chromosome, which had experiment-wise significance in the single-QTL analysis for the same phenotypic trait. Some QTL positions were different from those of the single QTL analysis, possibly because in the two-unlinked-QTL analyses, families without informative markers on either chromosome were discarded. For the same reason, there was no clear increase in the test statistics due to fitting an unlinked QTL of relatively large effect (results not shown).

VC analysis:
Single QTL analysis: Table 5 contains parameter estimates and test statistics from VC analysis with heritability (h²) estimated or fixed at 0.5, and for comparison, LS position estimates and test statistics. The results in Table 5 pertain to those QTL above or near experiment-wise or suggestive thresholds from the LS or VC analyses. Estimates of the QTL parameters ² (ratio of QTL allelic to total additive genetic variance) and d (QTL map position) and likelihood ratios from both VC analyses (with h² estimated or fixed) were very similar except for the QTL position on chromosome 28 for trait F%, where the likelihood ratio profile was very flat, and the likelihood ratios at the two positions estimated (0.19 and 0.73) were very similar. The C x T combinations with an experiment-wise significant QTL from the VC analysis were exactly the same as those from the LS analysis. Most of the suggestive findings were also in agreement with those from the LS analysis. There were some minor discrepancies, because for C1 and PY, for C9 and MY, and for a few other combinations, LS statistics were not significant while VC statistics were. For C28 and P%, however, the LS analysis identified a significant QTL, while VC did not.

Likelihood ratio profiles from VC analyses with heritability fixed at 0.5 are depicted in Figure 3 and Figure 4, for the same C x T combinations as those shown in Figure 1 and Figure 2 for LS analyses. The LS and VC estimates of the QTL positions were generally in close agreement (Table 5), a finding that is consistent with the agreement between the LS and VC test statistic profiles, and given the width of the CIs (see Table 2). The largest difference in the estimates for QTL position from the LS and VC analyses was found for chromosome 4 and trait SCS and amounted to 43 - 0 cM (11 cM) = 43 cM (32 cM), with the numbers in parentheses pertaining to VC analysis with heritability fixed.

View larger version (36K): In this window In a new window Download PPT slide   Figure 3. Likelihood ratio profiles from VC analysis. The straight lines represent experiment-wise significance thresholds from 2-d.f. 2 distribution.

View larger version (31K): In this window In a new window Download PPT slide   Figure 4. Likelihood ratio profiles from VC analysis. The upper and lower straight lines represent experiment-wise and suggestive thresholds from 1-d.f. 2, respectively.

Table 6 contains test statistics, estimates of QTL locations and estimates of QTL variance contributions from VC analysis for QTL exceeding chromosome-wise 1-d.f. chi-square thresholds with _c = 0.05 but not reaching suggestive thresholds. Again, for comparison, the corresponding LS test statistics and estimates of QTL locations were also given. Ten such QTL were found with an expected number of six type-I errors under the null hypothesis of no QTL among the 10 + 18 + 6 = 34 QTL positions exceeding the chromosome-wise thresholds, with 18 QTL also exceeding suggestive thresholds and 6 exceeding experiment-wise thresholds.

For those QTL positions with test statistics exceeding experiment-wise significance thresholds, the LOD drop-off and bootstrap confidence intervals with 95% coverage are given in Table 2. The bootstrap CIs are considerably larger than the LOD drop-off ones. The bootstrap CIs in Table 2 were calculated by using all families in the original data and all bootstrap samples. When all samples but only those families that appeared to be segregating in the original data were used, virtually the same CIs were obtained with the exception of C3 and P%, where the interval was only nearly half as wide, but still wider than the LOD drop-off interval. When only those bootstrap samples where the QTL was significant were used, again virtually the same intervals were obtained, as the QTL was significant in over 90% of the samples.

Table 7 presents the variance explained by QTL exceeding experiment-wise or suggestive significance thresholds for each trait, obtained by adding the variance estimates for individual QTL in Table 5 for the same trait. The largest fractions of the additive genetic variance attributed to QTL were found for F% and SCS. In a simulation study with a single QTL and analysis across families by the VC method (results not shown), we found that for true QTL variance ranging from 50 to 5% of the additive genetic variance, overestimation of this parameter increased from 0 to 114% for those replicates where the QTL was significant at the experiment-wise threshold. This finding is in agreement with GEORGES et al. 1995 , who simulated a single family and used a LOD score of 3. As a consequence, the QTL variance contributions in Table 7 are expected to overestimate the true variance explained by the identified QTL. However, our analysis did not include those sons in the same families that were not genotyped, and most of these sons were culled after progeny test. In this case, an underestimation of QTL variance is expected from theory (IM et al. 1989 ; MACKINNON and GEORGES 1992 ) and has been verified via simulation (MACKINNON and GEORGES 1992 ).

Two-QTL analyses: Test statistics and the corresponding QTL map positions under the two-QTL model are also given in Table 4 together with the results from LS analysis. None of these combinations seemed to have a second significant QTL, with the exception of the two MY QTL on chromosome 17. There was good agreement in the QTL positions under the two-QTL model between the LS and VC analyses, except for C6 and F% and C6 and P%. The VC analysis was also run with a second, unlinked and experiment-wise significant QTL fitted. Results (not reported here) were similar to the LS findings of very little increase in the test statistics.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

The breakthrough study of GEORGES et al. 1995 demonstrated that QTL affecting milk production can be identified in current populations using a granddaughter design. In this study, we have analyzed the same data set augmented by additional sons, additional traits, and additional markers. While GEORGES et al. 1995 analyzed 1518 sons and 159 markers with 138 markers assigned to 27 linkage groups, an estimated coverage of 1645 cM and an average bracket size of 14.8 cM (based on the Kosambi function), we analyzed 1794 sons (of the same 14 families) and 206 markers, with several markers assigned to each of the 29 autosomes, an estimated coverage of 2497 cM (using Kosambi's mapping function), and an average bracket size of 14.3 cM (Kosambi). There is also a major difference in the statistical methods employed for QTL mapping. GEORGES et al. 1995 used maximum likelihood with fixed QTL effects, analyzed each family separately, and employed a rather stringent significance threshold, not accounting, however, for the actual marker map and correlation structure of the phenotypic traits analyzed. Here, we analyzed all families jointly using least-squares and variance components methods. We also used data permutation techniques and canonical transformation to determine an "effective number of independent traits," leading to (approximate) experiment-wise significance thresholds accounting for multiple tests per chromosome, multiple chromosomes, and multiple traits. We computed and compared confidence intervals with LOD drop-off and bootstrap, and estimated the variances explained by individual QTL.

The VC analysis with random QTL allelic effects requires fewer parametric assumptions than an ML analysis across families with fixed QTL effects, as the number of alleles at a QTL does not need to be specified, and there is no need for estimating allelic or genotypic frequencies. The VC method is therefore particularly suited for analyses of segregating livestock or human pedigrees.

In this study, LS and VC analyses gave similar estimates of QTL locations. This finding is to be expected for a half-sib design with very large families, similar to the one analyzed here. An advantage of the LS analysis is that it is computationally feasible to perform a permutation test so that the distribution of test statistics can be determined empirically. Advantages of the VC analysis are that it provides an estimate of the additive genetic variance in the population attributable to a QTL, rather than only estimates of QTL substitution effects for specific sires, and that it is applicable to any design or pedigree. The VC analysis is therefore capable of utilizing all the available information, rather than only the half-sib relationships, for example. Since the LS analysis treats gene substitution effects as fixed rather than random as in the VC analysis, the estimates are sufficiently accurate only in very large families. Estimates of gene substitution or allelic effects and of QTL variance contribution are important for marker-assisted selection.

Our analysis of 29 chromosomes and 7 quantitative traits of economic importance in a very large US Holstein granddaughter design reveals 6 QTL with experiment-wise significance, 18 suggestive QTL locations (1 expected by chance out of 24), and 10 QTL achieving chromosome-wise significance (6 expected by chance out of 34). These findings provide very strong evidence for the segregation of QTL in our pedigree, despite the coarse nature of the current marker map. Estimates of QTL positions were consistent across both methods of analysis. However, CI were large, and bootstrap CIs were considerably larger than LOD drop-off CIs, emphasizing the need for using the bootstrap. For VC analysis with heritability fixed at 0.5 and for those QTL surpassing the experiment-wise significance thresholds, the average bootstrap CI (95%) was 47.7 cM (Haldane), the average LOD drop-off CI was 17.2 cM, and the minimum and maximum bootstrap CIs were 25 and 93 cM, respectively, using Haldane's mapping function.

This analysis involved the problem of multiple correlated testing. We followed the approach of SPELMAN et al. 1996 and UIMARI et al. 1996 to transform 7 x 29 multiple correlated tests to 4 x 29 independent tests. Very recently, WELLER et al. 1997 studied the empirical type-I error rates in QTL mapping for multiple correlated traits and found that in their case the empirical type-I error rates for seven correlated traits were in general between the theoretical type-I error rates for six and seven uncorrelated traits. We checked our results with thresholds calculated by assuming seven uncorrelated traits. The significance for the experiment-wise QTL remained the same, but four suggestive significant QTL became nonsignificant at the suggestive level. These are C2 and F%, C9 and FY, C28 and F%, and C28 and P%.

The current marker structure does not yet permit precision mapping of QTL for several reasons. First, the average CI (bootstrap) was much wider than a desired range of 10 to 20 cM. Second, with the exception of chromosome 17, none of the analyses under the two-linked-QTL model revealed a significant second QTL, most likely because the number of families with several informative markers per chromosome was too small (for LS analysis, two informative markers are needed between the QTL positions to ensure the estimability of QTL positions and effects; ZENG 1993 ; WHITTAKER et al. 1996 ; therefore, those sire families, which did not have an informative, empty marker interval between the two QTL, were discarded). Future genotyping efforts must concentrate on placing more informative markers in the regions identified to harbor QTL and on increasing the number of individuals genotyped. Only after CIs have been reduced to the desired 10- to 20-cM region, the next step of saturating a region with highly informative markers to fine-map and clone a QTL can be undertaken.

The analyses conducted here represent an initial genome scan and could be improved upon in several ways. We expect to reanalyze the most promising regions in the future, in particular after additional informative markers have been added to the data. Improved analyses will include the fitting of multiple linked QTL and accounting for heterogeneous variances within families, due to different unlinked QTL segregating in these families, by fitting residual variances within families or by fitting multiple unlinked QTL. Further improvements of the analysis might result from including those sons that have not been genotyped (their data were not available to us), and from conducting a full pedigree analysis (possible only when marker alleles have unique codes across families), in which all paternal and maternal relationships are used.

Several chromosomes, in particular C6, C9, C14, C20, and C26, are likely to harbor QTL affecting more than one trait. This finding is expected due to the genetic correlations among the traits. The QTL on C6 (for F% and P%), C9 (for MY, FY, and PY), C14 (for F% and FY), and C20 (for F% and P%) have very similar position estimates, while on C6 the estimated position of the MY QTL is clearly different from those for F% and P%, on C14 the position of the SCS QTL is different from those for F% and FY, and on C26 the QTL for F% and SCS have different estimated locations. Given the sizes of the bootstrap CIs, however, the positions of QTL on the same chromosome cannot be declared different with certainty. For the remaining chromosomes, only QTL affecting a single trait were identified, most likely due to the stringent thresholds for experiment-wise and suggestive significance.

GEORGES et al. 1995 identified the following: a QTL on C1 for MY, which was not confirmed in this study; a QTL on C1 for PY, which was confirmed at the suggestive level; QTL on C6 for MY, F% and P%, which were all confirmed at the experiment-wise level; QTL on C9 for FY and PY, which were confirmed at or near the suggestive level; a QTL on C10 for FY, which was not confirmed; and a QTL on C20 for P%, which was confirmed at the experiment-wise level. All the confirmed QTL have similar estimated positions in both analyses.

RON et al. 1994 selected 10 microsatellite markers to search for QTL affecting milk production traits in a GDD consisting of seven Israeli Holstein families. These authors identified one marker on chromosome 21 associated with significant effects on MY and PY in one family. This finding was not confirmed in our study.

WELLER et al. 1995 analyzed 11 microsatellite markers and the Dairy Bull DNA Repository (DBDR) and concluded that several markers were associated with significant effects on milk production and health, including C2 for FY and F%, C4 for herdlife, C7 for SCS, and C15 for FY and F%. Of the seven effects found, four are expected by chance. Our study confirmed only that the QTL on C2 were at the chromosome-wise and suggestive levels, respectively, and that the estimated positions of both QTL were close to the marker ETH121, which was also the marker with significant allele effects for FY and F% in their study. On C4 we found a QTL for SCS instead of productive life at the suggestive significance level, which has the same marker (RM188) association as that for herdlife in their study.

A similar study using DBDR families was carried out by ASHWELL et al. 1997 . These authors reported ten significant effects with five expected by chance: C18 for SCS (not confirmed here), C21 for MY and FY (not confirmed), C23 for SCS, FY, and PL (only FY confirmed at suggestive level), C26 for FY and F% (both confirmed at suggestive level), and C27 for PY and P% (not confirmed; instead we identified QTL for F% and FY at chromosome-wise significance level). Because the marker system in their study was quite different from that in our study, a comparison of the QTL positions is not possible.

SPELMAN et al. 1996 identified a P% QTL on C6 in a Dutch Holstein-Friesian GDD, which was confirmed in this study at the experiment-wise level with almost the same position estimate.

VILKKI et al. 1997 analyzed a GDD in Finnish Ayrshires. Although these authors did not obtain any significant results, they reported some evidence in favor of a QTL on C9 for MY and PY. Both effects were confirmed here at the suggestive level.

The latest QTL findings were reported at the 6th World Congress on Genetics Applied to Livestock Production. RON et al. 1998 presented results from an analysis of DBDR families. They reported a significant effect of a marker on C3 for MY (confirmed at the suggestive level), F% (not confirmed), and P% (confirmed at the experiment-wise level), a marker on C10 for P% (not confirmed), and a marker on C14 for FY and F% (both confirmed at the suggestive level). MAKI-TANILA et al. 1998 reported a QTL on C1 for MY, a QTL on C6 for MY and P%, a QTL on C20 for MY, P%, and FY, and a QTL on C23 for P% in Finnish Ayrshire dairy cattle. Only the QTL on C6 for MY and P% and C20 for P% are confirmed at the experiment-wise level here. GOMEZ-RAYA et al. 1998 reported a QTL on C6 for MY in Norwegian dairy cattle, which is confirmed at the experiment-wise level with similar position estimate. REINSCH et al. 1998 found significant QTL effects on C23, C8, and C1 for SCS in three major cattle breeds in Germany, which are not confirmed in our study.

The main reasons why some of the findings in other studies were confirmed here while others were not are that at least some of the families in our study are not the same as those in the other studies, and that some of the other studies employed significance thresholds for which fairly large numbers of false positives are expected under the null hypothesis of no QTL segregating.

The fraction of the additive genetic variance explained by all QTL exceeding experiment-wise and suggestive significance thresholds was highest for the traits F% and SCS. No QTL was identified at the experiment-wise or suggestive levels for PL, which is a composite trait and expectedly less appropriate for QTL mapping than biological or component traits. Our simulation study reconfirmed the expected result that QTL variance contributions are overestimated on average for those QTL that surpass rather stringent significance thresholds. To obtain unbiased or less biased estimates, one might consider shrinkage estimation of the variances (those estimates with the least information have the largest positive errors on average but will be shrunken the most) using an informative Bayesian prior distribution with minor more likely than major variances (HOESCHELE and VANRADEN 1993 ), increasing the number of genotyped offspring in the same families, or re-estimating the QTL variance contributions in a different population.

For those chromosomes likely to harbor QTL affecting several traits (C6, C9, C14, C20, and C26), we investigated the direction of the substitution effects in those sires with significant regressions for more than one trait. In every single case, the direction was consistent with the genetic correlations among traits. As an example, for C6 and two families, the allele increasing MY decreased F%. A different situation was found when looking at two QTL situated on the same chromosome and affecting the same trait. For C17 and one family, the substitution effects for the two MY loci had opposite signs, i.e., were linked in repulsion phase. We then looked at all other two-linked-QTL analyses that had not quite reached significance but showed some evidence in favor of the two-QTL model. In all cases including C17-PY, C6-F%, C6-P%, C6-FY, and C6-PY, the two loci were linked in repulsion phase in those families where two QTL appeared to be segregating. Dairy cattle populations are undergoing selection for the milk production traits, and under selection negative covariances among loci are built up. This finding supports the need for adding additional, informative markers in the regions of interest, and for analyses that account for multiple QTL on the same chromosome, either by use of marker cofactors or by fitting several QTL simultaneously, as linked QTL in repulsion phase should be more difficult to detect in single QTL analyses.

In dairy cattle, implementations of marker-assisted selection for selection of young sires before progeny testing and for selection in nucleus breeding schemes have been shown to potentially produce additional genetic and economic gains (MEUWISSEN and VAN ARENDONK 1992 ; BRASCAMP et al. 1993 ; MACKINNON and GEORGES 1997 ). Hence, there is scope for QTL identification from an industry viewpoint. Application of MAS would be more efficient if essentially nonrecombining marker haplotypes bracketing the QTL could be identified. Furthermore, fine-mapping is a prerequisite for cloning QTL and for function evaluation. We confirmed using simulation that adding genotypes at reasonably polymorphic markers to the current GDD will reduce CIs to the desired 10- to 20-cM range. For example, we simulated a chromosome of length 1 M with 11 markers spaced 10 cM apart and 5 alleles per marker at equal frequencies. The bootstrap CIs for a QTL explaining 25 and 12.5% of the additive genetic variance were 13 and 17 cM, respectively. Other techniques will be then needed to reduce CIs to 1 cM in outbred populations, and these need to be investigated.

	ACKNOWLEDGMENTS

Financial support provided by the National Science Foundation (DBI-9696265/9740519), the US Department of Agriculture (92-01732), the US Holstein Associations and ABS Global Inc. to I. Hoeschele is gratefully acknowledged. Q. ZHANG is supported in part by the China National Foundation of the Natural Sciences.

Manuscript received December 21, 1997; Accepted for publication May 15, 1998.

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