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Effect of Quantitative Trait Loci for Milk Protein Percentage on Milk Protein Yield and Milk Yield in Israeli Holstein Dairy Cattle

Department of Genetics, Alexander Silberman Institute of Life Science, Hebrew University of Jerusalem, Jerusalem 91904, Israel

¹ Corresponding author: lipkin{at}vms.huji.ac.il

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
Although numerous quantitative trait loci (QTL) mapping studies involving milk protein percent (PP), milk yield (MY), and protein yield (PY) have been carried out, there has not been any systematic evaluation of the effects of individual QTL on these 3 interrelated traits. Consequently, the aim of the present study was to investigate the effects on MY and PY of QTL for PP previously mapped in various laboratories. The study, based on selective DNA pooling of milk samples, included 10 Israeli Holstein artificial insemination bulls, each the sire of 1,800 or more milk-recorded daughters. For each sire-trait combination across the 10 sires, milk samples of the highest and lowest daughters with respect to estimated breeding values for PP, PY, and MY were collected for pooling. A total of 134 dinucleotide microsatellites distributed over 25 bovine autosomes were used. An empirical standard error for marker-QTL linkage testing was calculated based on the variation among split samples within the same tail. Threshold comparison-wise error rate P-values were set to control proportion of false positives at P = 0.10 level for declaring significant effects at the marker-trait level. Estimates of the number of true null hypotheses for each trait were obtained from the histogram of marker comparison-wise error rate P-values. Based on these estimates, effective power of the experiment at the marker-trait level was estimated as 0.75, 0.41, and 0.73 for PP, PY, and MY. The proportion of heterozygosity at the QTL was estimated as 0.46, 0.39, and 0.40, respectively. After correcting for incomplete power and proportion of false positives, it was estimated that 38.7 and 37.5% of the markers affecting PP and MY, respectively, also affected PY. Of the markers affecting PY, 68.9 and 76.5%, respectively, also affected PP and MY. Apparently, none of the significant markers affected PY exclusively, and only 6.5 and 16.0%, respectively, affected PP or MY exclusively. Thus, almost all significant markers, and by inference almost all QTL, had effects on at least 2 of the 3 traits.

Key Words: quantitative trait loci mapping • selective DNA • proportion of false positive

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
A large number of studies have consistently documented a very high positive genetic correlation between milk yield (MY) and protein yield (PY), a moderate negative genetic correlation between MY and protein percentage (PP), and a very low, although generally positive, genetic correlation between PP and PY (Sölkner, 1989; Chauhan and Hayes, 1991; Welper and Freeman, 1992). For marker-assisted selection, it is important to know whether these relationships hold at the level of the individual QTL, or if there are QTL that have exclusive effects on PP, MY, or PY. Estimates of effects of β-CN A1 and A2 alleles and for the DGAT K232A allele on PP, MY, and PY were reported previously and are summarized in Table 1. Overall, directions of effects of the various alleles are consistent across populations and are consistent with the genetic correlations among the traits, namely specific alleles affect MY and PY in the same direction and PP in the opposite direction. On the other hand, estimated effects of specific alleles on the individual traits change in different populations. This may be due to sampling, to interaction of the allele with genetic background of the population, or to differences in the DNA sequence of the allele in different populations. On average, standardized effects of β-CN and DGAT alleles on PP were the same, but DGAT alleles appeared to have a greater effect on MY than β-CN alleles; the opposite was true for the effects of DGAT and β-CN alleles on PY. Thus, effects of individual alleles on the 3 traits may differ among genes. Viitala et al. (2003) used combined analysis of multiple chromosomes to map QTL affecting PP, MY, and PY in Finnish Ayrshire dairy cattle, at relatively high power. Assuming that QTL affecting PP, MY, or PY that map to within 20 cM of one another represent multiple effects of the same QTL, results by Viitala et al. (2003) can be interpreted as having identified 12 QTL affecting MY, of which 5 (45%) also affected PY, and 6 QTL affecting PP, of which only 1 affected PY (Table 2). Thus, the Viitala et al. (2003) study indicates that a majority of QTL affecting MY or PP did not affect PY and that effects of individual sire haplotypes on MY and PP were in opposite directions. On the basis of these results, Viitala et al. (2003) proposed that many QTL affect the volume of the liquid component of milk through primary effects on concentration of osmotic molecules (such as lactose and some of the Ca and P components). Such QTL would affect MY and PP in opposite directions and hence would be essentially neutral with respect to PY. Recently, Bagnato et al. (2008) reported a genome-wide scan of Brown Swiss dairy cattle for PP and MY using selective DNA pooling (Darvasi and Soller, 1994; Lipkin et al., 1998; Mosig et al., 2001). They identified a total of 55 QTL regions (QTLR), of which 16 affected MY exclusively and 13 affected PP exclusively. Eight of the 16 QTLR exclusively affecting MY, and 10 of the 13 exclusively affecting PP, also had reported results in 1 or more of the 3 Web cattle QTL databases (Cattle QTLdb, Hu et al., 2007; QTL Map, Khatkar et al., 2004; QTL Viewer, Polineni et al., 2006). Remarkably, all 8 QTLR in the Brown Swiss that exclusively affected MY were also found to exclusively affect MY in the databases. Similarly, all 10 QTL in the Brown Swiss that exclusively affected PP also exclusively affected PP in the databases. Following the Lander and Kruglyak (1995) validation criteria, and considering that the databases are based mainly on data obtained from Holstein populations, the completely independent replicated specificity of effects across different populations can be taken as a validation of these specific effects. Thus, in the study by Bagnato et al. (2008), an appreciable fraction of QTL appear to affect MY or PP primarily or exclusively, with little or no effect on the other trait.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
Selective DNA Pooling
Large half-sib or full-sib families are routinely produced in dairy cattle populations as part of routine genetic improvement programs. The size of those families provide statistical power for QTL mapping within population, which can be accessed by use of a daughter design (Soller and Genizi, 1978; Weller et al., 1990). However, achieving the high power theoretically available with the daughter design requires genotyping very large numbers of daughters against large numbers of markers, resulting in high genotyping costs (Soller, 1994). These costs can be greatly reduced by the use of selective DNA pooling (Darvasi and Soller, 1994; Lipkin et al., 1998; Mosig et al., 2001). In this procedure, determination of linkage between a molecular marker and a QTL is based on the distribution of parental marker alleles among pooled DNA samples of the extreme high and low phenotypic groups of the offspring population. Densitometric estimates of sire allele frequencies in the pools were obtained after correction for shadow bands, as previously described (Lipkin et al., 1998; Mosig et al., 2001).

Population and Samples
The study included 10 half-sib daughter families of Israeli Holstein AI bulls, each the sire of 1,800 or more milk-recorded daughters and 134 markers. This would have required a total of almost 2 million genotyping data points if done by individual genotyping. Thus, the study was made feasible only through selective DNA pooling, which enabled it to be carried out with a total of about 25,000 genotyping data points. Herd book data and milk samples of these daughters were collected at different times, generating a series of data sets (DS), which are summarized in Table 3. In particular, daughters of 4 of the sires, comprising DS1 were previously sampled and mapped for PP in 1996. In 1998, for purposes of the present study, daughters of these 4 sires were independently resampled for PY and MY (DS2), and 6 additional sire families were sampled for all 3 traits (DS3). Based on EBV, lists of the highest and lowest 220 (DS1) or 230 (DS2, DS3) daughters were prepared for each sire-trait-tail combination. Milk sampling was as previously described (Lipkin et al., 1998; Mosig et al., 2001). For each sire-trait-tail combination, 2 subpools (DS1) or a single pool (DS2, DS3) were prepared in completely independent duplicate. Genotyping of individual and pooled milk samples was as described (Lipkin et al., 1998). Densitometric values for the marker and sire-marker tests of DS1 were obtained from the original data of Lipkin et al. (1998) and Mosig et al. (2001) as described in those studies. These were reanalyzed using the empirical standard error obtained in the present study. All other densitometric values were obtained on the basis of data collected in the present study.

Microsatellite Markers
A total of 134 dinucleotide microsatellites distributed over 25 bovine autosomes were used to scan chromosomal intervals indicated previously to harbor QTL affecting PP (Lipkin et al., 1998; Mosig et al., 2001). All markers were obtained from the public Web sites (USDA, http://www.marc.usda.gov/genome/genome.html; IBRP, http://www.cgd.csiro.au/cgd1.html).

Marker-QTL Linkage Tests
The test for linkage between a marker and each of the 3 study traits was carried out at 2 levels: the sire-marker-trait level, which tests for association of marker and trait at the level of the individual sire, and the marker-trait level, which tests for association of marker and trait across all sires.

Sire-Marker-Trait Combinations.
For each sire-marker-trait combination for which the sire was heterozygous at the marker, the comparison-wise error rate (CWER) P_ijk-value, for the ith sire-jth marker-kth trait combination was obtained as twice the area of the normal curve from Z_ijk to + , where

D_ijk = (DL_ijk – DS_ijk)/2 is the difference in sire-allele frequencies between the high and low daughter pools of the ith sire with respect to the jth marker and the kth trait, averaged over the long and short sire alleles (Lipkin et al., 1998; Mosig et al., 2001). DL_ijk is the difference in allele frequency of the long sire allele between the high and low daughter pools. DS_ijk is the difference in allele frequency of the short sire allele between the high and low daughter pools. DL_ijk and DS_ijk will necessarily have opposite algebraic sign; hence, the minus sign in the expression for D_ijk.

Empirical SE(D').
Lipkin et al. (1998) and Mosig et al. (2001) calculated SE(D) on a priori grounds, on the assumption that it was determined by binomial sampling of sire and dam alleles and technical error of densitometric estimation of allele frequency in a pool. For the present study a novel empirical standard error was used, denoted SE(D'), based on a D-value (Dtail), obtained between 2 independent subpools at the same tail. Details on calculation of SE(D') are presented in Bagnato et al. (2008). To obtain an estimate of SE(D') for use in the present study, we reanalyzed 3 datasets (DS4, DS5, DS6; Table 3) for which 2 subpools were prepared for each tail. Data set 4 consisted of high and low daughters according to EBV for PP, of each of 7 Israel-Holstein sires. For each sire, the daughters comprising each tail were divided into 2 subpools. The 2 subpools in each tail were not completely independent, because the most extreme daughters within tails were assigned to the external subpools and the remainder to internal subpools (Lipkin et al., 1998; Mosig et al., 2001). Nevertheless, average Dtail was not significantly different from zero (data not shown), allowing the use of this DS to estimate SD(Dtail). Data set 5 consisted of high and low daughters according to EBV for PP of a new set of 7 sires. For each sire, the daughters in each tail were divided at random among 2 independent subpools. Data set 6 consisted of high and low daughters according to EBV for female fertility and a second set of high and low daughters according to EBV for milk SCC for 6 sires, 5 of which were included in DS5 and 1 which was collected independently. Here too, for each sire, the daughters in each tail were divided at random among 2 independent subpools.

Marker-Trait Combinations.
The CWER P_jk-value, for the jth marker-kth trait combination, was obtained as the area of the ² distribution from _jk² to + , where

The parentheses in the subscript of Z_i(jk)² and Z_i(jk)² indicate that the summation is over sires heterozygous at the jth marker, within the jth marker-kth trait combination, and s_i(jk) is the number of heterozygous sires for the jkth marker-trait combination (Weller et al., 1990; Lipkin et al., 1998; Mosig et al., 2001).

Proportion of True and Falsified Null Hypotheses Out of All Tests.
The total number of tests (N) represents a mixture comprised of n₁ tests for which the null hypothesis is false (i.e., marker-QTL linkage is present) and n₂ tests for which the null hypothesis is true (i.e., marker-QTL linkage is not present). Thus, the observed distribution of CWER P-values is a mixture of P-values representing these 2 classes of tests. On this basis, given the observed distribution of CWER P-values for the individual tests, the number of true null hypotheses (denoted n₂) out of all N tests can be estimated by a number of procedures (Nettleton et al., 2006). For the present study, the histogram-based procedure first described by Mosig et al. (2001) and simplified by Nettleton et al. (2006) was used with the following algorithm:

Count the P-values in each of the H histogram intervals of width 1/H

Let y_i be the count in the ith interval for i = 1,..., H,

Let x_j be the mean of the y_i from i = j to H,

then,

n₂ = H_xj', where j'= the lowest value of j for which y_j is lower than x_j.

In the present study, H was set to 10 so that bin width was 0.10.

The number of false null hypotheses (denoted n₁) is then obtained by subtraction, n₁ = N – n₂. Both n₂ and n₁ are useful statistics for a number of purposes, as will be shown in the following sections.

Proportion of False Positives: Setting Significance Levels for Experiment-Wise Linkage Tests.
To control for the multitest situation while retaining power, the proportion of false positive (PFP) criterion (Fernando et al., 2004), also termed aFDR (Mosig et al., 2001), was used to set CWER threshold P-values for declaration of significance at the marker-trait (PFP_M) and sire-marker-trait (PFP_S) levels. Following Mosig et al. (2001) and Fernando et al. (2004), PFP_Mj(k) for the jth marker test within the kth trait was calculated as:

where P_Mj(k) = the CWER P-value of the jth marker test within the kth trait, when the marker tests are ranked by their P-values from lowest to highest within a given trait; R_Mj(k) = the rank number of the jth marker test within the kth trait, and n_2Mk = the number of true null hypotheses for marker tests within the kth trait, estimated as shown above.

Values for the ith sire-jth marker combination within the kth trait [PFP_Sij(k)] were obtained in an exactly analogous manner, except that at the sire-marker level, the number of tests for which null hypothesis is true (n_2Sk) represents tests for which either the marker is not in linkage to a QTL or the marker is in linkage to a QTL, but the QTL is homozygous in the sire.

Significance Thresholds.
Significance thresholds were calculated separately by traits at the marker level and at the sire-marker level. At the marker level, marker-trait tests having CWER P-values corresponding to PFP_M 0.10 were taken as significant. At the sire-marker level, PFP were calculated across all markers, but only sire-marker-trait tests having CWER P-values corresponding to PFP 0.20 within significant markers were taken as significant.

Estimating Power of the Test
Power of the statistical tests used to determine marker-QTL linkage for the kth trait at the given significance threshold for the marker-trait and sire- marker-trait levels (denoted V_Mk and V_Sk, respectively) were estimated as observed number of significant tests at each level (n_OMk and n_OSk) after correction for proportion of false positives, divided by the estimated number of false null hypotheses in the DS at that level (n_1M, n_1S) obtained as described above:

where the factor (1 – PFP) represents the correction for PFP.

Estimating the Proportion of Heterozygosity at the QTL
At the marker-trait level, a false null hypothesis represents a marker in linkage to a QTL. The proportion of false null hypotheses out of all marker-trait tests for a given trait (n_1Mk/N_Mk) thus represents the proportion of markers in linkage to QTL for the kth trait (denoted Q_Mk). At the sire-marker-trait level, the proportion of false sire-marker-trait null hypotheses out of all sire-marker-trait tests for a given trait (n_1Sk/N_Sk, denoted Q_Sk) represents the joint proportion of markers in link-age to QTL (Q_Mk) and of QTL that are heterozygous in the sires (denoted H_k). It follows that Q_Sk = Q_MkH_k, and H_k can readily be estimated as H_k = Q_Sk/Q_Mk. This expression is algebraically equivalent to the corresponding expression given in Mosig et al. (2001). As pointed out by Mosig et al. (2001), QTL that are not represented in the sample by at least 1 sire heterozygous at both the marker and the QTL will not be included among the significant markers, so that Q_Mk is an underestimate. This, in turn, leads to the H_k being overestimates. Mosig et al. (2001) also presented a procedure for correcting for the bias. However, when they applied this procedure to their data, the bias was close to 10%, and should be even lower for the present DS, because it includes a larger number of sires. Given the negligible bias, the correction procedure was not implemented in the present study.

Allele Substitution Effects
Allele substitution effects were calculated as described (Lipkin et al., 1998), based on shadow-corrected allele frequency estimates and the mean EBV of the pools (Table 4). The effects were calculated for all sire-marker-trait combinations defined as significant on the above PFP_M and PFP_S criteria.

Let O_Mij be the observed number of markers that affect both traits. Because the observed marker effects include false positives, the number of observed marker effects on the 2 traits that represent true effects on both traits is equal to O_Mij(1 – PFP_M)². On the other hand, because of incomplete power of the experiment, the actual number of markers affecting the 2 traits will be n_1Mij = O_Mij(1 – PFP_M)²/V_iV_j, where V_i and V_j = the power for detecting marker effects on traits i and j, respectively. The true proportion of markers affecting trait i that also affect trait j (Q_Mij) will then be given by the proportion of n_1Mij among the total number of estimated false null hypotheses involving i, (n_1Mi): Q_Mij = n_1Mij/n_1Mi. Similarly, the true proportion of markers affecting j that also affect i (Q_Mji) will be given by Q_Mji = n_1Mji/n_1Mj, where n_1Mji and n_1Mj are obtained as described above. Because the estimated numbers of false null hypotheses n_1Mi and n_1Mj can be different for different traits, it follows that Q_Mij and Q_Mji need not be equal. That is, the proportion of QTL affecting trait i that also affect trait j need not be the same as the proportion of QTL affecting j that also affect i. For example, it might be that a small fraction of QTL affecting MY also affect PY, but almost all QTL affecting PY also affect MY. On the same argument, the true proportion of markers affecting 3 traits (i, j, k) will be n_1Mijk = O_Mijk(1 – PFP_M)³/V_iV_jV_k.

As calculated above, n_1Mi represents the total number of markers that affect trait i, including those that also affect j and k, and n_1Mij represents the total number of markers that affect traits i and j, including those that affect i, j, and k. From this, it follows that the number of markers n_1Mi, n_1Mij, and n_1Mik that exclusively affect traits i, j, or k will equal

and similarly for the other traits.

The proportion of markers affecting trait i that exclusively affect trait i, and trait combinations ij, ik, and ijk, are obtained by dividing n_1Mi, n_1Mij, n_1Mik, and n_1Mijk, respectively, by n_1Mi.

In principle, it would have been preferable to perform the mapping for each trait in an independent set of sires or daughters. This was achieved in part by the separation of daughters for the same sires in DS1 and DS2. But the logistical and analytical problems posed by extending such an approach to the entire DS seem insuperable. Had such an experiment been performed, we can expect that the proportion of QTL showing pleio-tropic effects would have been somewhat less than found in the present study.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
Sampling and Population Phenotypic Means
The mean size of the sire half-sib families was 2,779 (1,827 to 4,769) for PP and 2,893 (2,135 to 4,769) for PY and MY (Table 5). With target number of daughters in the designated tails of 220 (DS1) and 230 (DS2, DS3), the average proportion selected in each tail was about 0.08. For PY and MY, the proportion of targeted daughters actually sampled was greater in the high pools (0.83) than in the low pools (0.78), indicating higher herd retention and hence positive selection for these traits. For PP, the proportion actually sampled was the same for high and low pools (0.79).

Empirical Standard Error
For DS4, SE(Dtail) was calculated across 1,375 sire-marker-trait-tail combinations and was found equal to 0.072 so that SE(Dnull) = 0.072/2 = 0.051. For DS5 and DS6, SE(Dtail) was calculated across 1,338 sire-marker-trait-tail combinations and was found equal to 0.073 so that again SE(Dnull) = 0.051. Independent subpools were not prepared for the samples of DS2 and DS3. Given that the same methodology was used, we took the average SE(Dnull) = 0.051 obtained in DS4, DS5, and DS6 as the SE(D) to analyze the DS2 and DS3 data as well. This value is somewhat less than the value of 0.056 reported by Bagnato et al. (2008).

The Proportion of False Null Hypotheses Among All Null Hypotheses
A total of 2,563 sire-marker-trait tests and 402 marker-trait tests were implemented in the present study. Table 6 shows the frequency distribution in bins of width 0.10 of CWER P-values by traits, for sire marker, and for marker tests. At both levels, there was an excess of low (significant) P-values, compared with the null hypothesis expectation of 10% of total tests in each bin. This indicates a high proportion of false null hypotheses in the DS, which are generating the excess low P-values. The excess of low P-values was about twice as great at the marker level than at the sire-marker level. This is as expected, because even when a sire is tested at a marker in linkage to a QTL, a significant sire-marker effect can be obtained only if the QTL is present in a heterozygous state as well. At both marker and sire-marker levels, the excess of low P-values was similar for PP and MY but considerably less for PY. This is due to the generally smaller D-values found for PY. The mean absolute magnitude of D-values was 0.056, 0.048, and 0.057 for MY, PY, and PP, respectively.

Critical CWER P-Values and Power According to PFP
Table 6 also shows critical CWER P-values for declaration of linkage, according to PFP criteria for significance set at a level of 0.10 for marker-trait tests and 0.20 for sire-marker-trait tests within significant markers. Because PFP values are in direct proportion to n₂, PP and MY had similar critical P-values, which were distinctly higher than the corresponding values for PY. Critical P-values for PP were comparable to the values reported for this trait by Mosig et al. (2001).

The Number of Significant Marker-Trait Tests
A total of 134 markers covering 25 chromosomes were tested against each of the 3 traits. Thus, there were 402 tests in all, of which 165 (41.0%) were significant at PFP_M 0.1 (appendix Table I). Of the markers tested, 30 were not significant for any of the traits. Of the 104 significant markers, 20 were exclusively significant for PP, 2 for PY, and 27 for MY; 6 were exclusively significant for PP and PY, 36 for PP and MY, 7 for PY and MY, and 6 markers were exclusively significant for all 3 traits. Considering the traits individually, 68 markers (50.7%) on 23 chromosomes had a significant effect on PP (i.e., this includes markers significant exclusively for PP and those significant for PP and PY, PP and MY, and PP, PY, and MY), 21 markers (15.7%) on 15 chromosomes had a significant effect on PY, and 76 markers (56.7%) on 23 chromosomes had a significant effect on MY.

View this table: [in this window] [in a new window]   Table 7. Allele substitution effect () of all sires significant at proportion of false positive (PFPS) 0.20 within markers significant at PFPM 0.101

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

The Number of True and False Null Hypotheses Among All Null Hypotheses
The present study made extensive use of estimates of the number of true null hypotheses (n₂) among all null hypotheses. These were obtained by a histogram-based approach first proposed by Mosig et al. (2001) using an iterative procedure and later simplified to a short algorithm by Nettleton et al. (2006). Evaluation of this procedure in simulations involving QTL mapping (Fernando et al., 2004) and DNA expression analysis (Nettleton et al., 2006) showed that the procedure was effective in estimating n₂ and much simpler to implement relative to a variety of alternative procedures (Nettleton et al., 2006). The estimate of n₂ is primarily of interest for application of the PFP criterion for setting statistical significance levels (Mosig et al., 2001; Fernando et al., 2004). However, once an estimate of n₂ is available, the corresponding n₁, an estimate of the number of false null-hypotheses is obtained by simple subtraction and can be used to estimate power of the experiment with respect to uncovering marker-QTL linkage (Mosig et al., 2001). As shown in Mosig et al. (2001), and somewhat differently in the present study, estimates of statistical power can be used within the framework of a multiple-sire daughter design to estimate proportion of heterozygosity at the QTL. In the present study, power estimates were further utilized to estimate the proportion of QTL affecting 2 or more traits.

QTL Effects on PP, MY, and PY
As far as PP is concerned, the high estimated proportion of false null hypotheses at the marker level (61.4%, Table 6) derives from the fact that the markers tested were for the most part chosen from QTLR previously shown to affect PP. The estimated 38.6% of true null hypotheses can be attributed to false positive results in the previous studies, chance sampling such that the new sires were homozygous at some of the QTLR identified in previous studies, and new markers added to explore the flanking regions of the previously identified QTLR, or QTLR reported from other populations. Given that the scan was concentrated on QTLR affecting PP, and that the calculations in this study indicate that three-fourths of markers affecting PP also affect MY, the proportion of false null hypotheses for MY would have been expected to be somewhat less than what was found for PP. Nevertheless, MY showed an even higher proportion of false null hypotheses (70.1%) than PP (Table 6). A simple explanation for this observation was not found. The proportion of false null hypotheses for PY (34.5%) was considerably less than for PP or MY. This is as expected if most of the markers affecting PP and MY are more or less balanced in their effects on the 2 traits. In this case, the net effect on PY is reduced by the negative correlated effects of MY and PP so that detectable signal strength of PY extends to fewer markers than the signal for MY or PP. The generally lower D-values observed for PY compared with MY and PP noted in the results section are attributed to this factor.

The estimated numbers of true marker-QTL linkages (n_1M, Table 6) were 82, 46, and 94 for PP, PY, and MY, respectively, with corresponding power after correction for 10% of false positives of 0.75, 0.41, and 0.73. The power for PP is somewhat higher than the value 0.71 (uncorrected for false positives) reported by Mosig et al. (2001). The increase in power in the present study may reflect the use of 10 sires, whereas only 7 sires were surveyed in Mosig et al. (2001), and the fact that the present study was focused on QTLR found in that study.

Averaging over PP taken as trait i and MY taken as trait j, over two-thirds (0.71) of QTL affecting PP also affect MY and vice versa. The proportion of markers affecting PP that also affect PY was 0.39; the corresponding value for MY and PY was 0.37. In the reverse direction, the proportion of markers affecting PY that also affect PP was 0.69; the corresponding value for PY and MY was 0.77. Thus, about one-third of markers that affect PP or MY also affect PY, whereas about two-thirds of markers that affect PY also affect PP or MY. This is plausible. Many QTL affecting PP or MY will not affect PY because of the inverse relationship between MY and PP. In the converse direction, however, we would expect a QTL affecting PY to have effects on MY or PP or both. Thus, the results of the present study are broadly consistent with Viitala et al. (2003) but also support the presence of an appreciable body of QTL that affect MY or PP without major effects on the alternative trait (see below). These may exert their effects through other mechanisms.

Although most markers, and by implication QTL, were estimated to have effects on both MY and PP, it was also estimated that an appreciable proportion (about one-third) of markers affecting MY did not have major effects on PP and vice versa. Thus, these results imply that effects of individual QTL on MY, PP, and PY can differ. This is supported by studies of the effects of alleles at individual known genes on the 3 traits, MY, PY, and PP.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
In any experiment involving effects of a QTL on a number of traits, some of the markers will present statistical significance for a single trait only. The analytical problem is to distinguish those QTL that are truly limited in their effect to a single trait from those that affect multiple traits but because of limited experimental power of the study present statistical significance for a single trait only. In the present study, a method was developed to correct for incomplete power. Using this approach, estimates of the proportion of markers affecting PP that also affect MY (and vice versa) averaged 0.71. This agrees well with the Viitala et al. (2003) hypothesis. However, the results of the present study also indicate that there may be a proportion of almost 30% of QTL that affect either PP or MY in a major way, presumably via a mechanism other than liquid volume, with only minor effects on the other trait. This agrees very closely with the QTL mapping results of Bagnato et al. (2008) for MY and PP in Brown Swiss dairy cattle and their homologues in the Holstein breed as represented by the main QTL databases.

The estimate of 30% of QTL that affect either MY or PP without effects on the alternative trait is close to the estimate of about one-third (0.32) of QTL affecting PP or MY that also affect PY. Thus, those QTL that affect primarily PP or MY with only minor effect on the other main trait may be the QTL that have significant effects on PY. As expected from the arithmetical relationships among PP, MY, and PY, QTL affecting PY alone were absent from Viitala et al. (2003) and were estimated as absent in the corrected analysis of the present study. The high proportion of QTL estimated as affecting MY and PP with neutral effects on PY should enable PP to be maintained even when selection for PY results in an increase in MY. Assuming a diallelic QTL, average QTL heterozygosity equal to 0.40 as found in the present study implies allele frequencies in the range 0.7 or more for the more frequent QTL allele. This would be consistent with the longstanding selection for MY that has been underway in the Holstein breed for many generations and suggests that, for the most part, alleles with positive effects on MY (and associated negative effects on PP) may already be at moderately high frequency in the breed.

	Appendix 1

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 
This research was supported by the FP5 program of the European Union (BovMAS project QLK5-CT-2001- 02379). We thank Jack Dekkers (Iowa State Univ., Ames) and the reviewers for useful comments.

Received for publication August 31, 2007. Accepted for publication December 18, 2007.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS Appendix 1 ACKNOWLEDGEMENTS REFERENCES

 


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