Predictability of Bull Merit from Genetic Evaluations of Sires and Maternal Grandsires Using an Animal Model1

GENETICS AND BREEDING Predictability of Bull Merit from Genetic Evaluations of Sires and Maternal Grandsires Using an Animal Model1 B. REKIK and P. J. BERGER2 Department of Animal Science, 239 Kildee Hall, Iowa State University, Ames 50011

ABSTRACT The ability of animal model evaluations to predict the genetic potential of a bull from his sire and maternal grandsire was investigated. Theoretical coefficients were derived for different combinations of progeny records on the bull, sire, and maternal grandsire. Coefficients >0.50 for sires and >0.25 for maternal grandsires were associated with bulls with few daughters. Ten animal model evaluations of Holsteins, July 1989 to January 1994, were used to estimate coefficients realized in three populations: 1 ) all AI bulls ( n = 6924), 2 ) current AI bulls ( n = 1344), and 3 ) elite AI bulls ( n = 6116). The PTA were analyzed for milk, fat, and protein yields, and for fat and protein percentages. Birth year of sons nested within the birth year of their sire was included as a random effect with a first-order autoregressive process for the regression model used to estimate the realized coefficients for sires and maternal grandsires. After adjustment for the genetic trend for estimates of sires, the correlation coefficient between predicted merit of sons from 2 consecutive yr ranged from 0.34 to 0.87. The PTA of bulls from first-crop evaluation were accurately predicted from PTA of sire and maternal grandsire for yield and percentage traits. ( Key words: animal model, genetic evaluation, maternal grandsire, sire) Abbreviation key: AR = autoregressive, FCE = first-crop evaluation, MGS = maternal grandsire, MRE = most recent evaluation. INTRODUCTION Improvement of the average genetic merit for an individual cow for yield has resulted in a substantial

Received February 20, 1996. Accepted November 18, 1996. 1Journal Paper Number J-16730 of the Iowa Agriculture and Home Economics Experimental Station, Ames; Project Number 3009. 2Reprint requests. 1997 J Dairy Sci 80:957–964

increase in the volume of milk, fat, and protein produced in the US, despite a decrease in the number of cows since the early 1940s. For the Holstein population, male selection has resulted in larger genetic gains than has female selection (9, 16, 17). Selection of young bulls is carried out in two stages in the AI industry: pedigree index selection, followed by progeny testing of the best candidates from the first stage (2, 6, 10). Effective pedigree selection depends on the accuracy of the genetic evaluation of parents (5, 7, 8). Breeding organizations and dairy producers base their selection decisions on the USDA evaluations (7, 11, 22). Thus, USDA evaluations must accurately predict the merit of a young bull. Several studies (4, 14, 15, 18, 20, 21) using less extensive data than are available to the USDA on a national basis have reported low to fairly accurate coefficients for predicting merit of young bulls (15, 18) and heifers (20, 21) from pedigree information. Compared with theoretical coefficients, early records provided more accurate coefficients for sire, dam, and maternal grandsire ( MGS) than did late records (16, 20). The objective of this study was to assess the effectiveness of the animal model evaluations of USDA in predicting the genetic potential of a young bull from the predicted merit of his sire and maternal grandsire. MATERIALS AND METHODS Data Data were animal model evaluations for milk, fat, and protein yields and for fat and protein percentages from 10 genetic evaluations (July 1989 to January 1994) of the Animal Improvement Programs Laboratory (USDA, Beltsville, MD). All bulls included in the analyses were born after 1969, were required to have at least 10 daughters with records, and included reliabilities for both milk and fat, and protein subsets. The data were divided into three populations: 1 ) all AI bulls ( n = 6924), 2 ) current bulls ( n = 1344), and 3 ) elite bulls ( n = 6116). A bull was determined to be an AI bull if coded as a “progeny test”, “alive

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AI”, or “active AI” bull in any one of the 10 evaluations. The second data file of current bulls were either progeny tested or current AI bulls in January 1994. The third data file of elite bulls were all sons of sires in the AI data file that had at least 20 AI sons through their breeding history. Each population was studied in terms of first-crop evaluations ( FCE) and most recent evaluation ( MRE) . After the AI bull data were sorted by year and month of evaluation, FCE was the first evaluation published for a bull conditional on the number of daughters being >10 and <75. This definition of FCE is similar to the one used by Cassell et al. ( 1 ) . Bulls with >75 daughters with records in their first animal model evaluations were deleted because these bulls were heavily sampled, as categorized by Cassell et al. ( 1 ) . The MRE was defined as the evaluation from January 1994 on bulls with >75 daughters. These evaluations involved bulls that were used before and after the implementation of the animal model in July 1989. Clearly, current and elite AI bulls are subpopulations of the AI population and allow comparisons among different subpopulations of the Holstein male population. These comparisons, however, do not account for different breeding objectives across AI organizations. All bull populations were considered to be samples from the same population. The AI sires were the basis for comparison. Current bulls constitute the segment of the population that has been systematically and probably the most effectively evaluated, and, finally, sires with 20 sons or more represent the population of sires that have been heavily used as sires of sons. Each data subfile was edited to construct a pedigree file and to identify the genetic evaluations of bulls, their sires, and their maternal grandsires. Records were deleted for bulls with unknown sires or MGS. The exclusion from the analysis of bulls with incomplete pedigree information greatly reduced the number of bulls born before the mid-1980s. Regression of Bull PTA on Sire and Maternal Grandsire PTA Theoretical regression coefficients. The animal model evaluation of bulls involves use of records on daughters of the bull ( b ) , daughters of the sire ( s ) , and daughters of bull MGS ( g ) , plus records on all other relatives. In this section, however, only evaluations for the bull, his sire, and his MGS are considered to derive approximate theoretical weights to predict the PTA of an AI young bull (15). The general mixed model equations are set up as follows, assuming one son per sire and one son per maternal grandsire, all of which are unrelated to other bulls: Journal of Dairy Science Vol. 80, No. 5, 1997

nb

16 + a/det –8 –4

ns ng

–8 15 2

–4 2 12

aˆb aˆs aˆg

=

yb ys yg

[1]

where n = number of daughters for the bull ( b ) , his sire ( s ) , and his MGS ( g ) ; a = s2/s2; e s det = determinant of the relationship matrix; a = ETA of the bull ( b ) , his sire ( s ) , and his MGS ( g ) ; and y = sum of adjusted records for daughters of the bull ( b ) , his sires ( s ) , and his MGS ( g ) (i.e., records have been adjusted for fixed effects, and the effect of herds have been removed). Variances and covariances of the sums ( 1 5 ) are V( yi) where i = b, Cov ( y syg) Cov ( y bys)

= s, = =

ni( n i + 15) s2p/16, or g, 0, nbns s2p/32,

and Cov ( y byg) = nb ng s2p/64 where s2p is the phenotypic variance. The (co)variances described apply to yield but not to percentage traits. These equations were solved algebraically, retaining nb, ns, and ng and yb, ys, and yg to obtain solutions for the theoretical regressions baˆb,aˆs = Cov ( aˆ b,aˆs)/Var(aˆ s) = nb(11 nsng + 180ns + 225ng + 3600) [4( nb + 15)(120 ng + 1800) + 2ns(11 nbng + 180nb + 240ng + 3600) – 30nbng] + 2ns(120 ng + 1800) [nb (120 ng + 1800) + 2 ( ns + 15)(11 nbng + 180nb + 240ng + 3600)] + ngnb (900 + 60ns) [(1800 + 120ng) – 120( ng + 15)] 4nb (120 ng + 1800) [ ( nb + 15)(120 ng + 1800) + ns(11 nbng + 180nb + 240ng + 3600) – 15nbng] + 4ns( ns + 15) [(11 nbng + 180nb + 240ng + 3600) 2] + 3600( n2b) ng ( ng + 15),

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e utj =  t ru( t

and baˆb,aˆg = Cov ( aˆ b,aˆg)/Var(aˆ g) =

E( utj) = 0, Var ( u tj) = s2t , and Cov ( u tj, u( t

+ 2nbns (120 ng + 1800) [(60 ng + 900) – 60( ns + 15)] + ng (900 + 60ns) [nb(900 + 60ns) + 4 ( ng + 15)(11 nbns + 225nb + 240ng + 3600)] 4nb (60 ng + 900) [nb + 15)(60 ng + 900) + 0.5ng(11 nbns + 225nb + 240ns + 3600) – 30nbns] + 4ng( ng + 15) [(11 nbng + 180nb + 240ng + 3600) 2] + 3600( n2b) ns ( ns + 15).

These theoretical regressions were then evaluated for different combinations of nb, ns, and ng (Table 1). Heritability was 0.25 for yields and 0.5 for percentages (i.e., a = 15 for milk, fat, and protein yields and 7 for fat and protein percentages). Actual regression coefficients. The three data files defined earlier (all AI bulls, current AI bulls, and elite AI bulls) were analyzed to estimate the regression coefficients that relate the genetic evaluation of a bull to genetic evaluations of his sire and MGS. For each data file, the PTA of the sire and MGS were obtained from the same year and month of evaluation for the bull (i.e., January 1994 for MRE, and year and month of evaluation for the bull in FCE). The FCE and MRE were analyzed separately. Coefficients were estimated for all AI bulls, current AI bulls, and elite AI bulls. The model was [2]

where aˆbtjki m b1 and b2 aˆsji aˆgki utj dbti

for t = 1 + et for t > 1

[2a]

where

nb (11 nsng + 180ns + 225ng + 3600) [4( nb + 15)(60 ng + 900) + ng(11 nbns + 225nb + 240ns + 3600) – 60nbns]

aˆbtjki = m + b1aˆsji + b2aˆgki + utj + dbti

– 1) j

= = = =

bull PTA for trait i in birth year t, mean effect, partial regression coefficients, sire PTA for the trait i in birth year j, = MGS PTA for the trait i in birth year k, = bull birth year t nested within sire birth year j, and = residual.

The birth-year effect of the bull, utj, follows a firstorder autoregressive process ( AR( 1 ) ) [see ( 1 9 ) for a recent review] such that

–1) j)

rs2t ,

= r = a correlation coefficient for a single lag, and et = random error. The autocorrelation coefficient ( r) that relates genetic merit of sons produced by sires from the same genetic group and from birth years distant by a lag l is defined by the function r = rl ( l = 0, 1, 2, . . .). For an AR(1) process, the condition –1 < r < 1 must be true. The analysis was done with the MIXED procedure of SAS (13). RESULTS Theoretical Coefficients for Regression Analysis Approximate theoretical coefficients for predicting bull PTA from genetic evaluations of sires and MGS are given in Table 1. Theoretical coefficients were computed for selected numbers of daughters and from the data for both FCE and MRE. Coefficients from the data were computed as means of those corresponding to each bull rather than as the overall mean number of daughters for bulls, sires, and MGS. These results are in agreement with results of previous reports (15, 18, 20, 21). Coefficients of the sire evaluations closely agreed with those reported by Van Vleck (15), with or without inclusion of the dam or the MGS in the derivation of coefficients. The contribution of MGS, however, was in the same range as the value derived from regression of the PTA of bull on the PTA of dam and MGS PTA, which also agreed with the results of Van Vleck (15). In general, the coefficients corresponding to MGS differed from those previously reported ( 1 5 ) in which both dam and MGS were part of the regression equations. The number of daughters of the bull seemed to have the greatest effect on the coefficients; the number of daughters by the sire of the bull were nearly as important. Overall, large numbers of daughters resulted in a coefficient of 0.50 for the sire and a coefficient of 0.25 for the MGS, regardless of the heritability range. Coefficients >0.50 for sires and >0.25 for MGS were associated with few daughters. Low numbers of daughters, however, tended to have Journal of Dairy Science Vol. 80, No. 5, 1997

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more of an effect on the coefficients for low heritability. That is, the theoretical coefficients were much larger than the 0.50 limit with heritability at 0.25 than with heritability at 0.50 for similar numbers of daughters. In addition, progressively increasing the number of daughters did not induce as fast a convergence toward the limit as was true for the larger heritability. Theoretical coefficients from the FCE and for the 0.25 heritability seemed to be slightly greater than expected if the overall numbers of daughters were used for computation because the

theoretical coefficients were means of coefficients corresponding to an individual bull. If the number of daughters 28, 9994, and 28,028 (Table 1 ) for the bull, the sire, and the MGS, respectively, were used for computation, a coefficient of 0.500 would have resulted; the coefficient for the sire would have been 0.516. Because the number of high individual coefficients were large as a result of greater proportions of young bulls and sires with low numbers of daughters, the mean sire weight was relatively large. In the AI bull population, 40% of bulls had 20 daughters or less, and almost 20% of sires had <2500 daughters.

TABLE 1. Approximate theoretical coefficients for the regression of PTA of bulls ( b ) on PTA of sires ( s ) and maternal grandsires ( g ) PTA.1 Coefficient Daughters of Evaluation2

First crop AI Current Elite Most recent AI Current Elite

0.25

h2

0.50 h2

b

s

g

baˆb,aˆs

baˆb,aˆg

baˆb,aˆs

baˆb,aˆg

20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 100 100 100 100 100 1000 1000 1000 1000 1000 1000 1000 10,000

(no.) 20 50 50 500 500 10,000 10,000 40 50 50 50 100 500 500 10,000 10,000 50 50 500 500 10,000 50 50 500 500 10,000 10,000 100 10,000

20 50 10,000 50 1000 50 10,000 40 50 500 10,000 100 50 1000 50 10,000 50 10,000 50 1000 10,000 50 10,000 50 1000 50 10,000 10,000 10,000

0.662 0.569 0.568 0.507 0.507 0.500 0.500 0.612 0.591 0.591 0.591 0.547 0.510 0.509 0.500 0.500 0.613 0.613 0.512 0.512 0.501 0.633 0.663 0.514 0.514 0.501 0.501 0.569 0.500

0.343 0.287 0.250 0.286 0.252 0.285 0.250 0.311 0.299 0.255 0.250 0.274 0.298 0.252 0.298 0.250 0.311 0.250 0.310 0.253 0.250 0.322 0.250 0.321 0.254 0.321 0.250 0.250 0.250

0.553 0.519 0.519 0.501 0.502 0.500 0.500 0.521 0.515 0.516 0.516 0.507 0.501 0.501 0.500 0.500 0.511 0.512 0.500 0.500 0.500 0.507 0.507 0.500 0.500 0.500 0.500 0.501 0.500

0.268 0.255 0.250 0.255 0.250 0.255 0.250 0.255 0.253 0.250 0.250 0.251 0.254 0.250 0.254 0.250 0.252 0.250 0.252 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250

28 25 27

9,994 3,072 10,523

28,028 21,913 28,707

0.516 0.533 0.515

0.251 0.251 0.251

0.504 0.510 0.504

0.250 0.250 0.250

539 181 540

23,965 16,388 25,331

34,461 28,992 35,336

0.515 0.501 0.504

0.251 0.250 0.251

0.504 0.500 0.500

0.250 0.250 0.250

1AI = AI bulls from 10 evaluations (July 1984 to January 1994), current = progeny test or current AI bulls in January 1994, and elite = sons of AI bulls with at least 20 AI sons. 2First crop = First evaluation for an AI bull (July 1989 to January 1994) with 11 to 75 daughters; most recent = evaluation from January 1994 for bulls with >75 daughters.

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PREDICTABILITY OF BULL MERIT TABLE 2. Actual coefficients from the regression of PTA of first-crop bulls ( b ) on the PTA of sires ( s ) and maternal grandsires ( g ) . 1 Coefficient2 Trait

b

s

g

AI Milk Fat Protein Fat percentage Protein percentage Current Milk Fat Protein Fat percentage Protein percentage Elite Milk Fat Protein Fat percentage Protein percentage

6924

(no.) 287

290

1344

6116

85

56

b1

b2

r

Est.

SE

Est.

SE

Est.

SE

0.47 0.48 0.51 0.48 0.48

0.02 0.01 0.01 0.01 0.01

0.23 0.20 0.21 0.23 0.23

0.03 0.01 0.01 0.01 0.00

0.87 0.84 0.81 0.75 0.68

0.09 0.06 0.07 0.18 0.15

0.46 0.43 0.54 0.46 0.47

0.04 0.03 0.04 0.02 0.02

0.27 0.20 0.32 0.24 0.22

0.03 0.03 0.03 0.03 0.02

0.50 0.67 0.54 0.50 0.74

0.22 0.18 0.24 0.47 0.29

0.42 0.44 0.49 0.48 0.48

0.02 0.01 0.02 0.01 0.01

0.21 0.19 0.19 0.23 0.22

0.01 0.01 0.01 0.01 0.01

0.82 0.84 0.76 0.34 0.56

0.07 0.06 0.10 0.35 0.20

51

231

1AI = AI bulls from 10 evaluations (July 1984 to January 1994), current = progeny test or current AI bulls in January 1994, and elite = sons of AI bulls with at least 20 AI sons. 2Estimates from model defined by Equation [2].

In practice, genetic evaluations based on small numbers of daughters are expected to overestimate the genetic merit of a bull when predicted from the merit of his sire and MGS. The overestimation is less pronounced for highly heritable traits. Actual Coefficients for Regression Analyses Actual regression coefficients for predicting the PTA of young bulls from the PTA of sires and MGS for FCE and MRE are listed in Tables 2 and 3. Sire coefficients from FCE were consistent with results of previous reports (4, 14, 18). Estimates ranged from 0.42 to 0.54 (Table 2), which was near the range of the theoretical coefficients, 0.505 to 0.533 (Table 1). Conversely, the MGS coefficients were consistent with the theoretical expectations but not with previously reported results. The MGS coefficients ranged from 0.19 to 0.32 (Table 2 ) compared with an approximate theoretical weight of almost 0.25 (Table 1). Van Vleck et al. ( 1 8 ) reported an estimate of –0.29 from regressing bull evaluations on dam, sire, and MGS evaluations in which the sire, the dam, and the MGS were simultaneously evaluated with an animal model; those authors also reported an estimate of 0.06 from the Northeast genetic evaluation. Van Vleck ( 1 5 ) used simple linear regression to predict son PTA

for milk from dam PTA for milk, sire PTA for milk, and MGS PTA for milk for 2826 bulls sampled by AI organizations. From various regression models, Van Vleck ( 1 5 ) also reported a constant sire weight (0.41) but a wide range for the MGS coefficients (0.12 to 0.33). The negative weight reported by Van Vleck et al. ( 1 8 ) was because the dam accounted for all the information that would have otherwise been explained by the MGS. In this study, the slight departure of the MGS coefficients from the theoretical expectations might be explained by use of the same bulls as sires of sons and sires of dams to produce sons (i.e., sires and MGS were related). For example, if the sire and MGS are full sibs, as opposed to being unrelated, as assumed in the development of theoretical regression coefficients, then the coefficients for the sire converge toward 0.50; the coefficients for the MGS reach a limit of 0. Many sires and MGS are likely to be related in the current Holstein population because as many as 70% of the bulls being tested in a given 6-mo period are sired by <6 bulls (12). Recent comparisons of pedigree sources of information showed that parent average was a more accurate predictor of daughter yield deviation and PTA for milk, fat, and protein of AI-sampled bulls than was pedigree index (12). Also, genetic evaluation of dams was more accurate with an animal model than with former systems of genetic evaluation. Dams were not Journal of Dairy Science Vol. 80, No. 5, 1997

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REKIK AND BERGER TABLE 3. Actual coefficients from the regression of PTA of most recent evaluation of bulls ( b ) on the PTA of their sires ( s ) and their maternal grandsires ( g ) . 1 Coefficient2 Trait

b

s

g

AI Milk Fat Protein Fat percentage Protein percentage Current Milk Fat Protein Fat percentage Protein percentage Elite Milk Fat Protein Fat percentage Protein percentage

1213

(no.) 118

106

100

1094

22

53

b1

b2 Est.

r

Est.

SE

SE

0.43 0.39 0.43 0.48 0.48

0.03 0.02 0.03 0.03 0.02

0.17 0.20 0.17 0.21 0.16

0.03 0.03 0.03 0.03 0.03

0.71 0.41 0.63 0.45 0.47

0.10 0.11 0.13 0.11 0.09

0.32 0.17 0.41 –0.04 0.15

0.10 0.09 0.14 0.18 0.11

0.36 0.37 0.36 0.49 0.49

0.04 0.03 0.04 0.03 0.02

0.14 0.17 0.14 0.22 0.17

0.03 0.03 0.03 0.03 0.03

Est. 0.72 0.50 0.50

SE 0.47 . . .3 0.53 . . . 30.1

13 0.04 –0.62

. . . . . . 10.3 . . . 10.3

91 0.50 0.37 0.64

0.45 0.84 0.32 . . . . . .

1AI = AI bulls from 10 evaluations (July 1984 to January 1994), current = progeny test or current AI bulls in January 1994, and elite = sons of AI bulls with at least 20 AI sons. 2Estimates from model defined by Equation [2]. 3Regression model did not provide estimates for the first-order autoregressive process.

part of this study because we wanted to focus on the second stage of sire selection, that is, on bulls evaluated by information on their own progeny as well as progeny of their sire and MGS. Of course, information on the dams and other collateral relatives is included in the evaluation by the relationship matrix used in animal model evaluation. The number of bulls and their ancestors used in the regression seemed to affect the coefficients greatly (Tables 2 and 3). There was a disturbing trend in the regression estimates from relatively limited numbers of animals for MRE, especially for the current bull population. However, the genetic evaluation (FCE vs. MRE) slightly affected the sire coefficients in the AI and elite bull populations. The sire coefficients ranged from 0.36 to 0.49 (Table 2 ) in the AI and elite populations. The coefficients of MGS, however, ranged from 0.14 to 0.22 for these two populations. For the current bull population, however, coefficients of both sires and MGS were inconsistent with expectations. In fact, the MRE seemed to have resulted in increased regression coefficients for milk yield and protein yield and for both sire and MGS. Recently, milk and protein yields have been heavily weighted for selection, and daughters from outstanding bulls with respect to these two traits might have been preferentially treated during subsequent lactations. We should, Journal of Dairy Science Vol. 80, No. 5, 1997

however, be cautious in drawing such a conclusion because the regression was only for 100 bulls on 22 sires and 13 MGS (Table 3). The coefficients of MGS from MRE (Table 3 ) in the current bull population were more variable and inconsistent than those from FCE (Table 2). Thus, they were farther from their respective theoretical coefficients. This variability, of course, may be explained partially by the highly selected nature of the bulls included in the MRE data. Only bulls with second-crop daughters are included in these data, and these bulls tend to have received a better than average sample of genes from their parents. Theoretical regression coefficients, however, assume that the bulls were not selected on daughter performance. Effects of birth year groups were analyzed as a random effect with a first-order autoregressive process. To ignore birth years completely (i.e., equivalent to saying they have no effect) might seriously bias estimates of the regression coefficient relating genetic evaluations of bulls to genetic evaluations of sires and MGS. Fitting birth years as a fixed effect did not make efficient use of all information within and between birth-year groups. In addition, effects of some birth-year group subclasses with few bulls would not be estimated accurately. To model birth years of sons nested within the birth year of their sire

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PREDICTABILITY OF BULL MERIT

as a random effect following a first-order autoregressive process was more suitable than the other alternatives mentioned. This method allowed for covariances among effects and requires only two parameters. Further, an AR(1) process provided a way of addressing many factors that were likely to influence or bias the regression coefficients beyond biological processes. Group effects for birth year are generally included in models to account for the effects of selection on information not included in the model for estimation and prediction ( 3 ) . In this research, the structure of the data was organized so that an individual sire or group of sires from the same birth-year group might have sons within and across different birth-year groups. The PTA of sons from adjacent birth years are likely to be more highly correlated than those farther apart in time because of the assortative mating of sires of sons, genetic trend of dams of sires, and perhaps, more important, because of management differences that are confounded with generations (e.g., preferential treatment) of daughters of sires, dams of bulls being tested, or daughters of bulls being tested. To use all information in the data over the entire time period (since birth year 1970), the regression model should account for the genetic trend in the male and female populations. Furthermore, it is important to account for the correlations between genetic evaluations of progenies from different birthyear groups within the birth-year group of their sire. Indeed, estimates of the correlation coefficient, r, ranged from 0.34 to 0.87 (Table 2). The estimates corresponding to fat percentage in the current and elite AI bull populations were the only nonsignificant estimates. When compared across traits, estimates of r for yields (mainly milk yield and fat yield) were consistently greater than estimates for fat and protein percentages. The differences in estimates of r with respect to the various traits were better established in the AI and elite bull populations than in the current AI bull population. Significant AR ( 1 ) estimates suggest that, after adjustment for the genetic trend of sires (Equation 2), merit of bulls that are sons of sires in the same birth-year group and also born in 2 consecutive yr (i.e., the bulls are progeny of two consecutive genetic groups of dams) are related by only r. The relationship decreases as time between birth year of bulls increases because of the genetic trend from dam selection and also because of management differences. For example, for the estimate of r for milk yield in the AI population (Table 2), genetic merits of bulls from consecutive birth years were related by r = 0.87, by r2 = 0.76 if bulls were from

Figure 1. Autocorrelation among birth-year evaluations of sons within birth-year group of their sires for milk ( ◊) , fat ( ⁄) , protein (+), fat percentage ( * ) , and protein percentage ( o) for the AI population.

every other birth-year group, and by only r3 = 0.66 if sons were born 2 yr apart (see Figure 1). The AR ( 1 ) process was much less effective for MRE (Table 3 ) than for FCE (Table 2). In fact, some r estimates were either nonsignificant or not possible for the open interval (–1, 1 ) of the coefficient r, in the AI, current, and elite AI bull populations. This result might partially be due to random variation in the MRE of bulls born in different birth-year groups. Another reason might be the limited number of bulls in each birth-year group because of culling from earlier evaluations and also because of a limited number of birth-year classes within birth years of sires. CONCLUSIONS Comparisons of theoretical and actual coefficients for predicting PTA of a young bull from PTA of his sire and MGS proved that sires and MGS have contributed to the genetic composition of their sons as expected for yield traits and fat and protein percentages. Coefficients for predicting merit of a young bull from both sire and MGS were in the 90 to 100% range of their approximate expectations when PTA for yield traits were predicted from FCE; however, realized sire and MGS coefficients from MRE did not agree with expectations. The departure of realized coefficients from their expectations was reported in previous work for later lactation records. The animal model procedure is an effective tool for genetic evaluations. Young bulls can be selected based on their pedigree information from FCE. Journal of Dairy Science Vol. 80, No. 5, 1997

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ACKNOWLEDGMENTS We thank G. R. Wiggans, P. M. VanRaden, and other personnel at the USDA Animal Improvement Programs Laboratory for providing the animal model evaluations used in this research. Comments and suggestions by an anonymous reviewer are appreciated. REFERENCES 1 Cassell, B. G., R. E. Pearson, M. L. McGilliard, and T. R. Meinert. 1992. Genetic merit and usage patterns of bulls from different sampling programs. J. Dairy Sci. 75:572. 2 Dickerson, G. E., and L. N. Hazel. 1944. Effectiveness of selection on progeny performance as a supplement to earlier culling in livestock. J. Agric. Res. 9:459. 3 Famula, T. R., E. J. Pollak, and L. D. Van Vleck. 1983. Genetic groups in dairy sire evaluation under a selection model. J. Dairy Sci. 66:927. 4 Ferris, T. A., J. C. Schneider, and I. L. Mao. 1990. Relationship between dam’s age at bull’s birth and bull’s genetic evaluation. J. Dairy Sci. 73:1327. 5 Henderson, C. R. 1995. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423. 6 Lush, J. L. 1933. The bull index problem in the light of modern genetics. J. Dairy Sci. 16:501. 7 Meinert, T. R., and R. E. Pearson. 1992. Stability of evaluations of bulls sampled by artificial insemination and other organizations. J. Dairy Sci. 75:564. 8 Meuwissen, T.H.E. 1989. A deterministic model for the optimization of dairy cattle breeding based on BLUP breeding values. Anim. Prod. 49:193. 9 Powell, R. L., H. D. Norman, and F. N. Dickinson. 1977. Trends in breeding value and production. J. Dairy Sci. 60:1316. 10 Robertson, A., and J. M. Rendel. 1950. The use of progeny testing with artificial insemination in dairy cattle. J. Genet. 50: 21.

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