Genetic parameters for type traits in the French Holstein breed based on a multiple-trait animal model

Livestock Production Science, 36 ( 1993 ) 143-156

143

Elsevier Science Publishers B.V., Amsterdam

Genetic parameters for type traits in the French Holstein breed based on a multiple-trait animal model V. Ducrocq Station de G~n~tique Quantitative et Appliqu~e, INRA, Jouy-en-Josas, France (Accepted 15 December 1992 )

ABSTRACT Genetic parameters for 15 linear type traits and milking ease score in the French Holstein breed were estimated by Restricted Maximum Likelihood using a multiple-trait animal model. The analysis was based on 28738 cows, daughters of at least 3 generations of AI Holstein sires and distributed over 16 samples of about 1800 observations (i.e., 6000 animals when nonrecorded relatives are included) The fixed effects considered in the model included age at calving, stage of lactation, herd-roundclassifier and group of unknown parents. The genetic value of base sires were either treated as random, or fixed for sires with at least 10 daughters. Treating sires as fixed increased the heritabilities for udder traits while heritabilities of size traits and most genetic correlations were stable or slightly decreased. Most udder traits were rather highly correlated and exhibited heritabilities varying from 0.23 (Teat direction rear) to 0.35 (Udder-hocks distance). All size traits were very highly correlated (0.69 to 0.97 ) with heritabilities from 0.25 (Chest width ) to 0.47 (Height at sacrum ). The heritability of Rear legs side was found to be very low (0.07). These parameters are used in the multiple-trait animal model evaluation of type traits in the French Holstein breed. Key words: Type trait; Genetic parameters; Multiple trait animal model; Restricted maximum likelihood

INTRODUCTION

It is widely accepted that for most traits, efficient selection programs in domestic animals should be based on genetic evaluations using all the information available - i.e., in most cases in a multivariate setting - and assuming an animal model. Such an evaluation requires a good knowledge of genetic and environmental parameters. Based on theoretical grounds, it has been shown (e.g., Gianola et al., 1986) that these parameters should be obtained by Restricted Maximum Likelihood (REML, Patterson and Thompson, 1971 ) Correspondence to: V. Ducrocq, Station de G6n6tique Quantitative et Appliqu6e, INRA, 78352 Jouy-en-Josas, France.

0301-6226/93/$06.00

© 1993 Elsevier Science Publishers B.V. All rights reserved.

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using the same model as in the genetic evaluation. This is always a very demanding task, even on large mainframe computers or cheap workstations. However, algorithms exist (e.g., Meyer, 1985, 1991; Misztal, 1990) and large scale applications have been carried out (Misztal, 1990; Misztal et al., 1992 ). The French Holstein Association ("Unit6 pour la Promotion de la Race Prim'Holstein", Saint-Sylvain d'Anjou, France) is in charge of the type appraisal of all young females in "registered" herds in France. In 1986, the appraisal procedure was modified and traits were scored on a linear scale from 1 to 9. Since then, bulls were routinely evaluated for type using a Best Linear Unbiased Prediction sire model (Regaldo, 1989). Hence, estimates of genetic values for type and aggregate genotype including evaluation on dairy traits were not available for females. A feasability study for a routine multiple-trait animal model evaluation was undertaken (Ducrocq, 1991 ). The present study describes the procedure used and the results obtained in the estimation of the genetic and residual parameters required for this evaluation. MATERIALS AND METHODS

Data

Records on 15 linear type traits (scored from 1 to 9 by a technician) and on milking ease appraisal (scored from 1 to 5 by the dairyman) were collected by the French Holstein Association between 1986 and 1991 on 462162 first and second lactation cows. Less than 0.5% were recorded twice and only the first record was kept when this was the case. As the European Friesian type initial population has been intensively upgraded in France to North American Holstein (HF) for the past 15 years, it was intended to estimate genetic parameters for type and milking ease in the Holstein population and not in the crossbred one. More than 70% of the cows born in 1990 in France were at least 7/8 HF (Boichard et al., 1992). In the initial data set, 53% of the cows had identified AI sire, grand-sire and great-grand-sire and 54% of these cows were born in France, the USA or Canada and had known North American origins. Out of these 131511 animals which were at least 7/8 HF ( 3 generations ofAI HF sires), 38517 were recorded in herd-round-classifier cells with at least 10 such 7 / 8 HF records. From this subset, 16 samples (25941 and 2797 animals in first and second lactation, respectively) were drawn in such a way that each sample contained about 1800 recorded animals from herds in a same French region (8 regions defined). The sample size of 1800 was constrained by computing memory requirements related to the estimation procedure used. Each sample was completed with the parents of these recorded animals over 3 generations on the female side, i.e., sire and dam of females, but not of males were included. The reason why the pedigrees were not traced back on the male side will be made clear later on. As a result, each sample included about 6000 animals. Type traits of each animal were present

GENETIC PARAMETERSFOR TYPE TRAITS

145

in no more than one sample, but nonrecorded parents, especially sires, could be present in several samples. Some other characteristics of the samples are given in Table 1. The description of the recorded traits is given in Table 2 (see Regaldo, 1989, for details). TABLE1 Characteristics of the 16 samples used in the analysis

Records: Sires: Sires with at least 10 daughters: Animals, including relatives: Maximum number of daughters per sire: Herd-round-classifier ( H R C ) effects: Average number of records per HRC: Groups of unknown parents a: b: Rank of the absorbed a: coefficient matrix b:

Total

Average

Range

28738 1836 280 69736 1478 1958

1796 673 118 5977 216 122 14.7 33 151 1611 1494

1792-1804 488-827 95-141 5337-6210 120-372 118-140 13.0-15.2 128-174 1597-1625 1476-1518

528 2417

"All sires' breeding values are treated as random. bAll breeding values of sires with at least 10 daughters are treated as fixed. TABLE2 Description and elementary statistics of milking ease and type traits Trait

1. Milking ease a 2. Udder cleft 3. Udder-hocks distance 4. Udder balance 5. Teat placement side 6. Teat placement front 7. Teat direction rear 8. Teat length 9. Height at sacrum 10. Chest depth I I. Chest width 12. Rib depth 13. Rump length 14. Rump width 15. Rump angle 16. Rear legs side

Description

Mean

1

9

Slow Absent Low udder Low rear Close Close Internal Short Short Shallow Narrow Shallow Short Narrow High pins Sickled

Fast Deep High udder High rear Apart Apart External Long Tall Deep Wide Deep Long Wide Low pins Straight

aScale from 1 to 5 for Milking ease.

3.56 5.92 7.02 4.92 4.90 5.43 4.42 4.83 6.99 6.44 5.25 6.44 6.67 6.52 5.01 4.69

Standard deviation Lactation 1

Lactation 2

0.92 1.60 0.84 0.92 0.87 1.23 1.18 1.13 1.34 1.26 1.23 1.30 1.20 1.33 0.76 0.94

0.93 1.77 0,98 0.87 1.00 1.29 1.25 1,13 1,30 I, 17 1.23 1.23 1,12 1,18 0,75 0,88

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Models For each trait i, the model of analysis was, in matrix notation: Yi -~"Xbi "l"Z ~ i

( 1)

"l"Zai "l'ei

where: Yl is the vector of observations on trait i; bl is a vector of fixed effects including an "age at calving" effect (7 and 3 classes in first and second lactation, respectively), a "stage of lactation" effect (8 and 5 classes in first and second lactation), and a "herd-round-classifier" effect ( 118 to 140 classes); g~ is a vector of fixed group of unknown parents effects (Quaas, 1988 ); Q is a matrix relating animals to the groups of their unknown ancestors; ai is a vector of random, normally distributed additive genetic values for trait i for recorded animals only; ei is a vector of normally distributed residuals; X and Z = I are incidence matrices. Note that X, Z and Q do not depend on trait i, as all traits are available on all recorded animals (no missing data). Let A denote the numerator relationship matrix (NRM) between recorded animals. A can be obtained by computing A ÷, the extended NRM using Henderson's rules (1976) and then absorbing the rows corresponding to nonrecorded animals as proposed for example by Swalve and Van Vleck (1987). More simply, this can be done directly computing elements of A looking at the pedigree (including unrecorded animals) of pairs of recorded animals and applying the recurrent rules for constructing the relationship matrix (Van Vleck, 1983 ) on this small subset of the data. .

I-a]

Assume E(a) =0; E(e) =0 and var[e/=

[-A*G 0 -]

/ 0 I*aJ"

G = {aaij} and R = {aeij} are the genetic and residual variance-covariance matrices between traits. In univariate analyses, G and R are assumed to be diagonal. Groups of unknown parents were defined according to sex of the progeny (male or female); origin (born in France, the USA or Canada for males; one origin only for females) and year of birth (33 groups in total). Then, the breeding values of all base animals (in particular all sires) are considered to belong to the same normal distribution with the same mean and genetic variance. A first analysis was carried out under this assumption. However, it is well known that AI service sires are not a random sample of all males and are heavily selected on their milk evaluation, but also on their type trait evaluation. This selection implies a possibly strong reduction in genetic variance. To avoid obvious biases, many genetic parameter estimations (e.g., Colleau et al., 1989; Brotherstone et al., 1990) are carried out treating service sires as fixed in the version of model ( 1 ) extended to explicitly include animals without records in a~. By simulation, Van Der Weft (1992) showed that the bias on genetic parameter estimation due to selection can be reduced when a Restricted Maximum Likelihood procedure is used and when

GENETIC PARAMETERS FOR TYPE TRAITS

] 47

base animals are treated as fixed, as long as there is no selection among the nonrecorded generations between those base animals and the recorded ones. This may not be entirely true on the female side of the pedigrees here, but the selection differential is probably negligeable with respect to selection on sires. Unfortunately, it was not possible to accurately distinguish service sires from the other bulls in the data file used. Note that such a classification brings new difficulties anyway, as the same data set usually also includes daughters conceived while the sire was progeny-tested. Instead, it was arbitrarily decided that sires with at least ten daughters in the data file were going to be treated as fixed. This is the reason why there was no need to trace back the pedigree of these sires. Ten daughters may seem a very low limit but it is important to remember that this number is within sample. Van Der Weft (1992) showed that it was equivalent to consider a base animal as fixed or to assign that animal to a specific group of unknown parents. This latter approach was used here as it does not imply any modification in model ( 1 ). The average number of groups per sample in this second analysis was 151.

Estimation procedure Univariate and multivariate REML estimations were carded out on the 16 samples using a Fisher Scoring algorithm (Meyer; 1985). Since all traits were described by a same model and there were no missing data, it was greatly advantageous to use a canonical transformation (Meyer, 1985 ) which allows us to work on genetically and phenotypically uncorrelated traits. Then the multivariate REML equations at each iteration can be reduced to p = t (t + 1 )/ 2 independent systems (t is the total number of traits) of the form:

B,u 0,u

(2)

where/),u is the vector of estimates in sample s of [ Cra~ijtre~j ] ', the genetic and residual (co)variances between trait i andj on the canonical scale. At convergence, these components are equal to zero when i # j and the residual component is equal to 1 when i = j . (1/2 )Bsij is the information matrix. Of course, in univariate analyses, there is no transformation, p = t and i = j in (2). In practice, the matrix B, u involves the computation of elements like tr (Ci) or tr(C~Cj) (Meyer, 1985) where Ci denotes the inverse of the coefficient matrix of the modified mixed model equations for the ith canonical variable, after absorption of fixed effects:

[L'Z'MZL + a i l ] tic = [L'Z'My~ ]

(3)

where 9~ and fl~ refer to observations and breeding values for the ith canonical variable; M is the absorption matrix for fixed effects, including groups; o~i is the variance ratio for trait i on the canonical scale; L is the Cholesky factor ofA ( A = L L ' ) .

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Applying an orthogonal transformation P (with PP' = P ' P = I) to both sides of system (3), we get:

[ P ' L ' Z ' M ' Z L P + o t , I ] (P'dt~ ) = [P'L'Z'My~ ]

(4)

A transformation matrix P can be found in order to make P' L' Z' M Z L P = D diagonal. This is usually obtained by first applying a series of Householder transformations (Golub and Van Loan, 1983) to tridiagonalize L ' Z ' M Z L . For a matrix of the size considered here (about 1800) the CPU time required to diagonalize the resulting tridiagonal matrix using standard subroutines is marginal with respect to that necessary for the tridiagonalization (CPU time ratio of 10s: 10 min on an IBM 3090-17T computer). Then tr (Ci) = tr (D + ai I ) - ~is diagonal and tr (Ci) and tr (Ci Cj ) are computed in linear time. The expression used for B, u and d, u in (2) is identical to that given by Meyer ( 1985 ) multiplied by o/i ogj on both sides. This is required in order to get at convergence the asymptotic variance-covariance of the parameters in e, u as twice the inverse of B, u. In the multivariate case and as for the estimates of the parameters, these (co)variances are backtransformed onto the original scale. These values are then combined to calculate sampling variances of heritabilities and correlation coefficients, linearizing these nonlinear functions of the parameters around the expected values of their components (Colleau et al., 1989). To combine the estimates obtained from each sample, several alternatives could be envisioned. Babb (1986) suggested to pool the estimates using the principle of generalized least-squares in order to account for the covariance existing between samples due to relationships. Yerex (1988 ) found through simulation that in the case of equal sample size, Babb's method was not dearly superior to a simple unweighted average of the samples estimates. This last, easy solution was used in a univariate analysis for each of the 16 traits. Observed standard deviations of the estimates for each trait and across samples were computed. Also, a simplified version of the pooling procedure of Babb and Yerex was also implemented, in the univariate as well as in the multivariate case: assuming no relationship between samples, the restricted log-likelihood contributions of each sample can be simply added. It immediately follows that the REML equations (2) become in that case:

The corresponding information matrix is ½I~B,ul. At each iteration and for each sample, system ( 5 ) is solved using the pooled estimates of variance components obtained at the previous iteration.

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149

RESULTS

The phenotypic mean and standard deviations of each trait computed over all samples are presented in Table 2. Compared with the corresponding parameters from the initial data set, phenotypic means were 2 to 7% higher for all traits related to the animals' size and most standard deviations were slightly decreased. This is the result of the limitation to 7/8 (or more) HF cows. As in Regaldo (1989) and in contrast with other studies (Schaeffer et al., 1985; Brotherstone et al., 1990; Diers and Swalve, 1990; Misztal et al., 1992 ), most udder traits (except udder cleft), rump angle and rear legs side scores were somewhat less variable than "size" (height, lengths, widths and depths traits) traits scores. This may be due to possible differences in the scoring systems being analyzed by these authors. Means varied according to parity but phenotypic standard deviations (Table 2) were not very different between first and second lactations: the largest relative differences in standard deviation were for Udder-hocks distance ( + 17% in parity 2 ) and Teat placement side ( + 15%) and most other traits exhibited much lower differences in variability. The phenotypic correlations between traits were very similar across lactations. These observations led to the assumption that the same traits were expressed in first and second lactations, although this was not formally tested. Convergence of the REML procedure was measured as the norm of the vector of changes in genetic and residual components between iterations (on the canonical scale and including covariances in the multivariate case). A norm inferior to 10 -4 (as in Klei et al., 1988 or Colleau et al., 1989) was obtained after 7 to 11 iterations in univariate analyses, and 15 iterations in the multivariate analyses of the 16 traits. This illustrates the quadratic convergence rate of algorithms using the second derivatives of the likelihood function such as the Fischer-scoring algorithm (Meyer, 1985; Colleau et al., 1989 ). When performing separate univariate analyses on each sample with all sires treated as random (hereafter referred to as the "random sires" situation), the genetic variance of one trait (Milking ease, Teat direction rear and Rear legs side, each once) converged to zero in 3 samples. This was also the case for the two canonical variates corresponding to the lowest eigenvalues in the multivariate analysis when sires with at least l0 daughters were treated as fixed (hereafter called the "fixed sires" case ). Univariate heritabilities were almost identical whatever procedure was used to combine estimates - either averaging separate estimates or pooling REML equations. The approximate standard errors when REML equations were pooled were almost always less than the observed standard errors on the means when estimates were averaged. As the latter is likely to underestimate the true asymptotic standard error, the pooling procedure was preferred in subsequent analyses. Besides, no problem of convergence at the limit of the parameter

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space was encountered with the pooling procedure, at least in the univariate case. Univariate and multivariate REML analyses gave very similar heritability estimates, as already observed by Colleau et al. (1989). Therefore only multivariate results are reported here (Table 3 ). Given that sires are a selected sample of all sires and that the genetic relationship between sires was not taken into account in the random sires case, an increase in genetic variance was expected when treating sires as fixed (Van Der Weft, 1992 ). Indeed, that was not systematically observed: milking ease score and udder traits in particular did exhibit a strong increase in heritability (up to 70%) whereas Rear legs side score and all size traits except Height at sacrum were found slighly less heritable. Changes in variances may not be due to selection only (Visscher and Thompson, 1990). As pointed out by one referee, when sires are fixed, relatively more information comes from daughter-dam covariances and these covariances may be influenced by factors such as genotype × environment interactions, for example related to the fact that daughter and dam are often in the same herd. A multiple trait REML estimation was carded out considering all 16 traits together. Most of the genetic and residual correlations between the group of TABLE3

Heritability of type traits depending on the model of analysis Trait

I. Milking ease 2. Udder cleft 3. Udder-hocks distance 4. Udder balance 5. Teat placement side 6. Teat placement front 7. Teat direction rear 8. Teat length 9. Height at sacrum l 0. Chest depth 11. Chest width 12. Rib depth 13. Rump length 14. Rump width 15. Rump angle 16. Rear legs side

Heritability All sires random a

Sires >t l 0 daughters fixed b

0.19 0.17 0.23 0.20 0.24 0.26 0.14 0.28 0.43 0.39 0.28 0.35 0.34 0.36 0.28 0.09

0.32 0.26 0.35 0.34 0.25 0.30 0.23 0.30 0.47 0.36 0.25 0.34 0.29 0.32 0.34 0.07

aAll sires' breeding values are treated as random. bAll breeding values of sires with at least 10 daughters are treated as fixed. CApproximate standard errors: Sires random: from 0.017 (trait 16) to 0.024 (trait 8); Sires>~ l0 daughters fixed: from 0.038 (trait 9 ) to 0.047 (trait 5 ).

GENETIC PARAMETERS FOR TYPE TRAITS

151

milking ease score and udder traits (numbered 1 to 8 in Table 2) and the group of all the other traits (9 to 16) were small and less than twice their asymptotic standard errors, with random or fixed sires. The only noticeable exceptions were the genetic correlation between Teat placement side and Chest depth, Chest width and Rib depth (0.20 to 0.27 _+0.08 to 0.10 ) and between Udder-hocks distance and Height at sacrum (0.33 + 0.06 with random sires; 0.28 +_0.09 with fixed sires). Despite of this latter more logical value, it was decided to analyze the two sets of traits separately, hence assuming no correlations between them, in particular because most correlations between these two groups of traits would be rather difficult to interpret. This had the further advantage of reducing the number of parameters to estimate from 272 to only 72. The results of these analyses are given in Tables 4 and 5. Estimates of genetic and residual correlations seemed to differ less than estimates of heritabilities according to the way sires were treated. The main exceptions were between Udder-hocks distance and Udder cleft (0.38 (random sires) vs. 0.51 (fixed sires)), between Udder-hock distance and Teat direction rear ( - 0.32 vs. - 0.47) and between Teat placement front and Teat direction rear (0.70 vs. 0.85 ). Apart from these exceptions and a few others, most genetic correlations were slightly smaller in the fixed sires case. TABLE 4 Genetic (above the diagonal ) and residual ( below the diagonal ) correlations between udder traitsa All sires randomb

1

1. Milking ease 2. Uddercleft 3. Udder-hocksdistance 4. Udder balance 5. Teat placement side 6. Teat placement front 7. Teat direction rear 8. Teatlength

0.30 s 0.128 0.077 0.346 0.08 s 0.267 0.047 - 0.047 -0.067 -0.356 -0.088 -0.446 -0.056 -0.047

sires>_. 10 daughters fixed c 1 l. Milking ease 2. Uddercleft 3. Udder-hocksdistance 4. Udder balance 5. Teat placement side 6. Teat placement front 7. Teat direction rear 8. Teatlength

2

2

0.2912 0.109 0.13 s 0.327 0.05 s 0.21 s -0.029 - 0 . 0 7 l° -0.068 - 0 . 3 5 a -0.099 - 0 . 4 4 s - 0 . 0 8 s -0.099

3

4 0.427 0.556

0.13 s 0.38 s 0.506

0.236 - 0.166 -0.305 -0.287 -0.086

0.027 -0.146 -0.21 s 0.006

3

4 0.12 l° 0.559

0.197 -0.148 -0.277 -0.248 -0.12 s

5

6

7

8

-0.247 -0.17 s -0.377 0.148

-0.247 -0.467 -0.506 - 0.267 0.217

-0.219 -0.745 -0.32 s - 0.259 0.119 0.705

-0.307 -0.18 s -0.287 - 0.167 0.017 0.266 0.22 s

0.156 0.095 0.025 5

0.19 It 0.0712 0 . 5 1 1 0 -0.0114 0.499 -0.3911 0.1013 0.029 -0.12 a 0.169 -0.189 0.04 tl 0.00 s 0.02 l°

0.495 0.11 s

0.117

6

7

- 0 . 2 0 tt -0.4211 -0.549 - 0 . 2 9 l° 0.1613

-0.11 t3 - 0 . 1 6 II -0.631° 0.01 t2 - 0 . 4 7 II - 0 . 1 3 II -0.3112 - 0 . 1 4 t3 0 . 3 4 1 4 0.0013 0.858 0.29 tl 0.1813 0.121°

0.436 0.10 s

"Approximate standard errors ( × ! 00 ) are indicated as an exponant (e.g.: s = 0.08 ). bAll sires' breeding values are treated as random. CAll breeding values of sires with at least 10 daughters are treated as fixed.

8

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TABLE 5 Genetic (above the diagonal) and residual (below the diagonal) correlations between traits other than udder traits a All sires random b

9

10

9. Height at sacrum 10. Chest depth 11. Chest width 12. Ribdepth 13. Rump length 14. Rump width l 5. Rump angle 16. Rear legs side

0.792 0.482 0.293 0.562 0.432 0.721 0.472 0 . 4 7 2 0.392 0 . 4 4 2 0.115 0 . 0 7 5 0.048 0.048

sires/> 10 daughters fixed c

9

9. Height at sacrum 10. Chest depth l l . Chest width 12. Rib depth 13. Rumplength 14. Rump width 15. Rumpangle 16. Rear legs side

0.483 0.326 0.424 0.504 0.454 0.146 0.0318

11

12

13

14

15

0.694 0.872

0.743 0.971 0.832

0.902 0.882 0.833 0.833

0.792 0.872 0.873 0.842 0.922

-0.126 -0.127 -0.116

0.169 0.191° 0.149

--0.016

0.109 0.079

0.492 0.383 0.403 0.066

0.422 0.402 0.085

0.562 0.082

0.016

-0.206 0.085 - 0.011o

10

11

12

13

14

15

0.814

0.668 0.806

0.76 s 0.973 0.767

0.875 0.816 0.848 0.717

0.696 0.776 0.927 0.756 0.885

-0.038 -0.231° -0.1612 -0.201° -0.0612 - 0.18 II

0.525 0.406 0.406 0.079 0.0719

0.149

-0.01 l°

0.079 0.039 0.039 0.068

0.604 0.712 0.514 0.494 0.128 0.0316

16

0.485 0 . 4 4 5 0.594 0 . 1 1 7 0 . 0 9 9 0.088 0.0317 0.0418 0.0617 -0.0117

16 0.2220 0.2022 0.2622

0.1923 0.0622 0.0623 0.0423

a, b and c as in Table 4. DISCUSSION

There seems to be more and more alternative ways to implement REML estimation on large data sets using an animal model. With either a Derivative Free (DF; Graser et al., 1987; Meyer, 1991 ), an Expectation-Maximization (EM; Misztal, 1990, 1992 ) or a second derivative (Meyer, 1985 ) algorithm, it is possible to considerably reduce the difficulty of multivariate analyses by applying a canonical transformation. This requires that there is no missing values on some trait (s) and that the same model, including only one random effect other that the residual, describes all traits. Such a situation is typically encountered with type appraisal traits. Nevertheless, none of the 3 types of computing algorithms is really applicable on the extremely large data sets that animal breeders are dealing with, although this would be the most satisfying situation due to theoretical considerations (Gianola et al., 1986). The procedures using sparse matrices techniques with EM or DF REML do not seem to be applicable to algorithms based on the matrix of second derivatives. Considerable computation simplifications are still possible through proper orthogonal transformations but this always implies work on dense matrices stored in core memory. The strategy proposed here, although approximate in the sense that it assumes independence between samples, or in other words,

GENETIC PARAMETERS FOR TYPE TRAITS

153

no relationships between animals in different samples, bypasses this size limitation. It is still quite demanding in computing time (about 30 CPU min per sample in total on an IBM 3090-17T computer) but seems robust to the numerical problems sometimes encountered with DF-REML (Misztal, 1992), allows the inclusion of several fixed effects and groups of unknown parents without difficulty and offers a theoretically appealing estimate of asymptotic standard errors. The heritability of milking ease score (0.19 ) was in accordance with other studies based on similar assumptions (random sires) such as Meyer and Burnside ( 1987; 0.21 ); McClelland quoted by Meyer and Burnside (0.24) or Colleau et al. (1989; 0.19). However, the fact of considering heavily used sires as fixed led to a surprisingly high heritability (0.32) for such a subjective score. This value may require a further check in the future. In the random sires case, udder traits exhibited heritabilities generally in the range of those reported elsewhere (CoUeau et al., 1982; Schaeffer et al., 1985; Meyer et al., 1987; Klei et al., 1988; Diets and Swalve, 1990; Misztal et al., 1992). These authors virtually always found heritabilities in the range 0.20 to 0.30 with the most noticeable exception of udder cleft or suspensory ligament (around 0.15 ). The increase in heritability with fixed sires is very important and suggests that the selection on udder traits of widespread sires is probably not negligeable. Colleau et al. (1989) and Brotherstone et al. (1990) who also treated heavily used sires as fixed also observed high heritabilities on those traits. Comparisons are not easy though, as trait definitions vary considerably across countries, breeds and years. Regardless of the model used here, genetic correlations between udder traits - with the exception of Teat length - were higher than those reported in the literature, except in another situation where the REML evaluation was also based on an animal model (Misztal et al., 1992). In particular, teat placement front and Teat direction rear are strongly correlated (0.85 with fixed sires). With the fixed sires model, this resulted in 7 canonical variates with an heritability between 0.41 and 0.17, and the last one with an heritability of just 0.01, indicating a redundancy among the 6 (number 2 to 7) udder traits. With random or fixed sires, "size" traits had high heritabilities, in the usual range reported in the literature (between 0.25 and 0.50). Again, these6 traits were very higly correlated and at least two of them seem redundant (heritabilities of 0.00 and 0.02 on the canonical scale, the others varying from 0.51 to 0.10): Chest depth and Rib depth apparently characterize the same trait (genetic correlation of 0.97!), and are generally not found together in other studies. The same is true for Rump length and Rump width. The same kind of redundancy was also found by Colleau et al. (1982; 1989). If for some reason, it is deemed not possible to reduce the number of observed traits, these authors suggested that the information on those traits can be summarized applying a principal component analysis to the matrix of genetic corre-

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lations and presenting the results only on the components explaning most of the variance. This approach was not used here but deserves further consideration. Rump angle and Rear legs side were virtually correlated to no other traits. Rear leg side was found to have a very low heritability, at the bottom of the range usually reported (Diers and Swalve, 1990:0.1 l; Klei et al., 1988: 0.14; Brotherstone et al., 1990:0.15; Misztal et al., 1992:0.16 ). If this is confirmed by other studies, a better definition of this trait should be given to the technicians or other traits should be used to characterize feet and legs. CONCLUSION

These genetic and residual parameters computed in this study were required to implement a multiple-trait animal model evaluation of bulls and cows in the French Holstein breed, using a canonical transformation and along the lines of Ducrocq ( 1991 ). The proposed multiple-trait evaluation is making use of the parameters obtained with the model treating sires with more than 10 daughters as fixed. Traits are distributed into three categories: 6 udder traits are treated simultaneously as well as 6 "size" traits. Milking ease, Teat length, Rump angle and Rear legs side are treated separately, as they were found to be uncorrelated with most other traits.

REFERENCES

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Yerex, R.P., 1988. Pooling restricted maximum likelihood estimates from data subsets under the animal model. Ph.D. thesis, Cornell University, Ithaca, NY, 85pp. RESUME Ducrocq, V., 1993. Param~tres g6n6tiques des caract~res de morphologie en race Prim'Holstein sous l'hypoth~se d'un module animal multicaract~res. Livest. Prod. Sci., 36:143-156. Les param~tres g6n6tiques de 15 caract~res de morphologie et une note de facilit6 de traite ont 6t6 estim6s en race Prim'Holstein par Maximum de Vraisemblance Restreinte en utilisant un module animal multicaract~res. L'analyse repose sur 28738 vaches, filles d'au moins trois g6n6rations de taureaux Holstein utilis6s en Ins6mination Artificielle, et r6parties en 16 6chantillons d'environ 1800 observations (soit 6000 animaux, en incluant les apparent6s non point6s). Les effets fix6s consid6r6s dans le module incluaient un effet "~ge au v~lage", un effet "stade de lactation", un effet "visite-troupeau-pointeur" et un effet "groupe de parents inconnus". Les valeurs g6n6tiques des taureaux de base ont 6t6 trait6es soit comme un effet al6atoire, soit comme un effet fix6 pour les taureaux ayant 10 filles ou plus. Le fait de traiter les taureaux comme fix6s a augment6 l'h6ritabilit6 des caract~res de mamelle alors que l'h6ritabilit6 des caract~res de taille ainsi que la plupart des corr61ations g6n6tiques restaient stables ou diminuaient 16g~rement. La plupart des caract~res de mamelle 6taient relativement corr616s entre eux el pr6sentaient des h6ritabilit6s variant de 0,23 (Implantation arri~re des trayons) ~ 0,35 (Distanche plancher de la mamelle-Jarrets). Tousles caract~res de taille 6taient tr~s fortement corr61es entre eux (0,69/l 0,97 ) avec des h6ritabilit6s allant de 0,25 (Largeur de poitrine) ~ 0,47 (Hauteur au sacrum). L'h6ritabilit6 des aplombs arri~re 6tait tr~s faible (0,07). Ces param~tres sont utilis6s dans r6valuation "ModUle animal" multicaract6res de la morphologie en race Prim' Holstein. KURZFASSUNG Ducrocq, V., 1993. Sch~itzung genetischer Parameter ftir Merkmale des Typs in der franz6sischen Holstein Zucht mit Hilfe eines Mehrmerkmals-Tiermodelles. Livest. Prod. Sci., 36: 143-156. Genetische Parameter wurden ftir 15 lineare Markmale des Typs und die Melkbarkeits Punktierung in der franz6sischen Holstein mittels Restricted Maximum Likelihood unter Verwendung eines Mehrmerkmals-Tiermodelles gesch~itzt. Die Untersuchungen beruhten auf 28738 Kiihen, TiSchter von mindestens 3 Generationen KB Holstein V~itern und verteilt fiber 16 Proben zu ungef~.hr 1800 Beobachtungen (z.B. 6000 Tiere wo nicht eingetragene Verwandte einbezogen wurden). Die im Modell beriicksichtigten fixen Effekte waren Kalbealter, Laktationsstadium, HerdenRunden-Klassierer, Gruppe unbekannter Eltern. Der genetische Wert der Basis V~iter wurde entweder zuf~illig behandelt oder fix fiir V~iter mit mindestens 10 T6chtern. Die Behandlung yon Stieren als fixe Effekte erh6hte die Heritabilit~it fiir Eutermerkmale, w~ihrenddessen die jenigen fiir Gr6ssenmerkmale und die meisten genetischen Korrelationen stabil blieben oder leicht sanken. Die meisten Eutermerkmale waren eher eng korreliert und wiesen Heritabilit~iten von 0.23 (Zitzenstellung) bis 0.35 (Euter-Sprunggelenk Distanzen) auf. Alle Gr6ssenmerkmale waren eng korreliert (0.69-0.97), mit Heritabilit~iten von 0.25 (Brustbreite) bis 0.47 (Hiifthtihe). Die Heritabilit~it fiir die Hintergliedmassen erwies sich als sehr tief (0.07). Diese Parameter wurden in einem Mehrmerkmals-Tiermodell verwendet zur Evaluation der Merkmale des Typs in der franz6sischen Holstein zucht.