Estimation of genetic parameters of preweaning performance in the French Limousin cattle breed

Summary - Direct and maternal genetic and environmental parameters of preweaning growth and conformation at weaning were estimated in the French Limousin beef cattle field recording program using the tilde-hat approach of Van Raden and Jung (1988) with a sire, maternal grandsire (MGS) and dam within MGS model. The numerator relationship matrix among bulls was included in the estimation. The data available after editing contained 169 391 calves with performance records, from 43 683 dams, 7 265 sires, 5 664 maternal grandsires and 1 605 herds, for the years 1972-1989. The traits involved were: birth, 120-d and 210-d weights, average daily gains from birth to 120-d, from 120-d to 210-d, from birth to 210-d, muscular development (MD) and skeletal development (SD) scores at weaning. Estimates ranged from 0.22 to 0.32 for additive direct heritabilities and from 0.06 to 0.16 for maternal heritabilities. Correlations between direct and maternal genetic effects for these traits were negative, ranging from -0.23 to -0.49. Maternal permanent environmental effects were small for all traits, accounting for 5-9% of the phenotypic variances for preweaning growth performance, and 3% and 4% for MD and SD, respectively. beef cattle / variance components / preweaning growth / conformation score / direct and maternal effects / field data


INTRODUCTION
Knowledge of the magnitude of the variance and covariance components is critical for the genetic evaluation of animals and the development of sound breeding programs. For maternally influenced traits, direct as well as maternal effects need to be quantified. Direct and maternal effects seem to be correlated, but the sign and magnitude of this correlation is often a topic of some debate.
For the estimation of (co)variance components REML (Patterson and Thompson, 1971) is now the method of reference, due to its desirable properties, ie nonnegativity (Harville, 1977), ability to take account of selection (Sorensen and Kennedy, 1984;Werf and Boer, 1990). With large data sets, however, REML is almost unusable due to the need for inversion of the large coefficient matrix of the mixed model equations (Henderson, 1973) or the inverse of the complete covariance matrix of the vector of observations, despite a number of available numerical techniques (Meyer, 1990). Consequently, less expensive procedures with estimators reasonably close to REML solutions are desirable. Among approximate REML procedures like Henderson's method IV (Henderson, 1980), Schaeffer's method (Schaeffer, 1986) and the tilde-hat approach of Van Raden and Jung (1988), the last has been shown to yield estimates closest to REML solutions in data without or with little selection (Van Raden and Jung, 1988;Ouweltjes et al, 1988). Moreover, the tilde-hat approach of Van Raden and Jung (1988) does not require any inversion of a large matrix and is computationally easy even when the numerator relationship matrix and covariances between random effects are included (Manfredi, 1990;Manfredi et al, 1991). In the French Limousin breed, genetic trends for preweaning traits have been estimated by an animal model (Lalo6,personal communication). It appears that there has been only limited selection practised in the population. With a small data set, Shi and Lalo6 (1991) showed that the tilde-hat approach led to estimates comparable to those of REML.
The objective of this study was to estimate direct and maternal genetic and environmental parameters for preweaning weights, growth rate and conformation at weaning for the French Limousin cattle breed using the tilde-hat approach of Van Raden and Jung (1988).

Data description
The French Limousin Breeding Association (France Limousin Selection) provided an extensive data set for estimation of direct and maternal (co)variances for the entire breed in France. Data consisted of 309 530 records collected from 1972 to 1989.
Traits analysed were birth, 120-d, 210-d weights, average daily gain from birth to 120-d (GO-120), from 120-d to 210-d (G 120 -210 ), from birth to 210-d (GO-210)7 muscular development (MD) and skeletal development (SD) scores at weaning. The 120-d and 210-d weights were computed by interpolation between neighbouring records which were measured, at 3-month intervals, by technicians according to national rules (FNOCPAB-ITEB, 1983) Some weight records may be used in interpolation for both standard weights. Birth weight, declared by the breeder, was not used in this interpolation. MD and SD were linear functions of elementary scores given by experienced technicians. Primary edits were conducted by eliminating: 1) calf weights and scores outside 3.5 SDs from the mean values of the corresponding traits within each sex; 2) any calf with a common sire and maternal grandsire (MGS); and 3) calves born from a dam < 23 months or > 16 y old at calving, or later than the 12th parity. Further edits were performed to require, sequentially, sires to have at least 4 progeny, dams to have 2 progeny and MGS to have sired 2 dams, respectively. Herds were required to have a minimum of 8 records. In this way, the edited data set consisted of 169 391 records. For average daily gain traits, only 168 980 records were left after removal of records outside 3.5 SDs from mean values by sex. As a result, 2 data files were used. Further statistics of the data sets are given in tables I and II.

METHODS
A sire, MGS and dam within MGS model was used for estimating the (co)variance components of the assumed maternally influenced traits. The model in matrix notation was: where: y = vector of observations; b = vector of unknown fixed effects, including herd-year-season, sex and parity; Ul , u 2 and u 3 = vectors of unknown random effects for sire, MGS and dam within MGS effects, respectively; e = vector of random residual effects; Z, Z 1 , Z 2 and Z 3 = known matrices relating records to the fixed and random effects in the model.
Identification and distribution of the number of levels for the fixed effects are reported in table II.
The expectations and variance-covariance structure of the effects of the model were assumed to be: or 2,a2, 1 2 !3 and or2 = variances of sires, MGS, dam within MGS and residual effects, respectively; a 12 = covariance between sire and MGS effects; A = numerator relationship matrix among bulls which included both sires and MGS. In total, 10 348 pedigree bulls over 5 generations were generated from 9 400 bulls represented in the data. The relationships between dams were ignored. The corresponding mixed model equations after absorption of fixed effects were: The tilde-hat approach of Van Raden and Jung (1988) involves quadratics which are functions of solutions and approximate solutions for the random effects of the mixed model equations !l). The approximate solutions were obtained by (Bertrand and Benyshek, 1987): where D 11 , D 12 , D 22 and D 33 are diagonal matrices with diagonal elements identical to those of the matrices Z! MZ1 + A -1 k11, Z! MZ2 + A -1 k 12 , ZZMZz + A -1 k 22 and Z §MZ 3 + IA;!, respectively. In fact, the diagonals of matrix Z! Z2 were zero due to removal of calves having the same bull as sire and MGS. However, those of Z[MZ 2 (Z[ 22 after absorption of fixed effects) were not equal to zero.
The general formula for a model with p possibly correlated random effects is: where: i, j, h and k = 1, 2, ... , P, ie the number of random effects in the model.
For the model assumed in this study, 5 quadratics (û! A -1 u!, û! A-I U2, u2A-l u l , u2A-l u 2 and Û!U3) were used to estimate 4 (co)variance components (af, <!i2, o-22 , and 3 . As more quadratics were available than unknown variance components the least squares approach was used. The residual variance ( Q e) was estimated by the following formula: where: N = total number of observations in the analyses; r(X) = rank of matrix X.
The tilde-hat procedure requires only the diagonals of the coefficient matrix in equations [1] for (co)variance estimation. Consequently, the mixed model equations were not explicitly constructed, and solutions for random effects in equations [1] were obtained by the direct iteration approach on data (Schaeffer and Kennedy, 1986;Mandredi, 1990;Mandredi et al, 1991). Thus, 2 levels of nested iterations were involved for the analyses. Solutions for fixed and random effects were first obtained from the inner iterations. After 15 iterations or when the convergence criterion attained 10-7 , the outer iteration was then implemented for the estimation of the variance components. Iteration was finally stopped after a value of 10-7 for convergence was reached. The criterion of convergence (0) was calculated as follows: where: . o i = solutions for fixed and random effects for the inner iteration, and variance components for the outer interation; k = number of iterations; n = total levels for fixed and random effects in the inner iteration, and is 5 for the outer iteration.
The expectations of the (co)variances estimated from model [1] were as follows: where: 0' 7t and a 2 m = genetic variances of direct and maternal effects, respectively; 0' AM = covariance between direct and maternal genetic effects; a c 2 = variance of maternal permanent environmental effects; a 5 = variance of environmental effects.
The genetic and environmental parameters were estimated as: where u is the total phenotypic variance, hA is the direct heritability, h2 m is the maternal heritability and h 2 is the total heritability as defined by Dickerson (194?), c 2 is the proportion of phenotypic variance imputable to the maternal permanent environmental effects, r AM is the correlation between direct and maternal additive genetics effects, rs MGS is the correlation between sire and maternal grandsire effects. Table III and table IV show estimates of (co)variances and estimates of heritabilities and correlations, respectively. Direct and maternal parameters for preweaning growth traits Estimates of direct heritabilities of birth and weaning weights and preweaning gain from birth to weaning (fi 5 = 0.31, 0.26 and 0.25, respectively) were in close agreement with the median values of literature surveys (Petty and Cartwright, 1966;Baker, 1980;Meyer, 1992;Renand et al, 1992) but higher than values reported in the North American Limousin breed (0.22 and 0.16 for birth and weaning weights, respectively; Bertrand and Benyshek, 1987).

RESULTS AND DISCUSSION
Maternal heritability estimates in this study were lower than direct heritabilities of the corresponding traits (h Ã1 = 0.08, 0.13 and 0.13, respectively). Most literature estimates for maternal genetic heritability ranged from 0.05 to 0.25 for birth weight, and 0.10 to 0.35 for preweaning gain or weaning weight (Quaas et al, 1985;Bertrand and Benyshek, 1987;Wright et al, 1987;Trus and Wilton, 1988;Garrick et al, 1989;Kriese et al, 1991;M6nissier and Frisch, 1992;Meyer, 1992). The present estimates for maternal genetic effects in French Limousin breed were in the lower tail of the ranges.
The estimates of the ratio between the maternal permanent environmental variances and the phenotypic variances were small in the French Limousin breed, ranging from 0.05 to 0.09. These values were in accordance with the reports given by Bertrand and Benyshek (1987), Wright et al (1987) and Meyer (1992).
Correlation estimates between direct and maternal genetic effects were found to be negative in this study (table IV) and in accordance with the estimates in the North American Limousin breed (r AM = -0.16 and -0.30 for birth and weaning weights, respectively; Bertrand and Benyshek, 1987). Moreover, the majority of reports in the literature indicated negative r AM of similar traits (M6nissier, 1976;Quaas et al, 1985;Bertrand and Benyshek, 1987;Cantet et al, 1988;Trus and Wilton, 1988;Garrick et al, 1989;Kriese et al, 1991;M6nissier and Frisch, 1992;Meyer, 1992). These estimates frequently ranged from 0 to -0.5 However, some positive direct-maternal genetic correlations were also reported (Wright et al, 1987;Northcutt et al, 1991;Trus and Wilton, 1988;Meyer, 1992).
As a matter of fact, considerable variation exists in the literature estimates of direct and maternal effects and their covariance components. This can be attributed to a number of factors, eg methods of estimation, statistical models, data resources (experimental or field data, breeds and production systems), assortive matings or previous selection. On the other hand, even with the most realistic model, the maternal animal model, some effects were always assumed to be absent due to computational limitation. For instance, a covariance between maternal and direct environments may exist (resulting from side effects of high nutrition during rearing of heifers on their milk ability; Mangus and Brinks, 1971) and consequently may bias the estimation of covariance between direct and maternal genetic effects (Koch, 1972;Baker, 1980;Willham, 1980;Canter et al, 1988). Otherwise, relatively large sampling variances of the estimates could exist for maternally influenced traits (Thompson, 1976;Foulley and Lefort, 1978;Cantet, 1990;Meyer, 1992).
Weaning weights of beef calves depend primarily upon the joint expression of preweaning growth potential of calves and maternal traits (primarily the milk production) of their dams. The relative importance of direct and maternal effects on growth may be better expressed by the estimates for preweaning growth rate (Go-120, G 120 -210 or 120-d weight. The estimates for both direct and maternal effects of 120-d weight were very similar to those of 210-d weight, with maternal effects being slightly more important for 120-d weight (table IV). This is realistic since calves are able to eat supplemental feed at the later stage of lactation. As shown by Neville (1962) and Le Neindre et al (1976), milk production was more important during the early period of the calf's life, and declined slightly up to weaning. A much lower direct heritability was obtained using a dam-offspring relationship by Molinuevo and Vissac (1972) in the same breed. This confirms the negative relationship between direct and maternal effects. The estimates for GO-120 were very similar to those of 120-d weight for both heritabilities for, and correlation between direct and maternal effects. For the growth period from 120 d to 210 d, however, the maternal genetic variation had been greatly reduced compared to the earlier period of growth (table III) and consequently maternal heritability was lower (h Ã 1 = 0.07) than for GO-120 (h m = 0,15). It was the only trait with different (lower) total heritability (table IV). The maternal influence of 210-d weight was apparently a carry-over effect. Rutledge et al (1971) reported that when measures of milk yield for the first 4 months were in the model, inclusion of measures from the remaining 3 months did not lead to a significant reduction in the residual sum of squares. Further, the antagonism between direct and maternal effects was stronger in the later period of growth (table IV). This fact might be induced by more pronounced interaction between environmental factors (maternal, calf feed supplies) and calf growth compensation, for which interaction might contribute to the inflated negative covariance between maternal and direct environments that is always assumed to be zero in models. As suggested by Robison (1981), calves from dams producing less milk are forced to seek supplemental feed earlier which may over-compensate for the extra milk production by other dams. Such overcompensation is as important as the calf becomes older and concentrate is supplied. Moreover, especially for the growth period of 120-d to 210-d, the estimated ratio between maternal permanent environmental variances and phenotypic variances was small (table IV).

Direct and maternal parameters for conformation at weaning
The results of this study showed that MD and SD were moderately heritable and mainly controlled by direct genetic effects rather than maternal genetic effects ( Due to the antagonism between direct and maternal genetic effects, the total heritabilities for both MD and SD were slightly reduced. Moderate heritabilities indicate that direct selection for conformation at weaning should be efficient. However, a small negative response of the maternal ability will result. Muscularity is desirable for carcass quality. However, improved inuscularity may lead to a deterioration of maternal calving ability due to the late maturing rate of the pelvic opening (M6nissier and Frisch, 1992).
The estimates of the ratio between the maternal permanent environmental variances and the phenotypic variances were smaller for both conformation traits (0.03 to 0.04) than for weights or preweaning gain.

CONCLUSION
The preweaning growth genetic parameters in this study show that the growth genetic variability is different for different growth stages. Foetal growth, measured by birth weight, is largely influenced by direct genetic effects, with an important foeto-mateinal regulation as shown by a negative genetic correlation between direct and maternal effects. Otherwise, maternal effects are more important for early growth after birth, with a still negative but lower genetic correlation between direct and maternal effects. Close to weaning, maternal influences are smaller for growth, and, similarly, beef conformation at weaning is largely controlled by direct genetic effects.

& d q u o ;
From a selection point of view, weaning weight or growth to weaning is heritable enough to allow an efficient selection for direct genetic effects, ie for the calf's growth ability. However, selection solely for direct genetic effects does not lead to improvement of the cow's maternal ability, and could even result in deterioration of the maternal ability because of the negative correlation between maternal and direct genetic effects. Selection for combination of direct and maternal effects is necessary for the genetic improvement of beef cattle used both as sire and pure breeds such as the French Limousin cattle. The maternal genetic parameters of the different preweaning growth stages show that, among the analysed traits, 120 d weight or growth from birth to 120 d is a good selection criterion for carrying out a joint selection on cows' suckling ability (maternal effects) and calve's growth capacity (direct effects).
On the other hand, it is essential to have estimates of genetic correlations between traits for both maternal and direct effects, in order to optimize the choice of measurements and selection criteria for preweaning growth. ACKNOWLEDGMENT Support of this research by a grant from the INRA is gratefully acknowledged.