Genetic Parameters for Growth Traits of Australian ... - Semantic Scholar
Genetic Parameters for Growth Traits of Australian Beef Cattle from a Multibreed Selection Experiment’ K. Meyer, M. J. Carrick2, and B.J.P. Donnelly3 Animal Genetics and Breeding Unit, University of New England, Armidale, NSW 2351, Australia
ABSTRACT
Estimates of covariance components and genetic parameters were obtained for birth, weaning, 200-d, and 400-d weight for a herd of Polled Herefords and a herd of a multibreed synthetics, the so-called Wokalups. Data originated from an experiment in Western Australia selecting for preweaning growth rate. Analyses were carried out by REML fitting a n animal model including genetic and permanent environmental maternal effects. Wokalups
showed consistently more phenotypic variation, partly due to a scale effect, and higher direct and lower maternal heritabilities than Herefords. Maternal environmental effects were more than twice as important in Herefords than in Wokalups. Estimates of both genetic and environmental correlations among weaning and subsequent weights were essentially unity, identifying maternal effects found for postweaning weights as a “carry over” of those on weaning weight.
Key Words: Beef Cattle, Maternal Effects, Genetic Parameters, Crossbreeding
J. h i m . Sci. 1993. 71:2614-2622
Introduction Genetic theory on the effects of crossbreeding is well established, in particular concerning the exploitation of nonadditive genetic effects in improving mean levels of performance (e.g., Kinghorn, 1982a,b). Schemes such as rotational crossing, criss-crossing, or recurrent reciprocal selection are designed to make optimum use of heterosis, epistasis, or recombination effects, but they usually require the respective purebred populations t o be maintained. An alternative is the formation of a multibreed synthetic population. Although expected proportions of nonadditive genetic effects utilized and the resulting breed means of such synthetics are readily quantified, implications on the additive genetic variation in these populations and the resulting scope for selection are generally less clear-cut. A selection experiment in beef cattle was carried out a t the Wokalup research station in Western Australia to compare additive genetic variation and response to selection in pure- and multibreed popula-
lFinancial support for this paper mas provided by Australia’s Meat Research Cooperation (MRC); inputs from the Western Australian Department of Agriculture are acknowledged. %hrrent address: Queensland Dept. of Primary Industries, G.P.O. Box 46, Brisbane, Queensland 4001, Australia. 3W.A. Dept. of Agric., Baron Hay Court, South Perth, Western Australia 6151, Australia. Received December 28, 1992. Accepted May 5, 1993.
tions, contrasting straightbred Polled Herefords with a synthetic formed using British beef breeds, a large European beef breed, a dairy breed, and Bos indicus cattle (i.e., including each of the major cattle breed groups). The underlying rationale was that if it was possible to increase selection response by creating a synthetic from the breeds appropriate to the specific climatic and economic production conditions, knowledge of the increase in additive genetic variation would be required in planning appropriate breeding programs. This paper presents estimates of (colvariances and the resulting genetic and phenotypic parameters among growth traits for the two populations in the Wokalup selection experiment.
Materials and Methods The Experiment Data originated from a selection experiment conducted a t the Wokalup research station in the Southwest of Western Australia. Climatically, this location has a Mediterranean type of environment with an average rainfall of approximately 750 mm and an annual drought from November to the following April/May, which was almost always complete. Pastures were improved and were predominantly rye grass and subterranean clover, which were annually topdressed by air with superphosphate, the quantity of
2614
COVARIANCES FOR GROWTH FOR BEEF CATTLE
which was determined by soil tests. Planning for the experiment was begun in 1972 (some matings for the Wokalups had begun in 19691, and two herds of 300 cows each were established by 1978. The herds comprised straightbred Polled Herefords and a synthetic breed formed by mating Charolais x Brahman bulls with Friesian x Angus or Hereford cows. The latter became known as the Wokalup Multibreeds, or simply Wokalups. In 1978, all Wokalup females were first four-way cross or from interbred four-way cross parents and age structures in each herd were approximately equivalent. Selection for increased preweaning growth rate commenced in 1978 in both herds. No control herd was established until 1984 when the remaining cows in the herd that had calved in 1978 (approximately 75 in each herd) were multiple-ovulated and remated to the sires used in the 1977 mating whose semen had been stored. Embryos from this mating were frozen and stored until the completion of selection. Because of technical difficulties, however, there were few of these “control” animals, born in 1990, included in this study. Embryos had been stored in plastic-capped glass vials, and liquid nitrogen had leaked in, causing many of them to explode when thawing was attempted. The management of the project was unusual for Australian conditions in that cows were kept in 24 separate 20-ha paddocks of approximately 25 cows year-round, and were thus offered the same amount of grazing, rather than the more common practice of allowing them equal access to a common grazing area. Single-sire mating took place in each of these 12 paddocks per breed during a 7- to 8-wk period to result in April-May calving. Three hundred to 310 females of each breed were mated each year, made up of 60 heifers, 50 first calvers, and 190 to 200 adults. Calves were weaned in December. Cows were rerandomized into new paddocks between mating and calving each year and culling was on the basis of pregnancy test a t this time. Thus, sire groups and calving groups were not confounded. All calves were tagged, identified with their dam, and weighed, and their cannon-bone length was measured a t birth. Subsequently, calves were weighed at monthly intervals except for June (during calving). Calves normally lost weight or at best maintained their weight between weaning and 1 yr of age because of the seasonal drought. In the early years of the experiment, selection for preweaning growth was based on growth to October to avoid castrating culls in hot weather. In the later years, castration was not practiced and selection was on weaning weights taken in December. In 1985 the Wokalup herds joined BREEDPLAN,a within-herd multivariate genetic evaluation scheme for beef cattle by BLUP fitting a n animal model and accounting for direct and maternal effects on growth (Schneeberger et al., 1991). From then the selection criterion used was a n index of EBV corresponding to growth until
2615
weaning, namely EBV for weaning weight minus EBV for birth weight plus half of the “milk” EBV, with the latter denoting the estimate of the maternal genetic effect on weaning weight.
Analyses Traits considered were birth weight ( BWT) , weaning weight ( WWT), yearling or 400-d weight ( YWT), and final or 600-d weight ( FWT). Ranges allowed for age a t weighing were as for BREEDPLAN120 to 300, 301 to 500, and 501 to 700 d for WWT, YWT, and FWT, respectively. Basic edits eliminated records with missing weighing dates or sex codes and involved consistency checks of dates, ages, and weights. For a proportion of animals, age of dam could not be calculated because of unknown birth dates of the dams. For these animals, dam age was replaced by the mean age in the respectively data set. This occurred mainly in the early years of the experiment for foundation cows and about equally for both breeds. Weaning dates were available for each year and WWT records selected were the monthly weights for each animal taken closest to this date. Similarly, YWT and FWT records for each animal were the weights recorded closest to 400 and 600 d of age, respectively. Estimates of variance and covariance components were obtained by REML using a derivative-free algorithm, fitting a n animal model throughout and incorporating all pedigree information available. Maternal genetic and permanent environmental effects were taken into account by including appropriate random effects into the model of analysis as described by Meyer (1989, 1991a). All calculations were carried out using DFREML (Meyer, 1991b). Computational strategies used and problems associated with this kind of analysis have been discussed previously (Meyer, 1992a, 1993a). Fixed effects fitted were sex ( a t weighing), birth type (single vs twin), and year-paddock and yearmonth of weighing subclasses. Age at weighing and dam age were taken into account by fitting each of them as a linear and quadratic covariable. No breed or heterosis effects were fitted for Wokalups because the objective was to assess the amount of useable genetic variation in the synthetic population. Because generations of crossbreeding and years were confounded, fitting year-paddock and year-time of weighing effects was expected to account for any heterogeneity in breed composition in the early stage of the experiment. Univariate analyses for each trait and data set were carried out considering six different models of analysis to assess the importance of different maternal effects. Model 1 was a “simple” animal model fitting animals’ direct additive genetic effects only (i.e., ignoring any maternal effects). Model 2 allowed for a maternal effect in addition but attributed it solely to the permanent environmental effect of the dam. Conversely, Model 3 assumed all maternal influence was
2616
MEYER ET AL
of genetic origin. Whereas Model 3 assumed direct and maternal genetic effects to be uncorrelated, Model 4 allowed for a respective non-zero covariance. Models 5 and 6 corresponded to Models 3 and 4, respectively, but fitted both dams’ genetic and permanent environmental effects (i.e., three random factors altogether). The models were the same as those considered by Meyer (1992a, 1993a) and a more formal description was given there. Flexibility of the estimation procedure allowed different models to be fitted for individual traits in multivariate analyses. Univariate results had suggested that maternal environmental effects were absent for FWT in both breeds and for YWT in Wokalups and that direct-maternal genetic covariances were unimportant, Hence for both breeds, Model 5 was chosen for BWT and WWT and Model 3 for FWT; whereas for YWT, Models 5 and 3 were fitted for Herefords and Wokalups, respectively. Pairwise bivariate analyses were carried out for each combination of traits, estimating up to 12 (colvariance components simultaneously. Because the selection criterion had involved both BWT and WWT, subsequent trivariate analyses then considered YWT or FWT together with BWT and WWT so as to obtain estimates of covariance components for the two later weights unbiased by selection. Finally, multivariate analyses of all four traits together were performed, estimating 36 and 33 parameters for Herefords and Wokalups, respectively.
Results Characteristics of the data structure are summarized in Table 1. There was considerable variation in weights due to variation in both production conditions ( t h e data included several drought years) and, especially for WWT, age at weighing. Annual means for WWT in Wokalups, for instance, ranged from 203.3 kg in 1975 to 310.4 kg in 1988 with corresponding mean ages at weaning of 181.6 and 245.5 d. Wokalups were bigger and phenotypically more variable than Herefords, but, as CV demonstrate, the latter was mainly a scale effect. With monthly weighings available, ages at weighing for YWT and FWT were closer to the targets of 400 and 600 d and considerably less variable than in corresponding analyses of field data ( cf Meyer, 1992a, 199313). Year-paddock and yearmonth subclasses were frequently confounded, resulting in a reduced rank of the coefficient matrix for fixed effects.
Univariate Analyses Table 2 gives estimates of phenotypic variances ( u p ) and genetic parameters from univariate analyses. Differences in overall variability between breeds could to some extent again be attributed to the size differential. However, in spite of a 30-kg difference in mean WWT, estimates of ~7; for this trait were of equal magnitude for both breeds (i.e., Herefords were 2
Table 1. Characteristics of the data structure Hereford Traita
No. of records NO. of animal& No. of sires No. of dams‘ No. of P a d d No. of YMone Rankf Weight, kg Mean SD
cv, 5%
Age, d Mean SD Dam age, y Mean SD
BWT 3,414 3,683 3,783 174 1,033 167 65 22 1
WWT 3,088 3,331 3,421 174 956 155 39 184
Wokalup
YWT 1,229 1,378 1,482 160 643 56 54 101
FWT 1,114 1,308 1,415 159 600 78 47 111
BWT 3,769 3,961 4,518 189 1,473 153 67 208
WWT 3,191 3,438 3,857 189 1,201 144 43 177
YWT 1,373 1,491 1,740 175 800 59 59 107
FWT 1,242 1,411 1,638 174 7 16 79 45 111
31.46 5.29 16.8
227.6 51.5 22.6
262.9 47.2 18.0
409.8 62.3 15.2
35.98 6.32 17.6
257.7 52.9 20.5
209.4 49.5 17.0
440.2 77.6 17.6
-
213.8 32.0
399.3 18.5
592.0 22.2
-
210.5 32.4
397.8 17.7
584.8 28.0
-
4.39 1.88
4.50 1.96
4.23 1.69
4.21 1.72
4.64 2.13
4.68 2.18
4.42 1.92
aBWT: birth weight, WWT: weaning weight, YWT: yearling weight, FWT: final weight. univariate analyses, including parents without records: First line: Models 1 and 2; Second line: Models 3 to 6. ‘With progeny in the data. dYear-paddock subclasses. eYear-month subclasses. fOf coefficient matrix for fixed effects.
4.41 1.96
2617
COVARIANCES FOR GROWTH FOR BEEF CATTLE
relatively markedly more variable). This agreed with results of Boldman et al. (1991), who, in comparing genetic parameters for WWT in purebred and composite lines of beef cattle, found Herefords to have the highest CV among all lines examined and Herefords and the composite line to exhibit equal overall variance while differing in size by 42 kg. For both breeds, 6; for YWT was lower than for WWT, presumably reflecting both a n effect of the annual summer/autumn drought and of a reduction in variance due to selection of animals at weaning. As likelihood values clearly indicate, WWT and BWT in both breeds were determined by genetic as well as permanent environmental maternal effects. For YWT and FWT, some maternal influence could be detected, but it seemed t o be mainly of genetic origin. For Wokalups, estimates of the direct-maternal genetic covariance ( u r n ) were close to zero for all
traits, amounting a t most to 3.4% of 6$, with correspondingly small differences in likelihoods between Models 3 and 4 or 5 and 6, respectively. For Herefords, the same held for BWT and FWT. For WWT in this breed, the estimate of u r n was negative, amounting t o almost 6% of u$ with a corresponding estimate of the direct-maternal genetic correlation ( r ~ of)-.30. The increase in likelihood when fitting Model 6 over that for Model 5, however, was not significant. In contrast, for YWT in Hereford 6~ was -20% of 6; with a highly significant improvement in likelihood over that assuming that u r n was zero. As observed in other studies (e.g., Meyer, 1992a, 1993a; Swalve, 19931, estimates of u; ignoring and allowing for u r n remained more or less constant so that the large, negative estimate of u r n under Model 6
Table 2. Estimates of the phenotypic variance and genetic parametersa from univariate analyses of birth weight (BWT), weaning weight (WWT), yearling weight (YWT), and final weight (FWT) under different models of analysis Hereford Model
Wokalup
BWT
WWT
YWT
EWT
BWT
WWT
YWT
FWT
18.7 .57 -79.09
771.9 .45 -149.18
519.7 .27 -22.49
1,025.2 .42 -8.24
28.9 .58 -41.23
779.6 .38 -66.27
663.9 .25 -3.28
1,384.9 .34 -1.45
18.5 .48 .17 -5.04
745.9 .22 .31 -6.88
510.4 .23 .13 -8.58
1,0 11.3 .41 .04 -1.87
28.6 .55 .08 -3.81
762.4 .30 .16 -3.15
659.9 .22 .08 -1.68
1,382.7 .33
19.0 .39 .23 -5.85
795.9 .17 .36 -14.86
511.8 .20 .12 -6.92
1,008.3 .36 .08 -.21
28.4 .50 .09 -2.51
779.5 .26 .18 -7.49
662.1 .19 .09 -.08
1,381.7 .31 .03 -0.27
19.0 .37 .22 .06 -5.76
783.1 .20 .42 -.29 -12.93
505.8 .34 .27 -.65
1,006.9 .38
0
780.0 .26 .17 .02 -7.48
662.6 .18 .08 .12 -.03
1,383.9 .28 .02 .49
0
28.4 .47 .08 .14 -2.12
18.6 .43 .ll .09 -.09
752.5 .19 .14 .20 -1.23
511.1 .20 .09 .05 -6.48
1,009.6 .36 .08
28.4 .52 .05 .04 -.19
764.3 .27 .07 .ll -.13
661.7 .19 .08
1,381.7 .31 .03 .00 -.27
18.6 .42 .10 .07 .09
744.4 .22 .18
506.1 .34 .27 -.65
1,007.6 .39 .10 -.18
.oo
.oo
28.4 .49 .05 .12 .04
762.2 .29 .07 -.13 .12
662.1 .18 .07 .14 .o 1
1
4 h2 log L 2
4 h2 C2
log L
.oo -.76
3
4 h2 m2 log L 4
4 h2 In2
rAM log L
.10 -.19
0
5
4 h2 m2 C2
log L
.oo -.21
.01 -.06
6
4 h2 m2
"4:
-.30 .20
1,384.3 .28 .02 .47
.oo
phenotypic variance, h2: direct heritability, m2: maternal heritability, r u l : direct-maternal genetic correlation, c2: permanent environmental effect, log L: log likelihood, expressed as deviation from value for Model 6.
2618
MEYER ET AL.
(or 4) resulted in corresponding substantial increases of estimates of both the direct (ci) and maternal genetic variances over those under Model 5 ( o r 3 ) . In this case, the estimate of the direct heritability ( h 2 ) increased by 70% and the maternal heritability ( m 2 ) estimate tripled in value. Meyer (1992b) showed that h i , G&, and h h generally had large, negative sampling correlations and substantial sampling errors even for data structures specifically designed to enable the accurate estimation of maternal effects and large numbers of observations. The pattern of changes in estimates when allowing for a non-zero a m thus could be attributed, in part a t least, to the effects of sampling variation on the partitioning of the phenotypic variance (Meyer, 1992a, 1993a,b). Previous multivariate analyses of growth traits in beef cattle clearly identified maternal effects found for postweaning weights as a carry-over effect of those for WWT through a part-whole relationship, whereas estimates of the direct genetic correlations between WWT and YWT were large and positive (Meyer, 1993a,b). Hence it seemed somewhat implausible that a&- for YWT should be substantially different from zero when it was unimportant for WWT. With substantially fewer data available for YWT than for WWT, the estimate of a m obtained for YWT in Herefords was therefore considered unreliable, even though a n effect of the seasonal drought on YWT, potentially creating a negative environmental directmaternal covariance which in turn would bias CAM, could not be excluded. Regarding the importance of a m , results for the Herefords disagree with those from field data for Australian Polled Herefords. Considering eight subsets of data, Meyer (199313) reported consistently negative estimates of rm for WWT and YWT, on average amounting to -.67 and -.58, respectively, whereas the corresponding estimate for BWT (based on a single data s e t ) was -.57. “Field” estimates for the four traits for Australian Herefords (horned) were .04 (BWT), - 5 9 (WWT), -.48 (YWT), and -.20 ( F W T ) (Meyer, 1992a). In contrast, estimates of am1 for Herefords in a selection experiment in New Zealand amounted to 5.5, -5.2, 5.8, and 4.5% of 6$ for BWT, WWT, YWT, and FWT, respectively, with of .34, -.35, .97, and .95 corresponding values of (Waldron et al., 1993). Moreover, estimates of rm for an experimental Hereford herd in the United States using the same methodology as in this paper were .07 for BWT and -.20 for WWT (Koch, 1989, personal communication). There has always been concern about potential biases in estimates of UAV, €or instance due to a negative environmental direct-maternal covariance, which would alter the covariance between dams and ( a&)
their offspring (e.g., Koch, 1972). Summarizing literature estimates, Baker (1980) found average values of ?mfor BWT and WWT of -.45 and -.72, respectively, but corresponding values close t o zero when excluding estimates using information from dam-offspring covariances. Possible reasons for such environmental covariance included the so-called “fatty udder syndrome’’ (i.e., an effect of the plane of nutrition during growth on cows’ maternal ability) or differential management of animals. From the estimates quoted above, it seemed that data from experimental herds were much less subject to these effects, presumably due to a more standardized management. Although a weak adverse genetic relationship between direct and maternal effects was plausible (Cundiff, 19721, results from this analysis provided further indication that moderately to strongly negative estimates of rfif obtained in various studies were likely to be biased. Thus, Model 5 was considered the “best” model except for FWT (both breeds) and YWT in Herefords, for which Model 3 seemed most suitable. On the whole, estimates of genetic and phenotypic parameters under these models were well within the range of comparable literature results; see Meyer (1992a) for a recent summary. The multibreed Wokalups were not only phenotypically more variable but also showed more direct additive genetic variation than the straightbred Herefords, especially for growth until weaning. In part a t least, this presumably reflected the effect of retained heterosis in the synthetic breed. Examining milk yield and 200-d weights in composite lines of beef cattle, Gregory et al. (1992) reported an effect of retained heterosis on 200-d weight of 15.2 kg or 6.9%, just over half of which could be attributed to heterosis for maternal milk yield. Maternal effects on all four traits were markedly more important for Herefords. In this breed, limited milk production of the dam is often considered a limiting factor for growth of calves. For WWT in particular, maternal environmental effects ( c2) explained as much variation between animals as genetic differences in growth potential. The high estimate for c2 of 20% (Table 2 ) was in close agreement with previous results for Herefords (polled and horned), ranging from 21 to 34% (Koch, 1989, personal communication; Boldman et al., 1991; Meyer, 1992a, 1993a; Waldron et al., 19931, and strengthened the evidence for clear differences between breeds in the contribution of the different components of dams’ maternal effects of the growth of their calves.
Multivariate Analyses Numbers of animals with different combinations of traits recorded and the total number of animals with records for each pair of traits are shown in Table 3. Estimates of variance components and genetic parameters for each from all analyses involving a
2619
COVARIANCES FOR GROWTH FOR BEEF CATTLE
Table 3. Number of animals with different combinations of traits recorded and number of records for each pair of traits Trait(sIa
No. of animals with 1 record only 2 records only
BWT BWT+WWT BWT+YWT WWT+YWT 3 records only BWT+WWT+YWT BWT + YWT + FWT BWT + WWT + YWT 4 records No. of animals with pairs of traits recorded BWT+WWT BWT+YWT BWT + FWT WWT+YWT WWT+FWT YWT + FWT
Hereford
Woka 1up
334 1,855 3 11 108 1,107
485 1,910 46 0 86 47 1,194
3,077 1,218 1,114 1,226 1,114 1,107
3,191 1,373 1,242 1,280 1,195 1,241
0
+ FWT
aBWT: birth weight, WWT: weaning weight, YWT: yearling weight, FWT: final weight.
particular trait are summarized in Tables 4 and 5 for Herefords and Wokalups, respectively. For BWT and WWT, estimates from uni- and the various multivariate analyses agreed closely, in particular for ug. Some fluctuations in the individual components could be observed, illustrating the effects Of Sampling Variation
on the partitioning of phenotypic variances under the complex models fitted, in particular for analyses involving three or four traits. With selection based on a function of WWT and BWT; higher estimates of u; and heritabilities for W T and FWT due to the removal of selection bias
Table 4. Estimates of variance components and genetic parametersa for Herefords for birth (BWT), weaning (WWT), yearling (YWT), and final (FWT) weight from univariate and multivariate analyses Trait(s)
BWT
+ + + +
+ +
WWT YWT FWT WWT+YWT WWT + F W T WWT+YWT+FWT
WWT
+ + + + +
+
BWT YWT FWT BWTiYWT BWT+FWT BWT+YWT+FWT
YWT
+
BWT + w w T + FWT + BWT+WWT + BWT + WWT FWT + BWT + WWT + YWT + BWT+WWT + BWT + WWT
+ FWT
iYWT
."A
4
4
4
4
h2
m2
C2
8.02 8.04 8.54 8.27 8.49 7.52 8.43 145.9 152.3 128.3 161.0 156.4 152.5 156.2 102.0 142.2 129.8 116.0 148.8 149.8 357.5 501.7 474.5 396.8 402.6 500.2
1.97 1.86 1.86 1.54 1.67 1.71 1.98 102.6 101.3 131.2 181.1 131.0 130.9 164.3 45.9 42.8 102.8 63.3 112.2 97.7 78.7 86.6 212.2 72.3 214.1 215.6
1.74 1.73 1.78 1.21 1.81 2.05 2.20 146.5 156.7 126.0 70.7 144.6 117.3 124.4 25.1 32.7 56.8
6.86 6.88 6.61 6.78 6.75 6.39 6.58 357.5 362.3 375.4 357.5 372.7 353.7 372.4 338.0 317.2 396.6 340.9 378.4 369.1 572.0 497.1 604.2 571.9 568.5 596.7
18.59 18.51 18.78 18.80 18.73 17.66 19.19 752.5 772.5 760.9 770.2 804.7 754.3 817.3 511.1 534.9 685.9 520.2 701.9 677.4 1,008.3 1,085.3 1,290.9 1,041.0 1,185.2 1,312.4
.431 .434 ,455 ,440 ,454 ,426 ,439 ,194 ,197 ,169 ,209 ,194 ,202 ,191 .200 ,266 ,189 ,223 ,212 ,221 ,355 ,462 ,368 ,381 ,340 ,381
,106
.094 ,093 ,095 .065 ,097 ,116 ,115 ,195 ,203 ,166 ,092 ,180 .156 ,152 ,049 ,061 ,083
0.0 62.4 60.8
-
-
__ -
,101 .099 ,135 ,089 ,097 ,103 ,136 ,131 ,172 ,235 ,163 ,174 ,201 ,090 ,080 ,150 ,122 ,159 ,144 ,078 ,080 ,164 ,070 ,181 .164
,000 ,089 ,090 -
-
-
"u;: direct additive genetic variance, uk: maternal genetic variance, ug: permanent environmental variance, ug: residual variance, phenotypic variance, h2: direct heritability, m2: maternal heritability, and c2: permanent environmental maternal effect.
G;:
2620
MEYER ET AL.
Table 5. Estimates of variance components and genetic parametersa for Wokalups for birth (BWT),weaning (WWT), yearling (YWT), and final [FWT) weight from uni- and multivariate analyses Trait(s) BWT
+ + +
WWT YWT FWT
+ + +
WWT+YWT
WWT+FWT WWT+YWT+FWT
WWT
+
BWT
+
FWT BWT+YWT BWT+FWT BWT+YWT+FWT
+
m
+ + + YWT
+
BWT
+ w w T
+ + +
FWT BWT+WWT BWT + WWT
+ FWT
FWT
+
BWT + W W T
+ Y w T
+ +
BWT+WWT BWT + WWT
+ YWT
4
4
.“c
4
4
h2
In2
C2
14.63 14.99 15.01 15.10 14.99 14.50 14.78 209.5 244.0 221.9 211.4 258.1 231.9 226.3 123.9 203.5 319.6 146.7 322.6 262.3 429.4 662.6 786.2 507.0 762.6 698.7
1.52 1.58 1.38 1.51 1.53 1.73 1.04 49.4 45.9 101.8 58.1 97.2 68.7 84.0 60.7 59.9 119.6 58.0 115.7 115.0 47.0 37.6 105.9 44.6 110.8 97.0
1.21 1.19 1.39 1.14 1.55 1.12 1.50 85.3 80.1 33.8 69.1 33.0 64.7 35.4 -
11.02 10.86 10.82 10.83 10.73 10.95 10.95 420.1 419.4 430.9 424.3 442.3 436.7 454.3 477.6 454.6 510.5 465.8 514.1 516.5 905.3 820.7 922.3 884.0 914.4 1,045.3
28.39 28.61 28.61 28.58 28.80 28.30 28.28 764.3 789.5 788.4 762.8 830.7 802.2 800.0 662.1 718.0 949.7 670.6 952.4 893.8 1,381.7 1,520.8 1,814.5 1,435.6 1,787.9 1,841.1
,516 ,524 .525 .529 .521 .512 ,523 ,274 .309 ,282 ,277 ,311 ,289 .283 ,187 .284 ,337 .219 ,339 ,293 ,311 ,436 .433 ,353 ,427 .380
.054 .055 .048 ,053 .053 ,061 ,037 ,065 ,058 ,129 ,076 ,117 ,086 ,105 ,092 .083 ,126 .087 ,122 .129 ,034 ,025 ,058 ,031 ,062 ,053
,043 .042 ,049 ,040 .054 .040 .053 ,112 ,102 ,043 ,096 ,040 ,081 .044 -
-
-
-
-
-
-
-
-
-
-
4:
a& direct additive genetic variance, otf: maternal genetic variance, ug: permanent environmental variance, residual variance, phenotypic variance, h2: direct heritability, m2: maternal heritability, and c2: permanent environmental maternal effect.
0;:
Table 6. Estimates of direct genetic ( r A ) , maternal genetic (rM), maternal permanent environmental (rc), and phenotypic correlations between birth [BWT), weaning (WWT), yearling (YWT), and final (FWT) weight from bi-, tri-, and four-variate analyses Hereford
An.a
Trait
+ WWT
BWT
+
+
+
+m
+ +
+m
+ + WWT + YWT + + +
+ + YWT
+
FWT
+
FWT
2 3a 3b 4 2 3a 4 2 3b 4 2 3a 4 2 3b 4 2 4
rM
‘A
.693 ,714 .659 .703 .648 ,651 ,682 ,657 ,627 ,660 ,943 ,966 ,880 ,958 BO8 .923 1.000 .974
aAnalysis: 2 = bivariate, 3a = trivariate BWT
.476 ,508 ,345 ,414 ,722 .580 .442 1.000 .496 ,689 ,985 ,983 ,972 1.000 ,984 .916 ,859 ,918
+
WWT
Wokalup rP
‘C
,689 ,681 ,816 ,661 1.000 ,793 ,629 -
1.000 .985 .966 -
-
-
+ YWT,
‘A
.510 ,517 ,487 ,498 ,415 ,434 ,369 ,447 .356 .404 ,772 .774 ,755 ,699 ,641 ,645 ,727 ,722
3b = trivariate BWT
.735 ,745 .743 ,745 ,783 ,685 ,702 ,761 .706 ,720 .981 ,981 ,984 ,985 ,981 ,987 1.000 1.000
+
‘M
‘C
rP
,782 ,760 .743 ,705 ,987 ,813 .770 ,546 549 .421 1.000 ,996 ,995 1.000 ,967 ,881 .766 ,833
,386 ,372 ,366 ,384 -
,543 ,551 ,539 ,538 .519 ,511 ,499 .512 ,503 ,498 347 346 ,833 ,751 ,753 ,750 ,741 ,779
-
-
-
WWT + FWT, 4 = four-variate
262 1
COVARIANCES FOR GROWTH FOR BEEF CATTLE
Table 7. Phenotypic variances and correlation matrices for birth (BWT), weaning (WWT), yearling (YWTJ,and final (FWT) weight from four-variate analyses Hereford Trait
BWT
WWT
Wokalup
YWT
FWT
BWT
WWT
.38
.52 .75 .70 .72
.28 .98 .99
.16
.04 .71 .77 .42
YWT
FWT
Aa
BWT WWT YWT
FWT Mb BWT WWT YWT FWT CC BWT WWT YWT
.44 .70 .68 .66
.19 .88
.92
.10 .41 .44 .69
.20 .97 .92
.12 .66 .63
.15 .97
.22 .97
.14 .92
.29 1.00
.38
.13 .83
.05
893.8 .78
1,841.1
.10
.99 .88
.05 .38
.04
.09
Pd
BWT WWT YWT
FWT
19.3 .50 .37 .40
817.3 .76 .65
677.4 .72
1,312.4
28.3 .54 .50 .50
800.0
.83 .75
aDirect additive genetic effects: heritabilities on, correlations below the diagonal. bMaternal additive genetic effects: heritabilities on, correlations below the diagonal. ‘Maternal permanent environmental effects: “c-squared” effects on, correlations below the diagonal dPhenotypic effects: variances on, correlations below the diagonal.
were expected for multivariate analyses jointly with WWT or BWT than for univariate analyses or a bivariate analysis of YWT together with FWT. This could clearly be observed for 5;: estimates from univariate analyses and those from a bivariate analysis of YWT and FWT were very similar and consistently lower than estimates from the remaining analyses. Values for 3; from bivariate analyses with BWT were somewhat increased, whereas corresponding estimates from analyses with WWT were of similar magnitude to those from tri- or four-variate analyses. This reflected the fact that WWT contained most of the information determining selection. A similar pattern emerged for the additive genetic variances although it was not quite as consistent, presumably again attributable to sampling. Although little systematic differences in heritability estimates could be noted, estimates of h2 for YWT and FWT from four-variate analyses were higher than their univariate counterparts. Furthermore, estimates of m2 for WWT; W T ; and FWT were higher for the four-variate analyses, but for WWT this was associated with a corresponding decrease in e2 (i.e., to some extent at least again explicable by sampling variation in the partitioning of the overall variance). Estimates of correlations from the various analyses are given in Table 6. Considering three or all four traits together generally tended to “smooth out” extreme or implausible correlation estimates from bivariate analyses. Otherwise, there was good agreement between corresponding estimates from different analyses, suggesting that even with a search in more
than 30 dimensions, the maximum of the likelihood had been located with reasonable accuracy. Selection bias generally affected correlation estimates markedly less than heritabilities or variance components and correlations were subject to considerably larger sampling errors, so no systematic differences between estimates from bivariate and three- or four-variate analyses could be observed. Table 7 gives the complete correlation matrices from analyses considering all four traits simultaneously. As in previous studies (Meyer, 1993a,b), estimates of the maternal genetic ( r M ) and permanent environmental (rc) correlations among WWT, YWT, and FWT were essentially unity. Similarly, estimates of the direct genetic correlations ( r A ) between these traits were consistently high, especially for Wokalups. Estimates of r A between BWT and the other traits were with approximately .7 higher than those for Polled Herefords (Meyer, 199313) and Simmentals (Swalve, 1993) from field data but were comparable to results from an experimental Angus herd (Meyer, 1993a). Corresponding values for r M were, except for FWT, higher for Wokalups than for Herefords, whereas estimates of rc were higher for the latter, again reflecting the differing importance of the components of maternal performance in the two breeds.
Discussion Results strengthened the evidence for breed differences in the importance and mode of action of
2622
MEYER ET AL.
maternal effects for the early growth of beef calves. Except for FWT, estimates of direct heritabilities were higher in the multibreed Wokalups than in the purebred Herefords, suggesting that formation of a synthetic indeed increased the amount of additive genetic variation among animals available and thus the scope for selection. In contrast to many other studies, especially those based on field data, direct-maternal genetic correlation estimates were low and generally not significantly different from zero. This supported earlier speculations that large, negative estimates of rm found in numerous analyses did not reflect a marked adverse genetic relationship between growth and maternal performance but were due to management practices or environmentally induced negative damoffspring covariances. Estimates of maternal correlations between WWT, YWT, and FWT clearly identified maternal effects found for postweaning weights as a carry-over effect of those on WWT through a part-whole relationship. This implies that with appropriate scaling, a joint maternal effect (one each for genetic and permanent environmental effects) could be fitted in a multivariate genetic evaluation to account for the maternal influence on WWT, YWT, and FWT. Comparing estimates from uni- and various multivariate analyses demonstrated the effect of selection on estimates of variance components and genetic parameters for YWT and FWT. Estimates from bivariate analyses of YWT or FWT together with WWT were similar to those from trivariate analyses including BWT as well or analyses of all four traits simultaneously, indicating that WWT contained most information determining selection decisions. Although four-variate analyses fitting two maternal effects and thus involving close to 40,000 equations, and estimating up to 34 highly correlated covariance components simultaneously, proved feasible, their computational demands were excessive and, at present, they seem unsuitable for routine applications.
Implications Estimates of direct genetic correlations between weaning and later weights were close to unity, identifying the former as a suitable criterion in selecting for growth. Maternal effects till weaning were found to “carry over” to yearling weight and, to a lesser extent, final weight, and should be taken into account in genetic evaluation schemes for these traits. Levels of phenotypic variability and of direct additive
genetic variation in the multibreed synthetic line (Wokalups) were higher than in the purebred line (Polled Herefords), especially for growth till weaning. In addition, no antagonistic relationship between direct and maternal effects could be observed for the synthetic line. This suggests increased scope for selection in a crossbred population.
Literature Cited Baker, R. L. 1980. The role of maternal effects on the efficiency of selection in beef cattle. Proc. N. Z. SOC.Anim. Prod. 40:285. Boldman, K. G., L. D. Van Vleck, K. E. Gregory, and L. V. Cundiff. 1991. Estimates of direct and maternal parameters for 200 d weight in purebred and composite lines of beef cattle. J . Anim. Sci. 69rSuppl. 1):203 (Abstr.). Cundiff, L. V. 1972. The role of maternal effects in animal breeding: VIII. Comparative aspects of maternal effects. J. Anim. Sci. 35: 1335. Gregory. K. E., L. V. Cundiff, and R. M. Koch. 1992. Effects of breed and retained heterosis on milk yield and 200-day weight in advanced generations of composite populations of beef cattle. J. Anim. Sci. 70:2366. Kinghorn, B. P. 1982a. Genetic effects in crossbreeding. I. Models of merit. Z. Tierz. Zuechtungsbiol. 99:59. Kinghorn, B. P. 198210. Genetic effects in crossbreeding. 11. Multibreed selection indices. Z. Tierz. Zuechtungsbiol. 99:315. Koch, R. M. 1972. The role of maternal effects in animal breeding: VI. Maternal effects in beef cattle. J. Anim. Sci. 35:1316. Meyer, K. 1989. Restricted Maximum Likelihood t o estimate variance components for animal models with several random effects using a derivative-free algorithm. Genet. Sel. Evol. 21:317. Meyer, K. 1991a. Estimating variances and covariances for multivariate Animal Models by Restricted Maximum Likelihood. Genet. Sel. Evol. 23:67. Meyer, K. 1991b. DFREMLVersion 2.0 - Programs to Estimate Variance Components by Restricted Maximum Likelihood Using a Derivative - Free Algorithm. User Notes. Animal Genetics and Breeding Unit, University of New England, Armidale NSW (Mimeoj. Meyer, K. 1992a. Variance components due to direct and maternal effects for growth traits of Australian beef cattle. Livest. Prod. Sci. 31:179. Meyer, K. 1992b. Bias and sampling covariances of estimates of variance components due to maternal effects. Genet. Sel. Evol. 24:487. Meyer, K. 1993a. Estimates of direct and maternal correlations among growth traits in Australian beef cattle. Livest. Prod. Sci. ( I n press). Meyer, K. 1993b. Covariance matrices for growth traits of Australian Polled Hereford cattle. h i m . Prod. ( I n pressi. Schneeberger, M., B. Tier, and K. Hammond. 1991. Introducing the third generation of BREEDPLAN and GROUPBREEDPLAN. Proc. 9th Conf. of the Aust. Assoc. Anim. Breed. Genet., Melbourne. Swalve, H. H. 1993. Estimation of direct and maternal (colvariance components for growth traits in Australian Simmental beef cattle. J. Anim. Breed. Genet. ( I n press). Waldron, D. F., C. A. Morris, R. L. Baker, and D. L. Johnson. 1993. Maternal effects for growth traits in beef cattle. Livest. Prod. Sci. 34:57.
ABSTRACT
Estimates of covariance components and genetic parameters were obtained for birth, weaning, 200-d, and 400-d weight for a herd of Polled Herefords and a herd of a multibreed synthetics, the so-called Wokalups. Data originated from an experiment in Western Australia selecting for preweaning growth rate. Analyses were carried out by REML fitting a n animal model including genetic and permanent environmental maternal effects. Wokalups
showed consistently more phenotypic variation, partly due to a scale effect, and higher direct and lower maternal heritabilities than Herefords. Maternal environmental effects were more than twice as important in Herefords than in Wokalups. Estimates of both genetic and environmental correlations among weaning and subsequent weights were essentially unity, identifying maternal effects found for postweaning weights as a “carry over” of those on weaning weight.
Key Words: Beef Cattle, Maternal Effects, Genetic Parameters, Crossbreeding
J. h i m . Sci. 1993. 71:2614-2622
Introduction Genetic theory on the effects of crossbreeding is well established, in particular concerning the exploitation of nonadditive genetic effects in improving mean levels of performance (e.g., Kinghorn, 1982a,b). Schemes such as rotational crossing, criss-crossing, or recurrent reciprocal selection are designed to make optimum use of heterosis, epistasis, or recombination effects, but they usually require the respective purebred populations t o be maintained. An alternative is the formation of a multibreed synthetic population. Although expected proportions of nonadditive genetic effects utilized and the resulting breed means of such synthetics are readily quantified, implications on the additive genetic variation in these populations and the resulting scope for selection are generally less clear-cut. A selection experiment in beef cattle was carried out a t the Wokalup research station in Western Australia to compare additive genetic variation and response to selection in pure- and multibreed popula-
lFinancial support for this paper mas provided by Australia’s Meat Research Cooperation (MRC); inputs from the Western Australian Department of Agriculture are acknowledged. %hrrent address: Queensland Dept. of Primary Industries, G.P.O. Box 46, Brisbane, Queensland 4001, Australia. 3W.A. Dept. of Agric., Baron Hay Court, South Perth, Western Australia 6151, Australia. Received December 28, 1992. Accepted May 5, 1993.
tions, contrasting straightbred Polled Herefords with a synthetic formed using British beef breeds, a large European beef breed, a dairy breed, and Bos indicus cattle (i.e., including each of the major cattle breed groups). The underlying rationale was that if it was possible to increase selection response by creating a synthetic from the breeds appropriate to the specific climatic and economic production conditions, knowledge of the increase in additive genetic variation would be required in planning appropriate breeding programs. This paper presents estimates of (colvariances and the resulting genetic and phenotypic parameters among growth traits for the two populations in the Wokalup selection experiment.
Materials and Methods The Experiment Data originated from a selection experiment conducted a t the Wokalup research station in the Southwest of Western Australia. Climatically, this location has a Mediterranean type of environment with an average rainfall of approximately 750 mm and an annual drought from November to the following April/May, which was almost always complete. Pastures were improved and were predominantly rye grass and subterranean clover, which were annually topdressed by air with superphosphate, the quantity of
2614
COVARIANCES FOR GROWTH FOR BEEF CATTLE
which was determined by soil tests. Planning for the experiment was begun in 1972 (some matings for the Wokalups had begun in 19691, and two herds of 300 cows each were established by 1978. The herds comprised straightbred Polled Herefords and a synthetic breed formed by mating Charolais x Brahman bulls with Friesian x Angus or Hereford cows. The latter became known as the Wokalup Multibreeds, or simply Wokalups. In 1978, all Wokalup females were first four-way cross or from interbred four-way cross parents and age structures in each herd were approximately equivalent. Selection for increased preweaning growth rate commenced in 1978 in both herds. No control herd was established until 1984 when the remaining cows in the herd that had calved in 1978 (approximately 75 in each herd) were multiple-ovulated and remated to the sires used in the 1977 mating whose semen had been stored. Embryos from this mating were frozen and stored until the completion of selection. Because of technical difficulties, however, there were few of these “control” animals, born in 1990, included in this study. Embryos had been stored in plastic-capped glass vials, and liquid nitrogen had leaked in, causing many of them to explode when thawing was attempted. The management of the project was unusual for Australian conditions in that cows were kept in 24 separate 20-ha paddocks of approximately 25 cows year-round, and were thus offered the same amount of grazing, rather than the more common practice of allowing them equal access to a common grazing area. Single-sire mating took place in each of these 12 paddocks per breed during a 7- to 8-wk period to result in April-May calving. Three hundred to 310 females of each breed were mated each year, made up of 60 heifers, 50 first calvers, and 190 to 200 adults. Calves were weaned in December. Cows were rerandomized into new paddocks between mating and calving each year and culling was on the basis of pregnancy test a t this time. Thus, sire groups and calving groups were not confounded. All calves were tagged, identified with their dam, and weighed, and their cannon-bone length was measured a t birth. Subsequently, calves were weighed at monthly intervals except for June (during calving). Calves normally lost weight or at best maintained their weight between weaning and 1 yr of age because of the seasonal drought. In the early years of the experiment, selection for preweaning growth was based on growth to October to avoid castrating culls in hot weather. In the later years, castration was not practiced and selection was on weaning weights taken in December. In 1985 the Wokalup herds joined BREEDPLAN,a within-herd multivariate genetic evaluation scheme for beef cattle by BLUP fitting a n animal model and accounting for direct and maternal effects on growth (Schneeberger et al., 1991). From then the selection criterion used was a n index of EBV corresponding to growth until
2615
weaning, namely EBV for weaning weight minus EBV for birth weight plus half of the “milk” EBV, with the latter denoting the estimate of the maternal genetic effect on weaning weight.
Analyses Traits considered were birth weight ( BWT) , weaning weight ( WWT), yearling or 400-d weight ( YWT), and final or 600-d weight ( FWT). Ranges allowed for age a t weighing were as for BREEDPLAN120 to 300, 301 to 500, and 501 to 700 d for WWT, YWT, and FWT, respectively. Basic edits eliminated records with missing weighing dates or sex codes and involved consistency checks of dates, ages, and weights. For a proportion of animals, age of dam could not be calculated because of unknown birth dates of the dams. For these animals, dam age was replaced by the mean age in the respectively data set. This occurred mainly in the early years of the experiment for foundation cows and about equally for both breeds. Weaning dates were available for each year and WWT records selected were the monthly weights for each animal taken closest to this date. Similarly, YWT and FWT records for each animal were the weights recorded closest to 400 and 600 d of age, respectively. Estimates of variance and covariance components were obtained by REML using a derivative-free algorithm, fitting a n animal model throughout and incorporating all pedigree information available. Maternal genetic and permanent environmental effects were taken into account by including appropriate random effects into the model of analysis as described by Meyer (1989, 1991a). All calculations were carried out using DFREML (Meyer, 1991b). Computational strategies used and problems associated with this kind of analysis have been discussed previously (Meyer, 1992a, 1993a). Fixed effects fitted were sex ( a t weighing), birth type (single vs twin), and year-paddock and yearmonth of weighing subclasses. Age at weighing and dam age were taken into account by fitting each of them as a linear and quadratic covariable. No breed or heterosis effects were fitted for Wokalups because the objective was to assess the amount of useable genetic variation in the synthetic population. Because generations of crossbreeding and years were confounded, fitting year-paddock and year-time of weighing effects was expected to account for any heterogeneity in breed composition in the early stage of the experiment. Univariate analyses for each trait and data set were carried out considering six different models of analysis to assess the importance of different maternal effects. Model 1 was a “simple” animal model fitting animals’ direct additive genetic effects only (i.e., ignoring any maternal effects). Model 2 allowed for a maternal effect in addition but attributed it solely to the permanent environmental effect of the dam. Conversely, Model 3 assumed all maternal influence was
2616
MEYER ET AL
of genetic origin. Whereas Model 3 assumed direct and maternal genetic effects to be uncorrelated, Model 4 allowed for a respective non-zero covariance. Models 5 and 6 corresponded to Models 3 and 4, respectively, but fitted both dams’ genetic and permanent environmental effects (i.e., three random factors altogether). The models were the same as those considered by Meyer (1992a, 1993a) and a more formal description was given there. Flexibility of the estimation procedure allowed different models to be fitted for individual traits in multivariate analyses. Univariate results had suggested that maternal environmental effects were absent for FWT in both breeds and for YWT in Wokalups and that direct-maternal genetic covariances were unimportant, Hence for both breeds, Model 5 was chosen for BWT and WWT and Model 3 for FWT; whereas for YWT, Models 5 and 3 were fitted for Herefords and Wokalups, respectively. Pairwise bivariate analyses were carried out for each combination of traits, estimating up to 12 (colvariance components simultaneously. Because the selection criterion had involved both BWT and WWT, subsequent trivariate analyses then considered YWT or FWT together with BWT and WWT so as to obtain estimates of covariance components for the two later weights unbiased by selection. Finally, multivariate analyses of all four traits together were performed, estimating 36 and 33 parameters for Herefords and Wokalups, respectively.
Results Characteristics of the data structure are summarized in Table 1. There was considerable variation in weights due to variation in both production conditions ( t h e data included several drought years) and, especially for WWT, age at weighing. Annual means for WWT in Wokalups, for instance, ranged from 203.3 kg in 1975 to 310.4 kg in 1988 with corresponding mean ages at weaning of 181.6 and 245.5 d. Wokalups were bigger and phenotypically more variable than Herefords, but, as CV demonstrate, the latter was mainly a scale effect. With monthly weighings available, ages at weighing for YWT and FWT were closer to the targets of 400 and 600 d and considerably less variable than in corresponding analyses of field data ( cf Meyer, 1992a, 199313). Year-paddock and yearmonth subclasses were frequently confounded, resulting in a reduced rank of the coefficient matrix for fixed effects.
Univariate Analyses Table 2 gives estimates of phenotypic variances ( u p ) and genetic parameters from univariate analyses. Differences in overall variability between breeds could to some extent again be attributed to the size differential. However, in spite of a 30-kg difference in mean WWT, estimates of ~7; for this trait were of equal magnitude for both breeds (i.e., Herefords were 2
Table 1. Characteristics of the data structure Hereford Traita
No. of records NO. of animal& No. of sires No. of dams‘ No. of P a d d No. of YMone Rankf Weight, kg Mean SD
cv, 5%
Age, d Mean SD Dam age, y Mean SD
BWT 3,414 3,683 3,783 174 1,033 167 65 22 1
WWT 3,088 3,331 3,421 174 956 155 39 184
Wokalup
YWT 1,229 1,378 1,482 160 643 56 54 101
FWT 1,114 1,308 1,415 159 600 78 47 111
BWT 3,769 3,961 4,518 189 1,473 153 67 208
WWT 3,191 3,438 3,857 189 1,201 144 43 177
YWT 1,373 1,491 1,740 175 800 59 59 107
FWT 1,242 1,411 1,638 174 7 16 79 45 111
31.46 5.29 16.8
227.6 51.5 22.6
262.9 47.2 18.0
409.8 62.3 15.2
35.98 6.32 17.6
257.7 52.9 20.5
209.4 49.5 17.0
440.2 77.6 17.6
-
213.8 32.0
399.3 18.5
592.0 22.2
-
210.5 32.4
397.8 17.7
584.8 28.0
-
4.39 1.88
4.50 1.96
4.23 1.69
4.21 1.72
4.64 2.13
4.68 2.18
4.42 1.92
aBWT: birth weight, WWT: weaning weight, YWT: yearling weight, FWT: final weight. univariate analyses, including parents without records: First line: Models 1 and 2; Second line: Models 3 to 6. ‘With progeny in the data. dYear-paddock subclasses. eYear-month subclasses. fOf coefficient matrix for fixed effects.
4.41 1.96
2617
COVARIANCES FOR GROWTH FOR BEEF CATTLE
relatively markedly more variable). This agreed with results of Boldman et al. (1991), who, in comparing genetic parameters for WWT in purebred and composite lines of beef cattle, found Herefords to have the highest CV among all lines examined and Herefords and the composite line to exhibit equal overall variance while differing in size by 42 kg. For both breeds, 6; for YWT was lower than for WWT, presumably reflecting both a n effect of the annual summer/autumn drought and of a reduction in variance due to selection of animals at weaning. As likelihood values clearly indicate, WWT and BWT in both breeds were determined by genetic as well as permanent environmental maternal effects. For YWT and FWT, some maternal influence could be detected, but it seemed t o be mainly of genetic origin. For Wokalups, estimates of the direct-maternal genetic covariance ( u r n ) were close to zero for all
traits, amounting a t most to 3.4% of 6$, with correspondingly small differences in likelihoods between Models 3 and 4 or 5 and 6, respectively. For Herefords, the same held for BWT and FWT. For WWT in this breed, the estimate of u r n was negative, amounting t o almost 6% of u$ with a corresponding estimate of the direct-maternal genetic correlation ( r ~ of)-.30. The increase in likelihood when fitting Model 6 over that for Model 5, however, was not significant. In contrast, for YWT in Hereford 6~ was -20% of 6; with a highly significant improvement in likelihood over that assuming that u r n was zero. As observed in other studies (e.g., Meyer, 1992a, 1993a; Swalve, 19931, estimates of u; ignoring and allowing for u r n remained more or less constant so that the large, negative estimate of u r n under Model 6
Table 2. Estimates of the phenotypic variance and genetic parametersa from univariate analyses of birth weight (BWT), weaning weight (WWT), yearling weight (YWT), and final weight (FWT) under different models of analysis Hereford Model
Wokalup
BWT
WWT
YWT
EWT
BWT
WWT
YWT
FWT
18.7 .57 -79.09
771.9 .45 -149.18
519.7 .27 -22.49
1,025.2 .42 -8.24
28.9 .58 -41.23
779.6 .38 -66.27
663.9 .25 -3.28
1,384.9 .34 -1.45
18.5 .48 .17 -5.04
745.9 .22 .31 -6.88
510.4 .23 .13 -8.58
1,0 11.3 .41 .04 -1.87
28.6 .55 .08 -3.81
762.4 .30 .16 -3.15
659.9 .22 .08 -1.68
1,382.7 .33
19.0 .39 .23 -5.85
795.9 .17 .36 -14.86
511.8 .20 .12 -6.92
1,008.3 .36 .08 -.21
28.4 .50 .09 -2.51
779.5 .26 .18 -7.49
662.1 .19 .09 -.08
1,381.7 .31 .03 -0.27
19.0 .37 .22 .06 -5.76
783.1 .20 .42 -.29 -12.93
505.8 .34 .27 -.65
1,006.9 .38
0
780.0 .26 .17 .02 -7.48
662.6 .18 .08 .12 -.03
1,383.9 .28 .02 .49
0
28.4 .47 .08 .14 -2.12
18.6 .43 .ll .09 -.09
752.5 .19 .14 .20 -1.23
511.1 .20 .09 .05 -6.48
1,009.6 .36 .08
28.4 .52 .05 .04 -.19
764.3 .27 .07 .ll -.13
661.7 .19 .08
1,381.7 .31 .03 .00 -.27
18.6 .42 .10 .07 .09
744.4 .22 .18
506.1 .34 .27 -.65
1,007.6 .39 .10 -.18
.oo
.oo
28.4 .49 .05 .12 .04
762.2 .29 .07 -.13 .12
662.1 .18 .07 .14 .o 1
1
4 h2 log L 2
4 h2 C2
log L
.oo -.76
3
4 h2 m2 log L 4
4 h2 In2
rAM log L
.10 -.19
0
5
4 h2 m2 C2
log L
.oo -.21
.01 -.06
6
4 h2 m2
"4:
-.30 .20
1,384.3 .28 .02 .47
.oo
phenotypic variance, h2: direct heritability, m2: maternal heritability, r u l : direct-maternal genetic correlation, c2: permanent environmental effect, log L: log likelihood, expressed as deviation from value for Model 6.
2618
MEYER ET AL.
(or 4) resulted in corresponding substantial increases of estimates of both the direct (ci) and maternal genetic variances over those under Model 5 ( o r 3 ) . In this case, the estimate of the direct heritability ( h 2 ) increased by 70% and the maternal heritability ( m 2 ) estimate tripled in value. Meyer (1992b) showed that h i , G&, and h h generally had large, negative sampling correlations and substantial sampling errors even for data structures specifically designed to enable the accurate estimation of maternal effects and large numbers of observations. The pattern of changes in estimates when allowing for a non-zero a m thus could be attributed, in part a t least, to the effects of sampling variation on the partitioning of the phenotypic variance (Meyer, 1992a, 1993a,b). Previous multivariate analyses of growth traits in beef cattle clearly identified maternal effects found for postweaning weights as a carry-over effect of those for WWT through a part-whole relationship, whereas estimates of the direct genetic correlations between WWT and YWT were large and positive (Meyer, 1993a,b). Hence it seemed somewhat implausible that a&- for YWT should be substantially different from zero when it was unimportant for WWT. With substantially fewer data available for YWT than for WWT, the estimate of a m obtained for YWT in Herefords was therefore considered unreliable, even though a n effect of the seasonal drought on YWT, potentially creating a negative environmental directmaternal covariance which in turn would bias CAM, could not be excluded. Regarding the importance of a m , results for the Herefords disagree with those from field data for Australian Polled Herefords. Considering eight subsets of data, Meyer (199313) reported consistently negative estimates of rm for WWT and YWT, on average amounting to -.67 and -.58, respectively, whereas the corresponding estimate for BWT (based on a single data s e t ) was -.57. “Field” estimates for the four traits for Australian Herefords (horned) were .04 (BWT), - 5 9 (WWT), -.48 (YWT), and -.20 ( F W T ) (Meyer, 1992a). In contrast, estimates of am1 for Herefords in a selection experiment in New Zealand amounted to 5.5, -5.2, 5.8, and 4.5% of 6$ for BWT, WWT, YWT, and FWT, respectively, with of .34, -.35, .97, and .95 corresponding values of (Waldron et al., 1993). Moreover, estimates of rm for an experimental Hereford herd in the United States using the same methodology as in this paper were .07 for BWT and -.20 for WWT (Koch, 1989, personal communication). There has always been concern about potential biases in estimates of UAV, €or instance due to a negative environmental direct-maternal covariance, which would alter the covariance between dams and ( a&)
their offspring (e.g., Koch, 1972). Summarizing literature estimates, Baker (1980) found average values of ?mfor BWT and WWT of -.45 and -.72, respectively, but corresponding values close t o zero when excluding estimates using information from dam-offspring covariances. Possible reasons for such environmental covariance included the so-called “fatty udder syndrome’’ (i.e., an effect of the plane of nutrition during growth on cows’ maternal ability) or differential management of animals. From the estimates quoted above, it seemed that data from experimental herds were much less subject to these effects, presumably due to a more standardized management. Although a weak adverse genetic relationship between direct and maternal effects was plausible (Cundiff, 19721, results from this analysis provided further indication that moderately to strongly negative estimates of rfif obtained in various studies were likely to be biased. Thus, Model 5 was considered the “best” model except for FWT (both breeds) and YWT in Herefords, for which Model 3 seemed most suitable. On the whole, estimates of genetic and phenotypic parameters under these models were well within the range of comparable literature results; see Meyer (1992a) for a recent summary. The multibreed Wokalups were not only phenotypically more variable but also showed more direct additive genetic variation than the straightbred Herefords, especially for growth until weaning. In part a t least, this presumably reflected the effect of retained heterosis in the synthetic breed. Examining milk yield and 200-d weights in composite lines of beef cattle, Gregory et al. (1992) reported an effect of retained heterosis on 200-d weight of 15.2 kg or 6.9%, just over half of which could be attributed to heterosis for maternal milk yield. Maternal effects on all four traits were markedly more important for Herefords. In this breed, limited milk production of the dam is often considered a limiting factor for growth of calves. For WWT in particular, maternal environmental effects ( c2) explained as much variation between animals as genetic differences in growth potential. The high estimate for c2 of 20% (Table 2 ) was in close agreement with previous results for Herefords (polled and horned), ranging from 21 to 34% (Koch, 1989, personal communication; Boldman et al., 1991; Meyer, 1992a, 1993a; Waldron et al., 19931, and strengthened the evidence for clear differences between breeds in the contribution of the different components of dams’ maternal effects of the growth of their calves.
Multivariate Analyses Numbers of animals with different combinations of traits recorded and the total number of animals with records for each pair of traits are shown in Table 3. Estimates of variance components and genetic parameters for each from all analyses involving a
2619
COVARIANCES FOR GROWTH FOR BEEF CATTLE
Table 3. Number of animals with different combinations of traits recorded and number of records for each pair of traits Trait(sIa
No. of animals with 1 record only 2 records only
BWT BWT+WWT BWT+YWT WWT+YWT 3 records only BWT+WWT+YWT BWT + YWT + FWT BWT + WWT + YWT 4 records No. of animals with pairs of traits recorded BWT+WWT BWT+YWT BWT + FWT WWT+YWT WWT+FWT YWT + FWT
Hereford
Woka 1up
334 1,855 3 11 108 1,107
485 1,910 46 0 86 47 1,194
3,077 1,218 1,114 1,226 1,114 1,107
3,191 1,373 1,242 1,280 1,195 1,241
0
+ FWT
aBWT: birth weight, WWT: weaning weight, YWT: yearling weight, FWT: final weight.
particular trait are summarized in Tables 4 and 5 for Herefords and Wokalups, respectively. For BWT and WWT, estimates from uni- and the various multivariate analyses agreed closely, in particular for ug. Some fluctuations in the individual components could be observed, illustrating the effects Of Sampling Variation
on the partitioning of phenotypic variances under the complex models fitted, in particular for analyses involving three or four traits. With selection based on a function of WWT and BWT; higher estimates of u; and heritabilities for W T and FWT due to the removal of selection bias
Table 4. Estimates of variance components and genetic parametersa for Herefords for birth (BWT), weaning (WWT), yearling (YWT), and final (FWT) weight from univariate and multivariate analyses Trait(s)
BWT
+ + + +
+ +
WWT YWT FWT WWT+YWT WWT + F W T WWT+YWT+FWT
WWT
+ + + + +
+
BWT YWT FWT BWTiYWT BWT+FWT BWT+YWT+FWT
YWT
+
BWT + w w T + FWT + BWT+WWT + BWT + WWT FWT + BWT + WWT + YWT + BWT+WWT + BWT + WWT
+ FWT
iYWT
."A
4
4
4
4
h2
m2
C2
8.02 8.04 8.54 8.27 8.49 7.52 8.43 145.9 152.3 128.3 161.0 156.4 152.5 156.2 102.0 142.2 129.8 116.0 148.8 149.8 357.5 501.7 474.5 396.8 402.6 500.2
1.97 1.86 1.86 1.54 1.67 1.71 1.98 102.6 101.3 131.2 181.1 131.0 130.9 164.3 45.9 42.8 102.8 63.3 112.2 97.7 78.7 86.6 212.2 72.3 214.1 215.6
1.74 1.73 1.78 1.21 1.81 2.05 2.20 146.5 156.7 126.0 70.7 144.6 117.3 124.4 25.1 32.7 56.8
6.86 6.88 6.61 6.78 6.75 6.39 6.58 357.5 362.3 375.4 357.5 372.7 353.7 372.4 338.0 317.2 396.6 340.9 378.4 369.1 572.0 497.1 604.2 571.9 568.5 596.7
18.59 18.51 18.78 18.80 18.73 17.66 19.19 752.5 772.5 760.9 770.2 804.7 754.3 817.3 511.1 534.9 685.9 520.2 701.9 677.4 1,008.3 1,085.3 1,290.9 1,041.0 1,185.2 1,312.4
.431 .434 ,455 ,440 ,454 ,426 ,439 ,194 ,197 ,169 ,209 ,194 ,202 ,191 .200 ,266 ,189 ,223 ,212 ,221 ,355 ,462 ,368 ,381 ,340 ,381
,106
.094 ,093 ,095 .065 ,097 ,116 ,115 ,195 ,203 ,166 ,092 ,180 .156 ,152 ,049 ,061 ,083
0.0 62.4 60.8
-
-
__ -
,101 .099 ,135 ,089 ,097 ,103 ,136 ,131 ,172 ,235 ,163 ,174 ,201 ,090 ,080 ,150 ,122 ,159 ,144 ,078 ,080 ,164 ,070 ,181 .164
,000 ,089 ,090 -
-
-
"u;: direct additive genetic variance, uk: maternal genetic variance, ug: permanent environmental variance, ug: residual variance, phenotypic variance, h2: direct heritability, m2: maternal heritability, and c2: permanent environmental maternal effect.
G;:
2620
MEYER ET AL.
Table 5. Estimates of variance components and genetic parametersa for Wokalups for birth (BWT),weaning (WWT), yearling (YWT), and final [FWT) weight from uni- and multivariate analyses Trait(s) BWT
+ + +
WWT YWT FWT
+ + +
WWT+YWT
WWT+FWT WWT+YWT+FWT
WWT
+
BWT
+
FWT BWT+YWT BWT+FWT BWT+YWT+FWT
+
m
+ + + YWT
+
BWT
+ w w T
+ + +
FWT BWT+WWT BWT + WWT
+ FWT
FWT
+
BWT + W W T
+ Y w T
+ +
BWT+WWT BWT + WWT
+ YWT
4
4
.“c
4
4
h2
In2
C2
14.63 14.99 15.01 15.10 14.99 14.50 14.78 209.5 244.0 221.9 211.4 258.1 231.9 226.3 123.9 203.5 319.6 146.7 322.6 262.3 429.4 662.6 786.2 507.0 762.6 698.7
1.52 1.58 1.38 1.51 1.53 1.73 1.04 49.4 45.9 101.8 58.1 97.2 68.7 84.0 60.7 59.9 119.6 58.0 115.7 115.0 47.0 37.6 105.9 44.6 110.8 97.0
1.21 1.19 1.39 1.14 1.55 1.12 1.50 85.3 80.1 33.8 69.1 33.0 64.7 35.4 -
11.02 10.86 10.82 10.83 10.73 10.95 10.95 420.1 419.4 430.9 424.3 442.3 436.7 454.3 477.6 454.6 510.5 465.8 514.1 516.5 905.3 820.7 922.3 884.0 914.4 1,045.3
28.39 28.61 28.61 28.58 28.80 28.30 28.28 764.3 789.5 788.4 762.8 830.7 802.2 800.0 662.1 718.0 949.7 670.6 952.4 893.8 1,381.7 1,520.8 1,814.5 1,435.6 1,787.9 1,841.1
,516 ,524 .525 .529 .521 .512 ,523 ,274 .309 ,282 ,277 ,311 ,289 .283 ,187 .284 ,337 .219 ,339 ,293 ,311 ,436 .433 ,353 ,427 .380
.054 .055 .048 ,053 .053 ,061 ,037 ,065 ,058 ,129 ,076 ,117 ,086 ,105 ,092 .083 ,126 .087 ,122 .129 ,034 ,025 ,058 ,031 ,062 ,053
,043 .042 ,049 ,040 .054 .040 .053 ,112 ,102 ,043 ,096 ,040 ,081 .044 -
-
-
-
-
-
-
-
-
-
-
4:
a& direct additive genetic variance, otf: maternal genetic variance, ug: permanent environmental variance, residual variance, phenotypic variance, h2: direct heritability, m2: maternal heritability, and c2: permanent environmental maternal effect.
0;:
Table 6. Estimates of direct genetic ( r A ) , maternal genetic (rM), maternal permanent environmental (rc), and phenotypic correlations between birth [BWT), weaning (WWT), yearling (YWT), and final (FWT) weight from bi-, tri-, and four-variate analyses Hereford
An.a
Trait
+ WWT
BWT
+
+
+
+m
+ +
+m
+ + WWT + YWT + + +
+ + YWT
+
FWT
+
FWT
2 3a 3b 4 2 3a 4 2 3b 4 2 3a 4 2 3b 4 2 4
rM
‘A
.693 ,714 .659 .703 .648 ,651 ,682 ,657 ,627 ,660 ,943 ,966 ,880 ,958 BO8 .923 1.000 .974
aAnalysis: 2 = bivariate, 3a = trivariate BWT
.476 ,508 ,345 ,414 ,722 .580 .442 1.000 .496 ,689 ,985 ,983 ,972 1.000 ,984 .916 ,859 ,918
+
WWT
Wokalup rP
‘C
,689 ,681 ,816 ,661 1.000 ,793 ,629 -
1.000 .985 .966 -
-
-
+ YWT,
‘A
.510 ,517 ,487 ,498 ,415 ,434 ,369 ,447 .356 .404 ,772 .774 ,755 ,699 ,641 ,645 ,727 ,722
3b = trivariate BWT
.735 ,745 .743 ,745 ,783 ,685 ,702 ,761 .706 ,720 .981 ,981 ,984 ,985 ,981 ,987 1.000 1.000
+
‘M
‘C
rP
,782 ,760 .743 ,705 ,987 ,813 .770 ,546 549 .421 1.000 ,996 ,995 1.000 ,967 ,881 .766 ,833
,386 ,372 ,366 ,384 -
,543 ,551 ,539 ,538 .519 ,511 ,499 .512 ,503 ,498 347 346 ,833 ,751 ,753 ,750 ,741 ,779
-
-
-
WWT + FWT, 4 = four-variate
262 1
COVARIANCES FOR GROWTH FOR BEEF CATTLE
Table 7. Phenotypic variances and correlation matrices for birth (BWT), weaning (WWT), yearling (YWTJ,and final (FWT) weight from four-variate analyses Hereford Trait
BWT
WWT
Wokalup
YWT
FWT
BWT
WWT
.38
.52 .75 .70 .72
.28 .98 .99
.16
.04 .71 .77 .42
YWT
FWT
Aa
BWT WWT YWT
FWT Mb BWT WWT YWT FWT CC BWT WWT YWT
.44 .70 .68 .66
.19 .88
.92
.10 .41 .44 .69
.20 .97 .92
.12 .66 .63
.15 .97
.22 .97
.14 .92
.29 1.00
.38
.13 .83
.05
893.8 .78
1,841.1
.10
.99 .88
.05 .38
.04
.09
Pd
BWT WWT YWT
FWT
19.3 .50 .37 .40
817.3 .76 .65
677.4 .72
1,312.4
28.3 .54 .50 .50
800.0
.83 .75
aDirect additive genetic effects: heritabilities on, correlations below the diagonal. bMaternal additive genetic effects: heritabilities on, correlations below the diagonal. ‘Maternal permanent environmental effects: “c-squared” effects on, correlations below the diagonal dPhenotypic effects: variances on, correlations below the diagonal.
were expected for multivariate analyses jointly with WWT or BWT than for univariate analyses or a bivariate analysis of YWT together with FWT. This could clearly be observed for 5;: estimates from univariate analyses and those from a bivariate analysis of YWT and FWT were very similar and consistently lower than estimates from the remaining analyses. Values for 3; from bivariate analyses with BWT were somewhat increased, whereas corresponding estimates from analyses with WWT were of similar magnitude to those from tri- or four-variate analyses. This reflected the fact that WWT contained most of the information determining selection. A similar pattern emerged for the additive genetic variances although it was not quite as consistent, presumably again attributable to sampling. Although little systematic differences in heritability estimates could be noted, estimates of h2 for YWT and FWT from four-variate analyses were higher than their univariate counterparts. Furthermore, estimates of m2 for WWT; W T ; and FWT were higher for the four-variate analyses, but for WWT this was associated with a corresponding decrease in e2 (i.e., to some extent at least again explicable by sampling variation in the partitioning of the overall variance). Estimates of correlations from the various analyses are given in Table 6. Considering three or all four traits together generally tended to “smooth out” extreme or implausible correlation estimates from bivariate analyses. Otherwise, there was good agreement between corresponding estimates from different analyses, suggesting that even with a search in more
than 30 dimensions, the maximum of the likelihood had been located with reasonable accuracy. Selection bias generally affected correlation estimates markedly less than heritabilities or variance components and correlations were subject to considerably larger sampling errors, so no systematic differences between estimates from bivariate and three- or four-variate analyses could be observed. Table 7 gives the complete correlation matrices from analyses considering all four traits simultaneously. As in previous studies (Meyer, 1993a,b), estimates of the maternal genetic ( r M ) and permanent environmental (rc) correlations among WWT, YWT, and FWT were essentially unity. Similarly, estimates of the direct genetic correlations ( r A ) between these traits were consistently high, especially for Wokalups. Estimates of r A between BWT and the other traits were with approximately .7 higher than those for Polled Herefords (Meyer, 199313) and Simmentals (Swalve, 1993) from field data but were comparable to results from an experimental Angus herd (Meyer, 1993a). Corresponding values for r M were, except for FWT, higher for Wokalups than for Herefords, whereas estimates of rc were higher for the latter, again reflecting the differing importance of the components of maternal performance in the two breeds.
Discussion Results strengthened the evidence for breed differences in the importance and mode of action of
2622
MEYER ET AL.
maternal effects for the early growth of beef calves. Except for FWT, estimates of direct heritabilities were higher in the multibreed Wokalups than in the purebred Herefords, suggesting that formation of a synthetic indeed increased the amount of additive genetic variation among animals available and thus the scope for selection. In contrast to many other studies, especially those based on field data, direct-maternal genetic correlation estimates were low and generally not significantly different from zero. This supported earlier speculations that large, negative estimates of rm found in numerous analyses did not reflect a marked adverse genetic relationship between growth and maternal performance but were due to management practices or environmentally induced negative damoffspring covariances. Estimates of maternal correlations between WWT, YWT, and FWT clearly identified maternal effects found for postweaning weights as a carry-over effect of those on WWT through a part-whole relationship. This implies that with appropriate scaling, a joint maternal effect (one each for genetic and permanent environmental effects) could be fitted in a multivariate genetic evaluation to account for the maternal influence on WWT, YWT, and FWT. Comparing estimates from uni- and various multivariate analyses demonstrated the effect of selection on estimates of variance components and genetic parameters for YWT and FWT. Estimates from bivariate analyses of YWT or FWT together with WWT were similar to those from trivariate analyses including BWT as well or analyses of all four traits simultaneously, indicating that WWT contained most information determining selection decisions. Although four-variate analyses fitting two maternal effects and thus involving close to 40,000 equations, and estimating up to 34 highly correlated covariance components simultaneously, proved feasible, their computational demands were excessive and, at present, they seem unsuitable for routine applications.
Implications Estimates of direct genetic correlations between weaning and later weights were close to unity, identifying the former as a suitable criterion in selecting for growth. Maternal effects till weaning were found to “carry over” to yearling weight and, to a lesser extent, final weight, and should be taken into account in genetic evaluation schemes for these traits. Levels of phenotypic variability and of direct additive
genetic variation in the multibreed synthetic line (Wokalups) were higher than in the purebred line (Polled Herefords), especially for growth till weaning. In addition, no antagonistic relationship between direct and maternal effects could be observed for the synthetic line. This suggests increased scope for selection in a crossbred population.
Literature Cited Baker, R. L. 1980. The role of maternal effects on the efficiency of selection in beef cattle. Proc. N. Z. SOC.Anim. Prod. 40:285. Boldman, K. G., L. D. Van Vleck, K. E. Gregory, and L. V. Cundiff. 1991. Estimates of direct and maternal parameters for 200 d weight in purebred and composite lines of beef cattle. J . Anim. Sci. 69rSuppl. 1):203 (Abstr.). Cundiff, L. V. 1972. The role of maternal effects in animal breeding: VIII. Comparative aspects of maternal effects. J. Anim. Sci. 35: 1335. Gregory. K. E., L. V. Cundiff, and R. M. Koch. 1992. Effects of breed and retained heterosis on milk yield and 200-day weight in advanced generations of composite populations of beef cattle. J. Anim. Sci. 70:2366. Kinghorn, B. P. 1982a. Genetic effects in crossbreeding. I. Models of merit. Z. Tierz. Zuechtungsbiol. 99:59. Kinghorn, B. P. 198210. Genetic effects in crossbreeding. 11. Multibreed selection indices. Z. Tierz. Zuechtungsbiol. 99:315. Koch, R. M. 1972. The role of maternal effects in animal breeding: VI. Maternal effects in beef cattle. J. Anim. Sci. 35:1316. Meyer, K. 1989. Restricted Maximum Likelihood t o estimate variance components for animal models with several random effects using a derivative-free algorithm. Genet. Sel. Evol. 21:317. Meyer, K. 1991a. Estimating variances and covariances for multivariate Animal Models by Restricted Maximum Likelihood. Genet. Sel. Evol. 23:67. Meyer, K. 1991b. DFREMLVersion 2.0 - Programs to Estimate Variance Components by Restricted Maximum Likelihood Using a Derivative - Free Algorithm. User Notes. Animal Genetics and Breeding Unit, University of New England, Armidale NSW (Mimeoj. Meyer, K. 1992a. Variance components due to direct and maternal effects for growth traits of Australian beef cattle. Livest. Prod. Sci. 31:179. Meyer, K. 1992b. Bias and sampling covariances of estimates of variance components due to maternal effects. Genet. Sel. Evol. 24:487. Meyer, K. 1993a. Estimates of direct and maternal correlations among growth traits in Australian beef cattle. Livest. Prod. Sci. ( I n press). Meyer, K. 1993b. Covariance matrices for growth traits of Australian Polled Hereford cattle. h i m . Prod. ( I n pressi. Schneeberger, M., B. Tier, and K. Hammond. 1991. Introducing the third generation of BREEDPLAN and GROUPBREEDPLAN. Proc. 9th Conf. of the Aust. Assoc. Anim. Breed. Genet., Melbourne. Swalve, H. H. 1993. Estimation of direct and maternal (colvariance components for growth traits in Australian Simmental beef cattle. J. Anim. Breed. Genet. ( I n press). Waldron, D. F., C. A. Morris, R. L. Baker, and D. L. Johnson. 1993. Maternal effects for growth traits in beef cattle. Livest. Prod. Sci. 34:57.
