Sire x Herd Interactions for Weaning Weight in Beef Cattle D. R. Notterl, B. Tier, and K. Meyer
Animal Genetics and Breeding Unit, Armidale, NSW,
adjustment for dam MBV yielded the smallest estimates of interaction variance and across-herd heritability. If sire x herd interactions were due only to genotype x environment interaction, within-herd heritabilities would range from .33 to .49. These estimates are larger than previously reported estimates. Thus, unreported environmental effects common to progeny of individual sires may also be involved in the observed interaction but could not be disentangled from true genotype x environment interaction effects using these data. Results of these analyses suggest that some accommodation of sire x herd interaction effects on weaning weight may be needed in beef cattle genetic evaluations, but a compelling case for development of herd-specific breeding value prediction cannot be made.
Key Words: Cattle, Breeding Value, Genotype Environment Interaction, Growth, Heritability J. Anim. Sci. 1992. 70:2359-2365
Introduction Studies of genotype x environment interaction for weaning weight using beef cattle field data have generally involved estimation of sire x environment variance components by analysis of variance techniques (Buchanan and Nielsen, 1979; Tess et al., 1979; Bertrand et al., 1985, 1987). Environmental factors that have been considered include regions, herds, and contemporary groups. In most cases, sire x region interactions have not been significant, whereas sire x herd interactions consistently have been large and significant. How-
'This research was conducted while the senior author was on study-research leave from the Anim. Sci. Dept., Virginia Polytechnic Inst. and State Univ., Blacksburg. 2The Animal Genetics and Breeding Unit is a joint unit of the Wniv. of New England and the NSW Dept. of Agric. 3The authors express appreciation to the Meat Res. Corp. of Australia for funding under project UNE.015. Received September 3, 1991. Accepted March 19, 1992.
ever, analysis of variance techniques are not optimal for variance component estimation from field data, and apparent variation due to sire x herd interaction can arise from heterogeneity of residual and(or1 additive genetic variance among herds (Dickerson, 19621, from use of small numbers of selected sires, from differential nonrandom mating among herds, or from preferential treatments of some paternal half-sib groups. In American Polled Hereford cattle, Bertrand et al. (1985) used data from relatively large numbers of sires (87 to 373) and still observed sire x herd variance components for weaning weight that approached or exceeded the between-sire variance component. However, these and other large sire x herd variance components have been met with some scepticism, especially in light of the apparently modest levels of sire x environment interaction observed in designed experiments (Mahrt et al., 1990; Notter and Cundiff, 1991) and in field-data analysis using different methodologies to evaluate sire x sex and sire x breed of dam interactions (Garrick et al., 1989). The purpose of this study
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ABSTRACT: Weaning weight records of 44,357 Australian Angus calves produced by 1,020 sires in 90 herds were used to evaluate the importance of sire x herd interactions. Models fitted fixed effects of contemporary group (herd-year-date of weighing subclass), sex, calf age, and dam age and random effects of sire or of sire and sire x herd interaction using REML. Effects of standardizing the data, including sire relationships and including dam maternal breeding values (MBV) as a covariate were also investigated. Sire x herd interactions were found ( P < .05)in all cases and, in the most complete model, accounted for 3.3% of phenotypic variance. Across-herd heritabilities ranged from .19 to .28. Differential nonrandom mating among herds seemed to occur in the data. Significant sire x herd effects were observed for dam MBV, and
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was, thus, to evaluate sire x herd interactions for weaning weight in beef cattle using REML.
Materials and Methods
ing for maternal breeding values (BVI of the dam (Analysis 4). Standardization was performed to remove potential heterogeneity among herds in phenotypic variance and was achieved by deviating records from the phenotypic mean of the herd and dividing by the within-herd residual standard deviation, which had been obtained after fitting fixed effects of contemporary group, calf age, and dam age for each herd. Sire relationships considered only relationships defined through common paternal grandsires. Inclusion of dam effects in the analytical model was desirable to remove effects of nonrandom mating, but available software allowed consideration of only two random effects. As a n alternative, maternal effects of the dam were incorporated using within-herd estimates of total maternal BV calculated as the sum of the net maternal (milk) BV plus half the additive direct BV for weaning weight. These maternal BV were deviated from the mean dam maternal BV for each herd and included as a continuous linear effect in the analysis. Concern about the selection of connecting sires and about the accuracy of data recording and contemporary group assignment led to an analysis of two subsets of the data (Table 1). Analysis 5 repeated Analysis 1 using data on only the 19,315 progeny of connecting sires. This analysis ensured that sire and sire x herd variance componetns would be derived from the same set of sires. Analyses 6 and 7 repeated Analyses 3 and 4, respectively, using records on 17,900 calves from 25 herds that were considered to practice exemplary data recording and reporting. Although this categorization was subjective, it allowed some consideration of the effect of quality of data recording on estimates of the sire x herd interaction.
Results Data Structure. Estimates of sire x herd interaction variances arise from comparisons of the relative performance of sires in different herds. Thus, the extent and nature of sire connections among herds may influence the precision of estimates of sire x herd interaction from field data. In designed experiments, random assignment of sires to herds and some degree of balance in these assignments can be assured, but this is not the case in field data. The 44,357 records for Analyses 1 through 4 came from 90 herds with 4 to 2,059 records per herd. Of the 1,020 sires, 263 had progeny in more than one herd; 180 were connecting sires (five or more progeny in two or more herds), 126 had 10 or more progeny in two or more herds, and 74 had 20 or more progeny in two or more herds. Individual
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Data for the study were 83,045 weights taken between 100 and 300 d of age on Angus cattle recorded in Australia’s National Beef Recording Scheme. Calves were born in 1972 through 1990. Initial edits removed calves born after embryo transfer or in multiple births, not reared by their genetic dam, not weighed in the same herd in which they were born, lacking dam age or sire information, or not born in a herd participating in the across-herd genetic evaluation program. Animals whose dams calved at < 20 or > 215 mo and those appearing in single-sire contemporary groups (contemporary group = herd-year-date of weighing subclass) were also deleted, leaving 65,186 records. At this point, 180 sires with progeny in 90 herds were designated as “connecting” sires; each had five or more progeny in each of two or more herds. Contemporary groups with no connecting sires were deleted, leaving 49,678 records representing 1,360 sires. Final edits removed progeny of sires with less than five total progeny, progeny of sires represented in only one contemporary group, repeated records for calves weighed more than once (the weight taken closest to 200 d was retained), records outside the range of 55 to 515 kg, and any newly created single-sire contemporary groups, leaving 44,357 records representing 1,020 sires. Of the sires, 263 (including the 180 connecting sires) had progeny in more than one herd. Data were analyzed using REML procedures described by Smith and Graser (1986) and Meyer (1987). The initial analysis (Analysis 1) included fixed effects of herd, contemporary group (nested within herd), and sex [heifer, bull, or steer); continuous linear and quadratic effects of calf age (days) and dam age (months); and random effects of sire or of sire and sire x herd interaction. Effects of interaction were tested by comparing log likelihoods of models that included the sire x herd interaction to those that included only sire effects (Meyer, 19871. Variance component estimates from analyses including both sire and interaction effects were used to estimate heritabilities within herds (as four times the ratio of sire plus sire x herd interaction variance to phenotypic variance) and across herds (as four times the ratio of sire to phenotypic variance). These heritability estimates were compared to that derived from a model with sire as the only random effect. Analysis 1 was subsequently modified (Table 1) by standardizing the data analysis 21, including relationships among sires (Analysis 31, and adjust-
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Table 1. Definition of analyses No. of Analysis
Observations
Sires
Herds
Description ~~~~~
1,020 1,020 1,063 1,063 180 503 503
~~
All observations; no relationships among sires; no dam effect Analysis 1 with standardized data Analysis 1 plus sire relationships Analysis 3 plus regression on dam total maternal breeding value Analysis 1 with data only on progeny of connecting sires Analysis 3 with data from selected herds Analysis 4 with data from selected herds
90 90 90 90 90 25 25
sires had a n average of 43.5 progeny. Connecting sires had a n average of 107.3 progeny and appeared a s connecting sires in a n average of 3.7 herds. Individual connecting sires appeared in 2 to 34 herds; 41% appeared in more than two herds, but only 14% appeared in more than five herds. Of the 90 herds, 57 had each used 10 or more connecting sires. There were 1,851 sire-herd subclasses, representing 2 % of the possible number of such subclasses. All herds were tied to one another through common use of connecting sires. Of the total 1,405 contemporary groups, 61% contained progeny of two or more connecting sires, and these contemporary groups contained 80% of the total records. The mean contemporary group size was 31.6; 2 0 % of contemporary groups had > 50 records and 4 % had > 100 records, but 23% contained e 10 calves and 12% contained less than five calves.
Fixed Effects Fixed-effect solutions were derived from Analysis 4, the most complete analysis. The phenotypic mean for weaning weight was 232.6 kg with a
residual standard deviation after adjusting for fixed effects of 22.1 kg. Effects of sex, calf age, and dam age were all highly significant. Sex differences, relative to heifers, were +24.3 kg for bulls and +12.2 kg for steers, corresponding to multiplicative adjustment factors of .901 and .951. The mean weaning age was 213.9 d with a standard deviation of 33.8 d. Weaning weight increased at a decreasing rate as calf age increased; the linear effect of age decreased from .94 kg/d a t 125 d to .80 kg/d at 200 d and 6 6 kg/d a t 275 d. The mean dam age was 63.4 mo. Weaning weight (W) was maximum at a dam age (D)of 96.4 mo and was predicted a s W = 189.8 + 1.007 D -.005222 D2.
Variance Components Base AnaZysis. Variance component estimates are shown in Table 2. For Analysis 1, when sire was the only random factor, the heritability estimate was .390. This estimate is higher than most of the estimates of heritability of weaning weight summarized by Woldehawariat et al. (19771 or Meyer (1992) but is within the range of the REML estimates of .23 to .39 reported by Garrick
2 Table 2. Estimates of sire (oi), interaction (oSxH), and error (ai)variance components, overall (h2),
between- (h:), and within-herd (hk) heritabilities, and log likelihoods for weaning weight [ kg] from different analyses Sire model
1 2c 3 4d 5 6 7d
52.3 ,101 64.8 43.0 41.9 65.9 48.9
Interaction model Log likelihood
Log likelihood
4
h2
484.2 ,910 483.8 338.6 515.2 459.2 323.6
,390 -156,998 ,400 -22,216 ,472 -156,986 ,451 (.324) -149,308 ,301 -86,528 .502 -83,073 .525 c.3831 -60,045
31.2 ,058
38.4 25.9 24.7 37.3 28.0
27.9 .053 27.2 17.9 35.1 26.1 17.7
479.0 .902 478.8 335.2 506.7 456.1 321.8
-156,914 ,052 ,439 .232 -22,173 ,052 ,438 .229 -156,913 .050 ,482 .282 ,273 (.192) ,047 (.033) ,462 [.326)-149,241 ,422 -66,486 ,062 .174 -63,053 .OS0 ,488 ,287 ,304 (.216) .048 (.034) ,498(.351) -60,026
~
&See Table 1 for definition of analyses. bRatio of interacti0n:phenotypic variance. ?3andardized data. dValues in parentheses for models including regression on dam maternal BV assume that phenotypic variance includes the mean square due to regression on maternal BV.
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44,357 44,357 44,357 44,357 19,315 17,900 17,900
~~
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the sire-model estimate of .472 were above the range of generally accepted values. The very high withinherd heritability estimates suggest that at least some of the enhanced within-herd resemblance among half-sibs was likely due to common environmental effects. Effect o f Dam Maternal Breeding Value. Dam maternal BV were not available for 822 of the 44,357 records (1.9%). In particular, maternal BV were not available for 4 of the 90 herds representing 813 records. Because maternal BV were deviated from herd means before analysis, all values for herds with completely missing data were set to zero, whereas the remaining nine records with missing data had maternal BV set to the respective herd mean. The resulting deviated maternal BV had a standard deviation of 5.2 kg. The regression of weaning weight on maternal BV was 2.69 ~tr .20 kg/kg. A relatively large regression coefficient is expected when comparing observed weaning weights to regressed BV derived from them, although a n exact expectation for the regression coefficient is not readily derivable. If these BV were used to predict future weaning weights not used in their derivation, the expected value of the regression coefficient would be 1.0 in the absence of a maternal BV x environment interaction. The inclusion of maternal BV as a covariate (Analysis 4 in Table 21 reduced the residual mean square due to removal of a portion of the total maternal genetic variance. However, this source of variation would have remained as a component of the phenotypic variance in sire-dam models. The mean square due to regression on maternal BV was 146.9kg2, and if this value is added to the sire, interaction, and error components for Analysis 4, the resulting sum of 525.9 kg2 is relatively close to the estimate of phenotypic variance of 544.4 kg2 from Analysis 3. This result suggests that the variance due to regression seems to be a reasonable approximation to the estimate of the total maternal genetic variance accounted for by dam maternal BV. Heritability estimates in Table 2 in parentheses were, therefore, calculated assuming a phenotypic variance of 525.9 kg2. When variance due to regression on maternal BV was included in the phenotypic variance, the sire x herd interaction component of variance was reduced to 3.3% of phenotypic variance. The sire component of variance was also reduced by this adjustment, however, and the ratio of interaction to sire variance was approximately .70 for both Analyses 3 and 4. Both within- and across-herd heritability estimates were within the range of values that have been previously reported, but the within-herd estimates remained substantially greater than the across-herd estimate. The withinherd heritability estimate of .326 from Analysis 4
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et al. (19891 from application of sire and sirematernal grandsire models to American Simmental data. Inclusion of sire x herd interaction effects substantially reduced the sire component. The across-herd heritability was reduced to .232, which was more similar to previously reported values. The sire x herd interaction component was 5.2% of the phenotypic variance (P e .05). If the resemblance among half-sibs in the same herd was due to sire additive genetic effects plus genotype x environment interaction effects, the within-herd heritability estimate would be .439.However, if a portion of the resemblance among half-sibs within a herd was due to correlated treatment of progeny of some sires, the within-herd heritability estimates would be correspondingly lower. Effect o f Standardization. Standardization of weaning weights using within-herd residual standard deviations had essentially no effect on the magnitude of the sire x herd interaction (Table 2). Across- and within-herd heritability estimates were .299 and .438,little different from estimates based on unstandardized data. The mean residual standard deviation was 23.6 kg with a range of 14.4 to 31.8 kg. However, little evidence of scaling Ke., proportionality of mean and standard deviation across herds; Dickerson, 19621 was observed. The correlation among herds between residual standard deviation and mean weaning weight (adjusted for sex, calf age, and dam age) was .02. Effect of Sire Relationships. Sire information was available for 989 of the 1,020 sires represented in the data. Of these, 673 were sired by 188 bulls that also had progeny in the data (i.e., 188 bulls were represented as both sires and paternal grandsires in the datal. An additional 96 sires were sons of 43 sires that had no progeny in the data but had grandprogeny in the data by more than one son. The remaining 220 bulls had known sires, but these sires had only one son in the data and, therefore, contributed no useful pedigree information. Thus, the number of sires considered in the analysis was increased by 43 to 1,063 when sire relationships were included. Inclusion of sire relationships analysis 3 in Table 21 increased the sire component of variance regardless of whether a n interaction component was also fitted. This increase was expected because inclusion of relationships recognized that the observed variance among a group of related sires is expected to be lower than that anticipated for a group of unrelated sires. However, the sire x herd interaction was not changed by inclusion of sire relationships; it remained at 5.0% of phenotypic variance. Heritability estimates for Analysis 3 were substantially higher than those for Analysis 1. The across-herd heritability estimate of .282 was within the range of previously reported values, but the within-herd estimates of .480 and
SIRE x HERD INTERACTIONS FOR WEANING WEIGHT
tively, were repeated using data from these herds. Variance components were very similar to those obtained from the overall data set. Thus, these subjectively selected herds seemed equally liable to expression of sire x herd interaction.
Discussion Sire x herd interaction components for weaning weight in these data were consistently large and significant, ranging from 63 to 91% of the sire component and from 3.3 to 6.2% of the phenotypic variance. Standardization of data, inclusion of sire relationships, or restriction to selected subsets of the data had little effect on the interaction component of variance. Differential nonrandom mating seemed to occur among herds and to account for perhaps one-third of the observed sire x herd interaction variance, but significant levels of interaction remained after adjustment for dam maternal BV. The sire x herd interaction, thus, seemed to account for a minimum of 3.3% of the phenotypic variance. Results of this study corresponded closely to those reported in a number of U.S. studies. In particular, Bertrand et al. (1985) reported sire x herd interaction variance components for weaning weight that approximately equaled the observed sire variances in Polled Hereford cattle. In that study, and in that of Tess et al. (19791, the sire x herd variance component accounted for 2.2 to 4.0% of the phenotypic variance. Previous estimates of sire x herd interaction variances have been derived primarily by analysis of variance techniques and often with limited numbers of connecting sires, Yet results were close to those observed in the current study. Models such as those used for this study cannot identify the source of observed sire x herd interaction. As pointed out by Meyer (19871, sire plus interaction models cannot discriminate between heightened resemblances among half-sibs within the same herd arising from genotype x environment interaction and those arising from common environmental effect within half-sib families. Within-herd heritability estimates in this study were generally larger than those previously reported and would suggest that common environmental effects were at least a partial component of the observed sire x herd interaction. However, when dam maternal BV was considered in the analysis, both the within- and across-herd heritability estimates were within the range of previously reported values. Also, the sires evaluated in this study included a number of imported sires. Of the 1,020 sires, herd or origin was reported for 955. Of these, 23 were from Canada, 47 were from New Zealand, 4 were
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agreed closely with the average within-herd heritability of weaning weight of .31 reported by Woldehawariat et al. (19771 from a number of designed studies. This correspondence suggests that the sire x herd variance component from Analysis 4 after adjusting for dam maternal BV may be a reasonable indicator of the true magnitude of genotype x environment interaction in these data. The reductions in sire and interaction variances observed for Analysis 4 suggested that nonrandom mating, and in particular differential nonrandom mating among herds, may have contributed to the relatively high heritability estimates observed in earlier models. To test this hypothesis, sire and sire x herd interaction variance components for dam maternal BV were calculated to assess sire variation in mates’ BV. The model used in Analysis 1 was applied to maternal BV data but without adjustment for calf sex or age or cow age. When interaction was ignored, the sire component accounted for 5.2% of the variance in maternal BV of the sires’ mates (P > .lo). Use of an interaction model reduced the across-herd sire component to 1.8% of the phenotypic variance, whereas the sire x herd interaction component accounted for 4.0% of variance (P < .05). Thus, differential nonrandom mating seemed to occur in the data and contributed to, but was not the sole source of, sire x herd interactions. Effects of Restricting the Data Set. The connecting sires likely represented a selected subset of the entire population of sires. Thus, the additive genetic variance among connecting sires may be less than that among all sires. Such selection is not expected to bias variance component estimates if the records upon which selection was based are included in the data (Henderson, 19751; however, a number of the connecting sires were imported or not bred within participating herds, so this assumption was not necessarily met. In response to this situation, Analysis 5 was conducted using only data from progeny of connecting sires. Sire variance components and corresponding overall and across-herd heritability estimates were lower than those for Analysis 1, suggesting that these sires were indeed a selected group. However, the interaction component was 26% larger than that observed in Analysis 1, implying that observed interactions were not associated with differences in additive genetic variance between sires used across versus within herds. Failure to report adequately the environmental differences among sires’ progeny may lead to sire x herd interactions, as may any form of preferential treatment of half-sib groups within herds. Analyses 6 and 7 used data from 25 herds subjectively chosen based on their greater experience and apparent commitment to accurate data recording and reporting. Analyses 3 and 4, respec-
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the seedstock herd is more similar to the customer environments than to the environments of other seedstock herds, a situation that in most cases seems unlikely. The use of herd-specific BV would be justified, then, only when commercial enterprises are maintained in the same environment as the seedstock herd. Based on data from the current analysis, some accommodation of sire x herd effects on weaning weight in beef herds seems to be needed, but a compelling case for development of herd-specific BV prediction procedures cannot be made. With rare potential exceptions, BV prediction should concentrate on estimation of mean BV across a n array of herds but with continued efforts to identify more precisely the source of the observed sire x herd interactions.
Implications Half-sib progeny of Angus sires produced within the same herd are more similar in weaning weight than half-sib progeny of the same sires in different herds, even after adjustment for all known cornmon environmental factors. This heightened resemblance may arise from interactions of sire breeding value with environmental factors unique to each herd or from unreported environmental factors that are common to progeny of individual sires within a herd. In either case, these results suggest that accurate across-herd evaluation of sires will require that the sires produce progeny in a number of herds.
Literature Cited Bertrand, J. K., P. J. Berger, and R. L. Willham. 1985. Sire x environment interactions in beef cattle weaning weight field data. J. Anim. Sci. 60:1396. Bertrand, J. K., J. D. Hough, and L. L. Benyshek. 1987. Sire x environment interactions and genetic correlations of sire progeny performance across regions in dam-adjusted field data. J. Anim. Sci. 64:77. Buchanan, D. S., and M. K. Nielsen. 1979. Sire by environment interactions in beef cattle field data. J. Anim. Sci. 48:307. Dickerson, G. E. 1902. Implications of genetic-environmental interaction in animal breeding. Anim. Prod. 4:47. Foulley, J. L., and C. R. Henderson. 1989. A simple method to deal with sire x treatment interactions when sires are related. J. Dairy Sci. 72:167. Gamck, D. J., E. J. Pollak, R. L. Quaas, and L. D. Van Vleck. 1989. Variance heterogeneity in direct and maternal weight traits by sex and percent purebred for Simmental-sired calves. J. h i m . Sci. 67:2515. Henderson, C. R. 1975. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423. Mahrt, G. S., D. R. Notter, W. E. Bed, W. H. McClure, and L. G. Bettison. 1990. Growth of crossbred progeny of Polled Hereford sires divergently selected for yearling weight and maternal ability. J. Anim. Sci. 68:1889. Meyer, K. 1987. Estimates of variances due to sire x herd interactions and environmental covariances between paternal
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from the United Kingdom, and 32 were from the United States. Other bulls may have had imported sires. Thus, genetic variance for weaning weight may be larger in this population than in populations with lower use of imported sires. Various genetic grouping strategies (Quaas and Pollak, 1981) could have been used to restrict estimates of genetic variances to within-group values. However, we chose to attempt to estimate the overall additive genetic variance within the population (regardless of source) and, thus, did not include genetic groups in the models. If additive genetic variance is homogeneous among herds, the average genetic correlation between performance in different herds can be estimated as the ratio of sire variance to the sum of sire plus interaction variance (Dickerson, 1962; Yamada, 1962). Herd sizes in this study were too small to allow definitive testing of homogeneity of additive genetic variances among herds, but under the assumption of homogeneity, estimates of the genetic correlation would range from .52 to .61 (excluding the selected data of Analysis 5). Again, these small values suggest that interaction is likely not due to genotype x environment interaction alone. The response to sire x herd interactions in national genetic evaluation programs depends on the assumed source of the interaction and on the goals of the evaluation program. If interactions arise only from common environmental effects, sire x herd effects may be included in analytical models to limit the accuracy of genetic evaluation that can be achieved for animals with individual and(or1 relatives’ records in only one herd (Meyer, 19871, but sire x herd interaction predictions should not be considered in making selection decisions. For example, sire x herd interactions have been observed for milk production in Friesian populations (Meyer, 1987) and have been included in analytical models for U.S. dairy sire and cow evaluations [Wiggans et al., 19881, but interaction equations are generally absorbed before prediction of the average across-herd BV for each animal. Within-herd interaction constants are assumed independent, even if sires are related, whereas Foulley and Henderson (1989) have noted that interaction constants for related sires within a herd should be correlated if interaction arises from genotype x environment interaction. If sire x herd interactions are manifestations of genotype x environment interactions, the potential to predict herd-specific BV exists but will be appropriate only under very specific circumstances. In most seedstock herds, the breeding objective is improvement of BV in a n array of commercial customer herds. Selection for improvement in the specific environment of the seedstock herd is thus warranted only if the environment of
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Tess, M. W., D. D. Kress, P. J. Burfening, and R. L. Friedrich. 1979. Sire by environment interactions in Simmental-sired calves. J. Anim. Sci. 49:964. Wiggans, G. R., I. Misztal, and L. D. Van Vleck. 1988. Implementation of a n animal model for genetic evaluation of dairy cattle in the United States. J. Dairy Sci. 7lLSuppl. 2):54. Woldehawariat, G., M. A. Talamantes, R. R. Petty, Jr., and T. C. Cartwright. 1977. A summary of genetic and environmental statistics for growth and conformation characters of beef cattle, second edition. Texas Agric. Exp. Sta. Tech. Rep. No. 103, College Station. Yamada, Y.1962. Genotype x environment interaction and genetic correlation of the same trait under different environment. Jpn. J. Genet. 37:498.
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half-sibs for first lactation dairy production. Livest. Prod. sci. 17:95. Meyer, K. 1992. Variance components due to direct and maternal effects for growth traits of Australian beef cattle. Livest. Prod. Sci. (In press]. Notter, D. R., and L. V. Cundiff. 1881. Across-breed expected progeny differences: Use of within-breed expected progeny differences to adjust breed evaluations for sire sampling and genetic trend. J. Anim. Sci. 69:4783. Quaas, R. L., and E. J. Pollak. 1982. Modified equations for sire models with groups. J. Dairy Sci. 64:1868. Smith, S. P., and H.-U. Graser. 1986. Estimating variance components in a class of mixed models by restricted maximum likelihood. J. Dairy Sci. 69:1156.
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adjustment for dam MBV yielded the smallest estimates of interaction variance and across-herd heritability. If sire x herd interactions were due only to genotype x environment interaction, within-herd heritabilities would range from .33 to .49. These estimates are larger than previously reported estimates. Thus, unreported environmental effects common to progeny of individual sires may also be involved in the observed interaction but could not be disentangled from true genotype x environment interaction effects using these data. Results of these analyses suggest that some accommodation of sire x herd interaction effects on weaning weight may be needed in beef cattle genetic evaluations, but a compelling case for development of herd-specific breeding value prediction cannot be made.
Key Words: Cattle, Breeding Value, Genotype Environment Interaction, Growth, Heritability J. Anim. Sci. 1992. 70:2359-2365
Introduction Studies of genotype x environment interaction for weaning weight using beef cattle field data have generally involved estimation of sire x environment variance components by analysis of variance techniques (Buchanan and Nielsen, 1979; Tess et al., 1979; Bertrand et al., 1985, 1987). Environmental factors that have been considered include regions, herds, and contemporary groups. In most cases, sire x region interactions have not been significant, whereas sire x herd interactions consistently have been large and significant. How-
'This research was conducted while the senior author was on study-research leave from the Anim. Sci. Dept., Virginia Polytechnic Inst. and State Univ., Blacksburg. 2The Animal Genetics and Breeding Unit is a joint unit of the Wniv. of New England and the NSW Dept. of Agric. 3The authors express appreciation to the Meat Res. Corp. of Australia for funding under project UNE.015. Received September 3, 1991. Accepted March 19, 1992.
ever, analysis of variance techniques are not optimal for variance component estimation from field data, and apparent variation due to sire x herd interaction can arise from heterogeneity of residual and(or1 additive genetic variance among herds (Dickerson, 19621, from use of small numbers of selected sires, from differential nonrandom mating among herds, or from preferential treatments of some paternal half-sib groups. In American Polled Hereford cattle, Bertrand et al. (1985) used data from relatively large numbers of sires (87 to 373) and still observed sire x herd variance components for weaning weight that approached or exceeded the between-sire variance component. However, these and other large sire x herd variance components have been met with some scepticism, especially in light of the apparently modest levels of sire x environment interaction observed in designed experiments (Mahrt et al., 1990; Notter and Cundiff, 1991) and in field-data analysis using different methodologies to evaluate sire x sex and sire x breed of dam interactions (Garrick et al., 1989). The purpose of this study
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ABSTRACT: Weaning weight records of 44,357 Australian Angus calves produced by 1,020 sires in 90 herds were used to evaluate the importance of sire x herd interactions. Models fitted fixed effects of contemporary group (herd-year-date of weighing subclass), sex, calf age, and dam age and random effects of sire or of sire and sire x herd interaction using REML. Effects of standardizing the data, including sire relationships and including dam maternal breeding values (MBV) as a covariate were also investigated. Sire x herd interactions were found ( P < .05)in all cases and, in the most complete model, accounted for 3.3% of phenotypic variance. Across-herd heritabilities ranged from .19 to .28. Differential nonrandom mating among herds seemed to occur in the data. Significant sire x herd effects were observed for dam MBV, and
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was, thus, to evaluate sire x herd interactions for weaning weight in beef cattle using REML.
Materials and Methods
ing for maternal breeding values (BVI of the dam (Analysis 4). Standardization was performed to remove potential heterogeneity among herds in phenotypic variance and was achieved by deviating records from the phenotypic mean of the herd and dividing by the within-herd residual standard deviation, which had been obtained after fitting fixed effects of contemporary group, calf age, and dam age for each herd. Sire relationships considered only relationships defined through common paternal grandsires. Inclusion of dam effects in the analytical model was desirable to remove effects of nonrandom mating, but available software allowed consideration of only two random effects. As a n alternative, maternal effects of the dam were incorporated using within-herd estimates of total maternal BV calculated as the sum of the net maternal (milk) BV plus half the additive direct BV for weaning weight. These maternal BV were deviated from the mean dam maternal BV for each herd and included as a continuous linear effect in the analysis. Concern about the selection of connecting sires and about the accuracy of data recording and contemporary group assignment led to an analysis of two subsets of the data (Table 1). Analysis 5 repeated Analysis 1 using data on only the 19,315 progeny of connecting sires. This analysis ensured that sire and sire x herd variance componetns would be derived from the same set of sires. Analyses 6 and 7 repeated Analyses 3 and 4, respectively, using records on 17,900 calves from 25 herds that were considered to practice exemplary data recording and reporting. Although this categorization was subjective, it allowed some consideration of the effect of quality of data recording on estimates of the sire x herd interaction.
Results Data Structure. Estimates of sire x herd interaction variances arise from comparisons of the relative performance of sires in different herds. Thus, the extent and nature of sire connections among herds may influence the precision of estimates of sire x herd interaction from field data. In designed experiments, random assignment of sires to herds and some degree of balance in these assignments can be assured, but this is not the case in field data. The 44,357 records for Analyses 1 through 4 came from 90 herds with 4 to 2,059 records per herd. Of the 1,020 sires, 263 had progeny in more than one herd; 180 were connecting sires (five or more progeny in two or more herds), 126 had 10 or more progeny in two or more herds, and 74 had 20 or more progeny in two or more herds. Individual
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Data for the study were 83,045 weights taken between 100 and 300 d of age on Angus cattle recorded in Australia’s National Beef Recording Scheme. Calves were born in 1972 through 1990. Initial edits removed calves born after embryo transfer or in multiple births, not reared by their genetic dam, not weighed in the same herd in which they were born, lacking dam age or sire information, or not born in a herd participating in the across-herd genetic evaluation program. Animals whose dams calved at < 20 or > 215 mo and those appearing in single-sire contemporary groups (contemporary group = herd-year-date of weighing subclass) were also deleted, leaving 65,186 records. At this point, 180 sires with progeny in 90 herds were designated as “connecting” sires; each had five or more progeny in each of two or more herds. Contemporary groups with no connecting sires were deleted, leaving 49,678 records representing 1,360 sires. Final edits removed progeny of sires with less than five total progeny, progeny of sires represented in only one contemporary group, repeated records for calves weighed more than once (the weight taken closest to 200 d was retained), records outside the range of 55 to 515 kg, and any newly created single-sire contemporary groups, leaving 44,357 records representing 1,020 sires. Of the sires, 263 (including the 180 connecting sires) had progeny in more than one herd. Data were analyzed using REML procedures described by Smith and Graser (1986) and Meyer (1987). The initial analysis (Analysis 1) included fixed effects of herd, contemporary group (nested within herd), and sex [heifer, bull, or steer); continuous linear and quadratic effects of calf age (days) and dam age (months); and random effects of sire or of sire and sire x herd interaction. Effects of interaction were tested by comparing log likelihoods of models that included the sire x herd interaction to those that included only sire effects (Meyer, 19871. Variance component estimates from analyses including both sire and interaction effects were used to estimate heritabilities within herds (as four times the ratio of sire plus sire x herd interaction variance to phenotypic variance) and across herds (as four times the ratio of sire to phenotypic variance). These heritability estimates were compared to that derived from a model with sire as the only random effect. Analysis 1 was subsequently modified (Table 1) by standardizing the data analysis 21, including relationships among sires (Analysis 31, and adjust-
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Table 1. Definition of analyses No. of Analysis
Observations
Sires
Herds
Description ~~~~~
1,020 1,020 1,063 1,063 180 503 503
~~
All observations; no relationships among sires; no dam effect Analysis 1 with standardized data Analysis 1 plus sire relationships Analysis 3 plus regression on dam total maternal breeding value Analysis 1 with data only on progeny of connecting sires Analysis 3 with data from selected herds Analysis 4 with data from selected herds
90 90 90 90 90 25 25
sires had a n average of 43.5 progeny. Connecting sires had a n average of 107.3 progeny and appeared a s connecting sires in a n average of 3.7 herds. Individual connecting sires appeared in 2 to 34 herds; 41% appeared in more than two herds, but only 14% appeared in more than five herds. Of the 90 herds, 57 had each used 10 or more connecting sires. There were 1,851 sire-herd subclasses, representing 2 % of the possible number of such subclasses. All herds were tied to one another through common use of connecting sires. Of the total 1,405 contemporary groups, 61% contained progeny of two or more connecting sires, and these contemporary groups contained 80% of the total records. The mean contemporary group size was 31.6; 2 0 % of contemporary groups had > 50 records and 4 % had > 100 records, but 23% contained e 10 calves and 12% contained less than five calves.
Fixed Effects Fixed-effect solutions were derived from Analysis 4, the most complete analysis. The phenotypic mean for weaning weight was 232.6 kg with a
residual standard deviation after adjusting for fixed effects of 22.1 kg. Effects of sex, calf age, and dam age were all highly significant. Sex differences, relative to heifers, were +24.3 kg for bulls and +12.2 kg for steers, corresponding to multiplicative adjustment factors of .901 and .951. The mean weaning age was 213.9 d with a standard deviation of 33.8 d. Weaning weight increased at a decreasing rate as calf age increased; the linear effect of age decreased from .94 kg/d a t 125 d to .80 kg/d at 200 d and 6 6 kg/d a t 275 d. The mean dam age was 63.4 mo. Weaning weight (W) was maximum at a dam age (D)of 96.4 mo and was predicted a s W = 189.8 + 1.007 D -.005222 D2.
Variance Components Base AnaZysis. Variance component estimates are shown in Table 2. For Analysis 1, when sire was the only random factor, the heritability estimate was .390. This estimate is higher than most of the estimates of heritability of weaning weight summarized by Woldehawariat et al. (19771 or Meyer (1992) but is within the range of the REML estimates of .23 to .39 reported by Garrick
2 Table 2. Estimates of sire (oi), interaction (oSxH), and error (ai)variance components, overall (h2),
between- (h:), and within-herd (hk) heritabilities, and log likelihoods for weaning weight [ kg] from different analyses Sire model
1 2c 3 4d 5 6 7d
52.3 ,101 64.8 43.0 41.9 65.9 48.9
Interaction model Log likelihood
Log likelihood
4
h2
484.2 ,910 483.8 338.6 515.2 459.2 323.6
,390 -156,998 ,400 -22,216 ,472 -156,986 ,451 (.324) -149,308 ,301 -86,528 .502 -83,073 .525 c.3831 -60,045
31.2 ,058
38.4 25.9 24.7 37.3 28.0
27.9 .053 27.2 17.9 35.1 26.1 17.7
479.0 .902 478.8 335.2 506.7 456.1 321.8
-156,914 ,052 ,439 .232 -22,173 ,052 ,438 .229 -156,913 .050 ,482 .282 ,273 (.192) ,047 (.033) ,462 [.326)-149,241 ,422 -66,486 ,062 .174 -63,053 .OS0 ,488 ,287 ,304 (.216) .048 (.034) ,498(.351) -60,026
~
&See Table 1 for definition of analyses. bRatio of interacti0n:phenotypic variance. ?3andardized data. dValues in parentheses for models including regression on dam maternal BV assume that phenotypic variance includes the mean square due to regression on maternal BV.
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44,357 44,357 44,357 44,357 19,315 17,900 17,900
~~
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the sire-model estimate of .472 were above the range of generally accepted values. The very high withinherd heritability estimates suggest that at least some of the enhanced within-herd resemblance among half-sibs was likely due to common environmental effects. Effect o f Dam Maternal Breeding Value. Dam maternal BV were not available for 822 of the 44,357 records (1.9%). In particular, maternal BV were not available for 4 of the 90 herds representing 813 records. Because maternal BV were deviated from herd means before analysis, all values for herds with completely missing data were set to zero, whereas the remaining nine records with missing data had maternal BV set to the respective herd mean. The resulting deviated maternal BV had a standard deviation of 5.2 kg. The regression of weaning weight on maternal BV was 2.69 ~tr .20 kg/kg. A relatively large regression coefficient is expected when comparing observed weaning weights to regressed BV derived from them, although a n exact expectation for the regression coefficient is not readily derivable. If these BV were used to predict future weaning weights not used in their derivation, the expected value of the regression coefficient would be 1.0 in the absence of a maternal BV x environment interaction. The inclusion of maternal BV as a covariate (Analysis 4 in Table 21 reduced the residual mean square due to removal of a portion of the total maternal genetic variance. However, this source of variation would have remained as a component of the phenotypic variance in sire-dam models. The mean square due to regression on maternal BV was 146.9kg2, and if this value is added to the sire, interaction, and error components for Analysis 4, the resulting sum of 525.9 kg2 is relatively close to the estimate of phenotypic variance of 544.4 kg2 from Analysis 3. This result suggests that the variance due to regression seems to be a reasonable approximation to the estimate of the total maternal genetic variance accounted for by dam maternal BV. Heritability estimates in Table 2 in parentheses were, therefore, calculated assuming a phenotypic variance of 525.9 kg2. When variance due to regression on maternal BV was included in the phenotypic variance, the sire x herd interaction component of variance was reduced to 3.3% of phenotypic variance. The sire component of variance was also reduced by this adjustment, however, and the ratio of interaction to sire variance was approximately .70 for both Analyses 3 and 4. Both within- and across-herd heritability estimates were within the range of values that have been previously reported, but the within-herd estimates remained substantially greater than the across-herd estimate. The withinherd heritability estimate of .326 from Analysis 4
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et al. (19891 from application of sire and sirematernal grandsire models to American Simmental data. Inclusion of sire x herd interaction effects substantially reduced the sire component. The across-herd heritability was reduced to .232, which was more similar to previously reported values. The sire x herd interaction component was 5.2% of the phenotypic variance (P e .05). If the resemblance among half-sibs in the same herd was due to sire additive genetic effects plus genotype x environment interaction effects, the within-herd heritability estimate would be .439.However, if a portion of the resemblance among half-sibs within a herd was due to correlated treatment of progeny of some sires, the within-herd heritability estimates would be correspondingly lower. Effect o f Standardization. Standardization of weaning weights using within-herd residual standard deviations had essentially no effect on the magnitude of the sire x herd interaction (Table 2). Across- and within-herd heritability estimates were .299 and .438,little different from estimates based on unstandardized data. The mean residual standard deviation was 23.6 kg with a range of 14.4 to 31.8 kg. However, little evidence of scaling Ke., proportionality of mean and standard deviation across herds; Dickerson, 19621 was observed. The correlation among herds between residual standard deviation and mean weaning weight (adjusted for sex, calf age, and dam age) was .02. Effect of Sire Relationships. Sire information was available for 989 of the 1,020 sires represented in the data. Of these, 673 were sired by 188 bulls that also had progeny in the data (i.e., 188 bulls were represented as both sires and paternal grandsires in the datal. An additional 96 sires were sons of 43 sires that had no progeny in the data but had grandprogeny in the data by more than one son. The remaining 220 bulls had known sires, but these sires had only one son in the data and, therefore, contributed no useful pedigree information. Thus, the number of sires considered in the analysis was increased by 43 to 1,063 when sire relationships were included. Inclusion of sire relationships analysis 3 in Table 21 increased the sire component of variance regardless of whether a n interaction component was also fitted. This increase was expected because inclusion of relationships recognized that the observed variance among a group of related sires is expected to be lower than that anticipated for a group of unrelated sires. However, the sire x herd interaction was not changed by inclusion of sire relationships; it remained at 5.0% of phenotypic variance. Heritability estimates for Analysis 3 were substantially higher than those for Analysis 1. The across-herd heritability estimate of .282 was within the range of previously reported values, but the within-herd estimates of .480 and
SIRE x HERD INTERACTIONS FOR WEANING WEIGHT
tively, were repeated using data from these herds. Variance components were very similar to those obtained from the overall data set. Thus, these subjectively selected herds seemed equally liable to expression of sire x herd interaction.
Discussion Sire x herd interaction components for weaning weight in these data were consistently large and significant, ranging from 63 to 91% of the sire component and from 3.3 to 6.2% of the phenotypic variance. Standardization of data, inclusion of sire relationships, or restriction to selected subsets of the data had little effect on the interaction component of variance. Differential nonrandom mating seemed to occur among herds and to account for perhaps one-third of the observed sire x herd interaction variance, but significant levels of interaction remained after adjustment for dam maternal BV. The sire x herd interaction, thus, seemed to account for a minimum of 3.3% of the phenotypic variance. Results of this study corresponded closely to those reported in a number of U.S. studies. In particular, Bertrand et al. (1985) reported sire x herd interaction variance components for weaning weight that approximately equaled the observed sire variances in Polled Hereford cattle. In that study, and in that of Tess et al. (19791, the sire x herd variance component accounted for 2.2 to 4.0% of the phenotypic variance. Previous estimates of sire x herd interaction variances have been derived primarily by analysis of variance techniques and often with limited numbers of connecting sires, Yet results were close to those observed in the current study. Models such as those used for this study cannot identify the source of observed sire x herd interaction. As pointed out by Meyer (19871, sire plus interaction models cannot discriminate between heightened resemblances among half-sibs within the same herd arising from genotype x environment interaction and those arising from common environmental effect within half-sib families. Within-herd heritability estimates in this study were generally larger than those previously reported and would suggest that common environmental effects were at least a partial component of the observed sire x herd interaction. However, when dam maternal BV was considered in the analysis, both the within- and across-herd heritability estimates were within the range of previously reported values. Also, the sires evaluated in this study included a number of imported sires. Of the 1,020 sires, herd or origin was reported for 955. Of these, 23 were from Canada, 47 were from New Zealand, 4 were
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agreed closely with the average within-herd heritability of weaning weight of .31 reported by Woldehawariat et al. (19771 from a number of designed studies. This correspondence suggests that the sire x herd variance component from Analysis 4 after adjusting for dam maternal BV may be a reasonable indicator of the true magnitude of genotype x environment interaction in these data. The reductions in sire and interaction variances observed for Analysis 4 suggested that nonrandom mating, and in particular differential nonrandom mating among herds, may have contributed to the relatively high heritability estimates observed in earlier models. To test this hypothesis, sire and sire x herd interaction variance components for dam maternal BV were calculated to assess sire variation in mates’ BV. The model used in Analysis 1 was applied to maternal BV data but without adjustment for calf sex or age or cow age. When interaction was ignored, the sire component accounted for 5.2% of the variance in maternal BV of the sires’ mates (P > .lo). Use of an interaction model reduced the across-herd sire component to 1.8% of the phenotypic variance, whereas the sire x herd interaction component accounted for 4.0% of variance (P < .05). Thus, differential nonrandom mating seemed to occur in the data and contributed to, but was not the sole source of, sire x herd interactions. Effects of Restricting the Data Set. The connecting sires likely represented a selected subset of the entire population of sires. Thus, the additive genetic variance among connecting sires may be less than that among all sires. Such selection is not expected to bias variance component estimates if the records upon which selection was based are included in the data (Henderson, 19751; however, a number of the connecting sires were imported or not bred within participating herds, so this assumption was not necessarily met. In response to this situation, Analysis 5 was conducted using only data from progeny of connecting sires. Sire variance components and corresponding overall and across-herd heritability estimates were lower than those for Analysis 1, suggesting that these sires were indeed a selected group. However, the interaction component was 26% larger than that observed in Analysis 1, implying that observed interactions were not associated with differences in additive genetic variance between sires used across versus within herds. Failure to report adequately the environmental differences among sires’ progeny may lead to sire x herd interactions, as may any form of preferential treatment of half-sib groups within herds. Analyses 6 and 7 used data from 25 herds subjectively chosen based on their greater experience and apparent commitment to accurate data recording and reporting. Analyses 3 and 4, respec-
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the seedstock herd is more similar to the customer environments than to the environments of other seedstock herds, a situation that in most cases seems unlikely. The use of herd-specific BV would be justified, then, only when commercial enterprises are maintained in the same environment as the seedstock herd. Based on data from the current analysis, some accommodation of sire x herd effects on weaning weight in beef herds seems to be needed, but a compelling case for development of herd-specific BV prediction procedures cannot be made. With rare potential exceptions, BV prediction should concentrate on estimation of mean BV across a n array of herds but with continued efforts to identify more precisely the source of the observed sire x herd interactions.
Implications Half-sib progeny of Angus sires produced within the same herd are more similar in weaning weight than half-sib progeny of the same sires in different herds, even after adjustment for all known cornmon environmental factors. This heightened resemblance may arise from interactions of sire breeding value with environmental factors unique to each herd or from unreported environmental factors that are common to progeny of individual sires within a herd. In either case, these results suggest that accurate across-herd evaluation of sires will require that the sires produce progeny in a number of herds.
Literature Cited Bertrand, J. K., P. J. Berger, and R. L. Willham. 1985. Sire x environment interactions in beef cattle weaning weight field data. J. Anim. Sci. 60:1396. Bertrand, J. K., J. D. Hough, and L. L. Benyshek. 1987. Sire x environment interactions and genetic correlations of sire progeny performance across regions in dam-adjusted field data. J. Anim. Sci. 64:77. Buchanan, D. S., and M. K. Nielsen. 1979. Sire by environment interactions in beef cattle field data. J. Anim. Sci. 48:307. Dickerson, G. E. 1902. Implications of genetic-environmental interaction in animal breeding. Anim. Prod. 4:47. Foulley, J. L., and C. R. Henderson. 1989. A simple method to deal with sire x treatment interactions when sires are related. J. Dairy Sci. 72:167. Gamck, D. J., E. J. Pollak, R. L. Quaas, and L. D. Van Vleck. 1989. Variance heterogeneity in direct and maternal weight traits by sex and percent purebred for Simmental-sired calves. J. h i m . Sci. 67:2515. Henderson, C. R. 1975. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423. Mahrt, G. S., D. R. Notter, W. E. Bed, W. H. McClure, and L. G. Bettison. 1990. Growth of crossbred progeny of Polled Hereford sires divergently selected for yearling weight and maternal ability. J. Anim. Sci. 68:1889. Meyer, K. 1987. Estimates of variances due to sire x herd interactions and environmental covariances between paternal
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from the United Kingdom, and 32 were from the United States. Other bulls may have had imported sires. Thus, genetic variance for weaning weight may be larger in this population than in populations with lower use of imported sires. Various genetic grouping strategies (Quaas and Pollak, 1981) could have been used to restrict estimates of genetic variances to within-group values. However, we chose to attempt to estimate the overall additive genetic variance within the population (regardless of source) and, thus, did not include genetic groups in the models. If additive genetic variance is homogeneous among herds, the average genetic correlation between performance in different herds can be estimated as the ratio of sire variance to the sum of sire plus interaction variance (Dickerson, 1962; Yamada, 1962). Herd sizes in this study were too small to allow definitive testing of homogeneity of additive genetic variances among herds, but under the assumption of homogeneity, estimates of the genetic correlation would range from .52 to .61 (excluding the selected data of Analysis 5). Again, these small values suggest that interaction is likely not due to genotype x environment interaction alone. The response to sire x herd interactions in national genetic evaluation programs depends on the assumed source of the interaction and on the goals of the evaluation program. If interactions arise only from common environmental effects, sire x herd effects may be included in analytical models to limit the accuracy of genetic evaluation that can be achieved for animals with individual and(or1 relatives’ records in only one herd (Meyer, 19871, but sire x herd interaction predictions should not be considered in making selection decisions. For example, sire x herd interactions have been observed for milk production in Friesian populations (Meyer, 1987) and have been included in analytical models for U.S. dairy sire and cow evaluations [Wiggans et al., 19881, but interaction equations are generally absorbed before prediction of the average across-herd BV for each animal. Within-herd interaction constants are assumed independent, even if sires are related, whereas Foulley and Henderson (1989) have noted that interaction constants for related sires within a herd should be correlated if interaction arises from genotype x environment interaction. If sire x herd interactions are manifestations of genotype x environment interactions, the potential to predict herd-specific BV exists but will be appropriate only under very specific circumstances. In most seedstock herds, the breeding objective is improvement of BV in a n array of commercial customer herds. Selection for improvement in the specific environment of the seedstock herd is thus warranted only if the environment of
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Tess, M. W., D. D. Kress, P. J. Burfening, and R. L. Friedrich. 1979. Sire by environment interactions in Simmental-sired calves. J. Anim. Sci. 49:964. Wiggans, G. R., I. Misztal, and L. D. Van Vleck. 1988. Implementation of a n animal model for genetic evaluation of dairy cattle in the United States. J. Dairy Sci. 7lLSuppl. 2):54. Woldehawariat, G., M. A. Talamantes, R. R. Petty, Jr., and T. C. Cartwright. 1977. A summary of genetic and environmental statistics for growth and conformation characters of beef cattle, second edition. Texas Agric. Exp. Sta. Tech. Rep. No. 103, College Station. Yamada, Y.1962. Genotype x environment interaction and genetic correlation of the same trait under different environment. Jpn. J. Genet. 37:498.
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half-sibs for first lactation dairy production. Livest. Prod. sci. 17:95. Meyer, K. 1992. Variance components due to direct and maternal effects for growth traits of Australian beef cattle. Livest. Prod. Sci. (In press]. Notter, D. R., and L. V. Cundiff. 1881. Across-breed expected progeny differences: Use of within-breed expected progeny differences to adjust breed evaluations for sire sampling and genetic trend. J. Anim. Sci. 69:4783. Quaas, R. L., and E. J. Pollak. 1982. Modified equations for sire models with groups. J. Dairy Sci. 64:1868. Smith, S. P., and H.-U. Graser. 1986. Estimating variance components in a class of mixed models by restricted maximum likelihood. J. Dairy Sci. 69:1156.
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