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J. Anim. Sci. 2002. 80:2071-2077
© 2002 American Society of Animal Science

Repeated-measure animal models to estimate genetic components of mature weight, hip height, and body condition score

Y. H. Choy1, J. S. Brinks and R. M. Bourdon

Colorado State University, Fort Collins 80523

1 Correspondence:
current address: Dongdo Biotech Res. Ctr., Seocho-gu Yangjae-dong 121-7 Jeied Building 4F; Seoul, Korea 137-130 (E-mail:
ychoy000{at}hanmail.net).


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results and Discussion
 Implications
 Literature Cited
 
Information on mature weight, hip height, and body condition score from Angus cows was analyzed to estimate variance components and compare prediction models. Observations from repeated measures were analyzed with animal models with or without condition score as a covariate and with or without an effect for permanent environment. Heritability (repeatability) estimates for mature weight, hip height, and condition score from Method {kappa} procedures were 0.40 (0.77), 0.62 (0.81), and 0.11 (0.38), respectively, from animal models containing a permanent environmental effect but without a covariate for condition score. Heritability estimates from animal models without a permanent environmental effect were similar to repeatability estimates from animal models with it, suggesting inflated estimates of genetic variance from models not containing a permanent environmental effect. Regressing mature weight on condition score reduced both additive genetic variance and permanent environmental variance, increasing the heritability estimate of mature weight to 0.54 and altering the biological interpretation of the trait. The covariate for condition score had little effect on hip height. Regressions of mature weight and hip height on condition score were 25.9 kg/unit of body condition score and 0.4 cm/unit, respectively. Least-squares means for mature weight and hip height tended to increase until 7 and 5 yr of age, respectively. Condition score tended to increase until 6 yr of age and decrease after 8 yr of age. Correlations between breeding value solutions for the same trait were high whether or not prediction models included a permanent environmental effect or a covariate for condition score, and whether or not the variance components used were derived from models containing a covariate for condition score. Results suggest the importance of including a permanent environmental effect in genetic prediction models for these traits. Whether mature weight should be adjusted for body condition is arguable, depending on availability of condition score predictions and tools for analyzing mature weight and condition score predictions in an environment-specific context.

Key Words: Angus • Body Condition • Body Weight • Height • Heritability


   Introduction
Top
 Abstract
 Introduction
Materials and Methods
 Results and Discussion
 Implications
 Literature Cited
 
The importance of accounting for body condition scores in the genetic evaluation of mature size in beef cows has been suggested by previous researchers (Benyshek and Marlowe, 1973; Gregory et al., 1992; Choy, 1997). Mature size of cows is important for calf production and maintenance cost. For a Colorado beef cattle management environment, Johnson (1984) estimated that the ratio of maintenance energy requirement (ME basis) to total energy requirement increases from 83 to 91% as cows mature from age 2 to 6. Because of the complex physiological nature of mature body weight (MW), other traits that support the understanding of body weight changes are needed. Producers who measure cow body weight often measure hip height (HH) and body condition score (CS) as well. These may be economically important traits in themselves. Moreover, they provide valuable information for enhancing our understanding of the genetic and physiological bases of body weight change. Repeated observations of these three traits offer the possibility of increasing accuracy of prediction and of predicting mature weight potential earlier in cow’s life (Choy, 1997). The objective of this research was to estimate variance components for MW, HH, and CS in an Angus cow herd and to examine the effects of including a permanent environmental (PE) effect and a covariate for CS in models used for genetic prediction and variance component estimation.


   Materials and Methods
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 Abstract
 Introduction
 Materials and Methods
Results and Discussion
 Implications
 Literature Cited
 
Data and Cow Management

We used data on MW, HH, and CS collected from 1986 to 1994 at the John E. Rouse Colorado State University Beef Improvement Center. All data were recorded at weaning in the fall. Condition scores were assigned using a 9-point scale, a score of 1 indicating extremely thin and a score of 9 indicating extremely fat. The data set consisted of measures on 840 cows in 81 contemporary groups, for a total of 2,488 observations. Contemporary group was defined by a combination of year of age of cow at measure (AAM) and year of measure (YOM). The youngest cows measured were 2-yr-olds. Observations on cows older than 10 were excluded.

The ranch is located southwest of Saratoga, WY, at an elevation of 2,194 m. Annual precipitation, mostly from winter snow, is 22.9 to 33.0 cm (Enns, 1991). Approximately 450 purebred, unregistered Angus cows and 100 replacement heifers are maintained each year. Semen for AI is obtained from ranch-raised bulls and two to four outside bulls each year. Cows are selected on weaning weight records of their progeny, and unsound cows and those that fail a pregnancy exam are culled. Cows and calves graze crested wheatgrass and irrigated pastures from mid-May to weaning in October. From weaning to the following May, cows graze native sagebrush range or improved crested wheatgrass pasture. When winter snows cover the range, supplemental native hay is provided.

Statistical Analyses

Variance Component Estimation. Variance components for each trait were estimated separately using the Method {kappa} algorithm (Reverter et al., 1994); with the Druet et al., 2001 software program developed by Golden (unpublished). This program uses a 50% random subsampling protocol. The convergence criterion for {kappa} estimates (regressions of current predictions on previous predictions) was set at 10E-10. We used four repeated-measure animal models, which differed only by the inclusion of a permanent environmental effect or a regression on CS.

Model 1: Simple repeated-measure animal model


Model 2: Simple repeated-measure animal model with regression on CS


Model 3: Repeated-measure animal model with permanent environmental effect


Model 4: Repeated-measure animal model with permanent environmental effect and regression on CS


where,

y=a vector of observations on MW, HH, or CS

ß=a vector of fixed contemporary group effects

b=a vector of regressions on CS

u=a vector of random additive genetic effects

p=a vector of random permanent environmental effects

e=a vector of random errors

X1, x2, Z, W=incidence matrices associated with ß, b, u, and p, respectively

Assumptions about the variance-covariance of random components were:



where, {sigma}u2, {sigma}p2 and {sigma}e2 are variances of additive genetic, permanent environmental, and temporary environmental effects, respectively. The term A is a relationship matrix composed of 1,657 animals, and I is an identity matrix representing 840 cows with observations. The group of 840 cows comprised offspring of 85 sires and 603 daughter-dam pairs.

Models 1 and 3 were used to analyze MW, HH, and CS. Models 2 and 4 were used to analyze MW and HH only.

Genetic Prediction. BLUP solutions were obtained using the "tkblup" program developed by B. L. Golden (unpublished documentation). BLUP models were identical to the four models used for parameter estimation except in analyses where least-squares means for AAM and YOM were of primary interest. In those few cases, fixed effects for AAM and YOM were substituted for contemporary group and any AAM by YOM interaction effects were ignored. Solutions for random effects were labeled according to the model used to compute variance components and the model used to compute solutions. For example, MW1,2 refers to breeding value for mature weight predicted from Model 2 using variance components from Model 1. In order to determine the effect of prediction model and source of variance components on BLUP solutions, we computed Pearson correlation coefficients and Spearman rank correlations between breeding value solutions from different model combinations.


   Results and Discussion
Top
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
Implications
 Literature Cited
 
Variance Component Estimation

Heritability and repeatability estimates from Method {kappa} procedures are listed in Table 1Go. Heritability estimates for MW from Models 3 and 4 were close to those reported by Brinks et al. (1964), Bullock et al. (1993), Choy et al. (1996), and Kaps et al. (1999). Repeatability estimates for MW were similar to the estimates of Brinks et al. (1962) for Herefords but were higher than the estimates of Schafer (1991) for Red Angus. Heritability estimates for HH from Models 3 and 4 were somewhat lower than the estimates of Brown and Franks (1964; 0.69), Jenkins et al. (1991; 0.71), and Northcutt and Wilson (1993; 0.83). The heritability estimate for CS from Model 3 was low (0.11), similar to the estimate of Meyer (1995) for Australian Hereford (0.14) but lower than the estimate of Morrow and Marlowe (1966) for Angus (0.31).


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  		Table 1. Heritability (h2) and repeatability (r) estimates from Method {kappa} analyses
 
For all three traits, heritability estimates from Models 1 and 2 were large and similar to repeatability estimates from Models 3 and 4. Because of the repeated nature of observations, it is likely that heritabilities estimated from Models 1 and 2 were inflated by permanent environmental variation. Further evidence for this conclusion, at least for MW, is contained in Table 2Go; sums of additive genetic and permanent environmental variance estimates from Models 3 and 4 were similar to estimates of additive genetic variance from Models 1 and 2. The picture is less clear for HH and CS. Addition of PE effects in Models 3 and 4 changed variance estimates across the board, making inferences difficult. The reasons for these changes in variance are not clear, but sampling errors in Method {kappa} procedures are probably involved.


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  		Table 2. Estimates of phenotypic (P), additive genetic (G), permanent environmental (PE), and temporary environmental (E, TE) variances
 
As a rule, addition of a covariate for CS had little or no effect on heritability and repeatability estimates. Only in the case of MW was there an appreciable increase in heritability due to adjustment for CS. (Compare estimates from Models 3 and 4 in Table 1Go.) Including CS in Model 4 decreased estimates of permanent and temporary environmental variation in MW. As suggested by Benyshek and Marlowe (1973), adjusting weight for body condition removes environmental variation that obscures underlying genetic variation. At the same time, because genetic variation in MW includes genetic variation in body composition, adjusting MW for CS also removes some genetic variation in MW. Reduction in genetic variation was slight in this model (1,142 to 1,121 kg2). It was considerably greater in the paternal half-sib analyses of Choy (1997). The animal models used in the current study appear to better separate genetic and environmental variation.

As expected, variance estimates for HH were unaffected by inclusion of CS in the model. Body condition should have little influence on skeletal size under normal nutritional conditions. The fact that the paternal half-sib analyses of Choy et al. (1996) using least-squares procedures (Becker, 1984) suggested an effect of CS on HH is further evidence for the preferred use of animal models and mixed-model estimation procedures.

Year and Age Effects

Least-squares means for AAM from Model 3 and Model 4 analyses of MW are shown in Figure 1Go. For MW and HH, fixed effect solutions from Models 1 and 2 were virtually identical to fixed effect solutions from Models 3 and 4, respectively. Mature BW increased through 7 yr of age. The effect of regression on CS (MW1,1 vs MW2,2; MW3,3 vs MW4,4) was negligible at younger ages. At older ages, least-squares means for MW were somewhat smaller after adjustment for CS.



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  		Figure 1. Least-squares means for mature weight (MW) by age at measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, MW3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 
The pattern of change in HH over ages was similar to that of MW, but HH plateaued at 5 yr of age (Figure 2Go). As with earlier paternal half-sib least-squares analyses (Choy, 1997), inclusion of a covariate for CS and choice of variance components had little effect on HH means. Least-squares means for CS increased until age 6, plateaued from 6 to 8, and then declined (Figure 3Go).



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  		Figure 2. Least-squares means for hip height (HH) by age at measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, HH3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 


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  		Figure 3. Least-squares means for condition score (CS) by age at measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, CS3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 
Least-squares means for MW, HH, and CS are shown by YOM in Figures 4, 5, and 6GoGoGo, respectively. Hip height increased approximately 3 cm from 1986 to 1994, whereas MW and CS decreased. The increase in HH was likely due to selection for increased frame size. Decreases in MW and CS were probably caused by poorer nutrition due to higher stocking rates. Changes in CS may have been caused, in part, by turnover in the technicians doing the scoring. The effect of regressing MW on CS was appreciable in earlier years, years when condition scores were especially high. In later years, when condition scores were near 5, the effect of regressing MW on CS was less noticeable. As a rule, MW was lighter after adjustment for CS. However, in the final years of the study, years in which condition scores were the lowest, adjustment for CS increased MW. Regression on CS had little effect on the pattern of change in HH over YOM.



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  		Figure 4. Least-squares means for mature weight (MW) by year of measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, MW3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 


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  		Figure 5. Least-squares means for hip height (HH) by year of measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, HH3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 


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  		Figure 6. Least-squares means for condition score (CS) by year of measure. The first subscript indicates the model from which variance components were derived, and the second subscript indicates the model used to produce predictions. For example, CS3,3 refers to breeding value for mature weight predicted from Model 3 using variance components from Model 3.

 
Regressions of MW on CS and HH on CS were positive, averaging approximately 26 kg per unit and 0.4 cm per unit, respectively (Table 3Go). Regressions of MW on CS were slightly smaller when variance components were estimated from models containing CS as a covariate (MW2,2 and MW4,4). Choice of variance components had a negligible effect on regressions of HH on CS. Likewise, inclusion of PE effects in prediction models had virtually no effect on the regressions of either MW or HH on CS.


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  		Table 3. Regression coefficients of mature weight (MW) and hip height (HH) on condition score (CS)
 
Correlations Between Solutions

In order to determine the effect of prediction model and source of variance components on BLUP solutions, we computed Pearson correlation coefficients and Spearman rank correlations between breeding value solutions (EBV) from different model combinations (Table 4Go). Simple correlations between EBV for the same trait ranged from 0.89 to 1.00 for MW and 0.98 to 1.00 for HH. Corresponding rank correlations ranged from 0.85 to 1.00 and 0.98 to 1.00, respectively. Predictions of HH were essentially the same regardless of prediction model or variance components used.


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  		Table 4. Pearson correlation coefficients (upper diagonal) and Spearman rank correlations (lower diagonal) between predicted breeding values (n = 1,657) from different combinations of models
 
For MW, correlations between EBV were lowest when models differed with respect to inclusion of both PE effects and CS, somewhat higher when models were the same with respect to inclusion of PE effects only, and highest when models were the same with respect to inclusion of CS. Although inclusion of PE effects had relatively little influence on MW solutions, they had a large influence on predictions of breeding value for CS. The simple correlation between solutions for CS from models with and without PE effects was 0.89—high but far from unity.

Correlations derived from analyses combining different prediction and variance component models were similar to related correlations from consistent models. This suggests only that no great surprises are to be expected by using variance components from one model to make predictions with another.

Correlations between EBV for MW and HH were highest when MW was adjusted for condition. Clearly, adjusting MW for condition provides a truer picture of skeletal size. Because variation in weight after skeleton and muscle growth near their physiological limits is largely due to variation in fat levels (Bergens, 1974), adjusting for condition provides a truer picture of lean body mass as well.

As expected, correlations between EBV for MW and CS were higher when MW was not adjusted for condition. Adjustment for condition removes the primary source of covariance between the traits. The fact that correlations between condition-adjusted MW solutions and CS solutions were not close to zero (0.29 to 0.35) raises the possibility that simple linear adjustment for CS is inadequate and(or) that the relationship between MW and CS is more complex than we think. Perhaps, in this population, cows with larger lean-body mass tend to have higher CS. Alternatively, these non-zero correlations may be explained by the fact that MW is adjusted for phenotypic condition, not estimated breeding value for condition. And with a heritability of only 0.11 (Table 1Go), a cow’s condition score at a given point in time is hardly a good substitute for her EBV for CS. Correlations between EBV for HH and CS were small and, as expected, greater when HH had not been adjusted for condition.

Conclusions

Several conclusions can be drawn from this study. First, in this data set, MW and HH were highly heritable and repeatable, and CS was lowly heritable and moderately repeatable.

Second, while adjustment for CS had virtually no effect on HH, it did affect MW. Condition-adjusted MW appears to be biologically different from unadjusted MW. It is more heritable and more representative of skeletal size and lean body mass. The correlation between EPD predicted for adjusted and unadjusted MW using comparable models was high (0.94) but not extreme. Although inclusion of CS as a covariate affected parameter estimates and BLUP solutions, predictions were similar whether or not parameters were derived from models containing CS as a covariate. Adjustment of cow weight for condition score is debatable. For adjusted weights to be useful at the level of national cattle evaluation, large amounts of CS data must be available. Also, the relative merit of condition-adjusted vs unadjusted weights as measures of cow maintenance likely depends on management and physical environment. Predictions for both unadjusted mature weight and condition score combined with location-specific environmental information could be analyzed with decision support tools to rank animals appropriately.

Permanent environmental effects—effects largely attributable to nutrition and calving history—were an important source of variation for all three traits in this study. Estimates of genetic variances and heritabilities were inflated when PE effects were ignored. Predictions of MW were slightly affected and predictions of CS were substantially affected by inclusion of PE effects in prediction models. Differences in PE effects accounted for 35, 18, and 26% of phenotypic variation in MW, HH, and CS, respectively (Model 3, Table 2Go). Given that the proportion of variation in MW accounted for by PE effects dipped from 35 to 25% when MW was adjusted for CS (Model 4), body condition appears to be a component of PE effects on MW. The same cannot be said for HH. The proportion of variation in HH accounted for by PE effects changed only 1% (18 to 17%) when HH was adjusted for CS.


   Implications
Top
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Implications
Literature Cited
 
Repeated-measure models used to predict breeding values for mature weight, hip height, or condition scores in beef cattle should include permanent environmental effects. Models containing these effects produce more reasonable parameter estimates and better predictions (especially for condition score). Whether cow weight should be adjusted for condition score is arguable. Condition-adjusted weight is a better indicator of lean body mass but does not convey as much information as predictions for unadjusted weight and condition score. Further research is needed to determine how relationships between mature weight, hip height, and condition score change as animals mature.

Received for publication March 6, 2001. Accepted for publication March 8, 2002.


   Literature Cited
Top
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Implications
 Literature Cited
 


Becker, W. A. 1984. Manual of Quantitative Genetics. 4th ed. Academic Enterprises, Pullman, WA.

Benyshek, L. L., and T. J. Marlowe. 1973. Estimating heritability of Hereford cow weights. J. Anim. Sci. 36:854–861.[Abstract/Free Full Text]

Bergens, W. G. 1974. Protein synthesis in animal models. J. Anim. Sci. 38:1079–1091.[Abstract/Free Full Text]

Brinks, J. S., R. T. Clark, N. M. Kieffer, and J. R. Quesenberry. 1962. Mature weight in Hereford range cows—heritability, repeatability, and relationship to calf performance. J. Anim. Sci. 21:501–504.[Abstract/Free Full Text]

Brinks, J. S., R. T. Clark, N. M. Kieffer, and J. J. Urick. 1964. Estimates of genetic, environmental and phenotypic parameters in Hereford females. J. Anim. Sci. 23:711–716.[Abstract/Free Full Text]

Brown, C. J., and L. Franks. 1964. Factors affecting size of young beef cows. J. Anim. Sci. 23:665–668.[Abstract/Free Full Text]

Bullock, K. D., J. K. Bertrand, and L. L. Benyshek. 1993. Genetic and environmental parameters for mature weight and other growth measures in Polled Hereford cattle. J. Anim. Sci. 71:1737–1741.[Abstract]

Choy, Y. H. 1997. Genetic evaluation of mature weight, hip height and body condition score in an Angus herd. Ph.D. dissertation, Colorado State University, Fort Collins.

Choy, Y. H., J. S. Brinks, and R. M. Bourdon. 1996. Genetic evaluation of mature weight, hip height, and body condition score in an Angus herd. J. Anim. Sci. 74(Suppl. 1):107 (Abstr.).[Free Full Text]

Druet, T., I. Misztal, M. Duangjinda, A. Reverter, and N. Gengler. 2001. Estimation of genetic covariances with Method {kappa}. J. Anim. Sci. 79:605–615.[Abstract/Free Full Text]

Enns, R. M. 1991. Parameter estimates of insulin-like growth factor I and performance traits in beef cattle. M.S. thesis, Colorado State University, Fort Collins.

Gregory, K. E., L. V. Cundiff, and R. M. Koch. 1992. Breed effects and heterosis in advanced generations of composite populations on actual weight, adjusted weight, hip height, and condition score of beef cows. J. Anim. Sci. 70:1742–1754.[Abstract]

Jenkins, T. G., M. Kaps, L. V. Cundiff, and C. L. Ferrell. 1991. Evaluation of between- and within-breed variation in measures of weight-age relationships. J. Anim. Sci. 69:3118–3128.[Abstract]

Johnson, D. E. 1984. Maintenance requirements for beef cattle: Importance and physiological and environmental causes of variation. In: Proc. Beef Cow Efficiency Forum. Michigan State Univ., East Lansing. pp 6–14.

Kaps, M., W. O. Herring, and W. R. Lamberson. 1999. Genetic and environmental parameters for mature weight in Angus Cattle. J. Anim. Sci. 77:569–574.[Abstract/Free Full Text]

Meyer, K. 1995. Estimates of genetic parameters for mature weight of Australian beef cows and its relationship to early growth and skeletal measures. Livest. Prod. Sci. 44:125–137.

Morrow, G. A., and T. J. Marlowe. 1966. Genetics of mature traits in Angus cows. J. Anim. Sci. 25:880 (Abstr.).

Northcutt, S. L., and D. E. Wilson. 1993. Genetic parameter estimates and expected progeny differences for mature size in Angus cattle. J. Anim. Sci. 71:1148–1153.[Abstract]

Reverter, A., B. L. Golden, R. M. Bourdon, and J. S. Brinks. 1994. Method {kappa} variance components procedure: Application on the simple breeding value model. J. Anim. Sci. 72:2247–2253.[Abstract]

Schafer, D. W. 1991. Within-herd predicted breeding value comparisons and genetic trend in Red Angus cattle. Ph.D. dissertation, Colorado State University, Fort Collins.


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