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Department of Animal Science, Iowa State University, Ames, 50011
2 Correspondence:
239 Kildee Hall (E-mail:
dewilson{at}iastate.edu).
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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Key Words: Adipose Tissue • Beef Cattle • Composition • Heritability • Repeatability
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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As the beef industry depends more on a value-based marketing system, accurate selection of parent animals and evaluation of genetic responses to selection become more crucial to producers. The genetic and residual variance components for UPFAT and other ultrasound measures in young beef breeding cattle need to be determined for a wide range of ages and production conditions.
Kirkpatrick et al. (1990) showed that variance components for longitudinal data could be modeled using covariance functions (CF). Application of this method to animal breeding data was considered in Meyer and Hill (1997). Meyer (1998b) showed that random regression models could be used to estimate covariance functions directly from data by restricted maximum likelihood (REML) procedures.
The objective of this study was to estimate variance components, heritability, and repeatability of serially measured UPFAT data in purebred Angus bulls and heifers.
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Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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Breeding and Management Procedures
This project was initiated in 1997 with the purchase of 285 spring 1996-born, purebred registered Angus heifers. Heifers were purchased from two herds in Nebraska and three herds in South Dakota. The heifers were randomly assigned to the two selection lines. Heifers were purchased based on their frame size (5 to 6), health condition, and EPD for birth weight (-0.45 to 2.72 kg), weaning weight (9.09 to 20.45 kg), yearling weight (18.18 to 31.82 kg), maternal weaning weight (milk) (2.27 to 9.09 kg), hot carcass weight (2.27 to 6.82 kg), ribeye area (-0.65 to 3.23 cm2), marbling (minimum of -0.15), carcass 12th to 13th rib fat thickness (maximum of 0.13 cm), and PRP (minimum of -0.5).
Both lines were managed under similar condition at the Rhodes research and demonstration farm in central Iowa. Each year, breeding took place in June and July, with calving the following spring. In the first year of breeding, the heifers were bred artificially with semen from industry sires. Mature cows and virgin heifers from the previous breed project were implanted with a combination of fresh and frozen embryo obtained from three industry herds.
Industry sires used in the Q-line during the first year of breeding included seven sires as determined primarily by their marbling EPD (minimum of 0.35). Similarly, seven industry sires were used in the R-line as determined primarily by PRP EPD (minimum of 0.20), carcass fat thickness EPD (minimum of 0.64 cm), and a minimal marbling EPD of zero. In addition, for both lines, maximum birth weight EPD and age of sires to be considered was set not to exceed 2.27 kg and 12 yr, respectively. Subsequent breeding has involved artificial breeding of the foundation cows and replacement heifers using semen from industry sires as well as from bulls selected in the project. The same criteria were used to select additional industry sires in the following years. Females within each line were bred as yearlings and were removed from the herd for reproductive failure.
The overall mean age at weaning across the 3 yr was 207 d (160 to 243 d). After weaning, bull calves were fed a 1.3 Mcal NEg/kg diet to allow a mean weight gain of 1.5 kg /d. Replacement heifers were fed a 1.1 Mcal NEg/kg diet to allow a mean daily weight gain of 0.70 to 1.1 kg /d.
Animals and Scanning Procedure
Serial ultrasound data were collected on progeny born at the Rhodes farm over a three-year period between 1998 and 2000. Each year the weaned bull and heifer calves were scanned four to six times for UPFAT and other ultrasound traits starting at a minimum age of 28 wk, with an average interval of 4 to 6 wk between scans. Bulls and heifers were scanned using an Aloka 500V real-time ultrasound machine equipped with a 3.5-MHz, 17.2-cm linear array transducer (Coromertics Medical Systems Inc., Wallingford, CT) and a Classic Scanner-200 equipped with a 3.5-MHz, 18-cm transducer (Classic Ultrasound Equipment, Tequesta, FL). A detailed description of scanning procedures and processing of UPFAT images is found in Hassen et al. (2001).
Data Analysis
Edits and Preliminary Evaluations.
After removing those animals with a single UPFAT observation, the present analysis included 3,358 observations from 675 bulls and heifers. Animals with single observations were calves that died at earlier ages and/or those with poor quality images at one or more of the scan sessions. Ages at scanning time were expressed in weeks, resulting in 36 different ages ranging from 28 to 63 wk.
Initially, data were subjected to individual animal plots and GLM regression procedures (SAS Inst., Inc, Cary, NC) to study individual animal UPFAT trends. Data collected over the 3 yr were then analyzed based on mixed-linear models to determine the degree of polynomial of ages at measurement to model mean UPFAT trend and to evaluate individual animal deviations. Models included fixed effects of contemporary group (CG) (birth year, sex, pen, and scan session), age at measurement as a covariate, and random effects of individual animal intercept and slope.
Single and Multiple Trait Analyses.
Data were divided into six groups based on scan sessions across years. The UPFAT measures from the first five scans across years were analyzed as different traits using a single-trait animal model that included fixed effects of CG (birth year, sex, and pen), linear effect of age, random effects of animal, and an error term. Results from this analysis were used to provide preliminary evidence on the general trend in additive genetic variance, error variance, and heritability values. A five-trait animal model was then used to determine phenotypic and genetic correlations between consecutive scans. Data from the sixth scan were excluded from this part of the analysis due to small sample size and convergence problems.
Random Regression Models.
Variance components were estimated by an average information REML algorithm using DXMRR (a program used to estimate CF for longitudinal data; Meyer, 1998a). Meyer and Hill (1997) and Meyer (1998b) provided comprehensive information on the estimation of (co)variance functions and likelihood values. A description of phenotypic and genetic random regression models can be found in Meyer (1999).
Initially, data were subjected to phenotypic models that included fixed effects of CG (birth year, sex, pen, and scan session), fixed Legendre polynomial of age at measurement, random effects of animal, and an error term. Animal effect was fitted as a function of Legendre polynomial of age at measurement. Animals in the analysis were considered unrelated, and maternal effects on UPFAT measures were assumed to be zero. Information from these models also was used to establish preliminary information on the need for models with heterogeneous error variances. At each step of this analysis, the degree of orthogonal polynomials of age at measurement (k) was increased by one, to a maximum of k = 5 (quartic), starting from a model that fit an intercept (k = 1) and a single error variance (NE = 1). Within each level of k, the number of error variances (NE) was increased by one, to a maximum of NE = 6. Measurement errors were assumed to be independently distributed for all analysis. Based on information from preliminary evaluations, the maximum order of fixed regression for all models was kept constant at k = 2 (linear).
Considering the limited number of records used, the main intent was to select models that best described data with a minimal possible number of parameter estimates. Although the likelihood ratio test is commonly used in animal breeding applications, this may not be the best approach because maximum likelihood values always favor models with the largest possible dimensionality (Mills and Prasad, 1992). Instead, information criteria that involve maximized likelihood and penalty functions could be used. These include Akaike’s Information Criteria (AIC) and Schwartz’s Bayesian Information criteria (BIC). However, AIC values may sometimes lead to model overfitting (Hurvich and Tsai, 1989; Mills and Prasad, 1992). Hence, phenotypic models with different k for animal effect (at any constant NE) were compared based on BIC values. Akaike’s Information criteria and maximal likelihood values also were considered to provide additional information.
Information from the best phenotypic model on k and NE were used to analyze data using genetic models that included random regression coefficients on Legendre polynomial of age at measurement for direct genetic and direct permanent environmental effects. In all cases, each model compared included the same order of polynomial to characterize direct additive genetic and direct permanent environmental effects. Fixed effects considered were the same as those of phenotypic models. The general genetic model (Meyer, 1998b) is:
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whereyij= thejth observation of theith animal;Fij= fixed effect of CG; ßm= fixed regression coefficients modeling population age trend;t*ij= standardized age at measurement for animali(-1 
tij
1); 
m(t*ij) = themth Legendre polynomial evaluated fort*ij; 
im, 
im= themth direct additive genetic and direct permanent environmental random regression coefficients for animali, respectively; 
ij= the error term; andkA, kR= order of polynomial fit for direct additive genetic and direct permanent environmental effects, respectively.
In matrix notation, the general genetic model is:
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where Y = vector of UPFAT observations;c = vector of fixed effects of CG; b = vector of fixed regression coefficients on Legendre polynomials of ages at measurement; , = vectors of random regression coefficients for direct additive genetic, and direct permanent environmental effect, respectively; = vector of random residual effects;T = incidence matrix relating vector of observations to CG effects;X = incidence matrix of orthogonal polynomials coefficients relating vector of observations to fixed regression coefficients;Zi = incidence matrix of orthogonal polynomial coefficients relating vector of observations to random regression coefficients for direct additive genetic (i = 1) and direct permanent environmental effects (i = 2);Ki = coefficient matrices for direct additive genetic (i = A) and direct permanent environmental (i = R) CF, respectively; A = numerator relationship matrix;I = identity matrix with size equal to number of animals with records; 
= direct matrix product; and R = diagonal matrix of residual variances.
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Results and Discussion |
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TopAbstractIntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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The general trends in mean UPFAT measures of bulls and heifers are shown in Figure 1
. Mean UPFAT values showed a nearly linear increase with age for both sexes. Heifer trends started at a higher mean and consistently outranked bulls for all measurement ages. The mean yearling UPFAT of bulls and heifers were 3.97% (SD = 0.84%) and 4.84% (SD =1.35%), respectively. The CV values suggest a similar relative variability for both sexes across all ages. The only exceptions were values at extreme ages represented by few observations.
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. Heritability increased from a minimum of 0.36 at a mean age of 37 wk (scan 1) to a maximum of 0.54 at a mean age of 54 wk (scan 5). The increase in heritability seems to be influenced by a relatively large increase in 
2awith advancing scan sessions. The 2aincreased by 163% from the first to the fifth scan. However, differences in 2ebetween scan sessions were not different from zero (P > 0.05) suggesting homogeneity of 2eacross mean ages.
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The genetic correlation between UPFAT measures at different scans decreased as the time between scan increased. The genetic correlation of UPFAT at first scan with measurements made in the second, third, fourth, and fifth scans were 0.93 ± 0.07, 0.97 ± 0.06, 0.90 ± 0.08, and 0.88 ± 0.09, respectively. Similarly, the genetic correlation between the yearling scan (scan 4) and UPFAT measures for the second, third, and fifth scans were 0.94 ± 0.06, 0.96 ± 0.04, and 0.99 ± 0.03, respectively.
Model Selection
Generally, the log likelihood (log L) values of phenotypic models with the same NE increased as the degree of polynomial fit (k) for animal effect increased. However, such an increase was significant (P < 0.05) only when k increased from 1 to 2. Similarly, the lowest BIC and AIC values were observed for models when k = 2. When models with k = 2 were compared for NE, BIC values favored a model with homogeneous 2e. Therefore, all genetic models compared in further analysis assumed homogenous 2e.
Maximum log likelihood, AIC, and BIC for genetic models with different degrees of polynomial fit for direct additive genetic and direct permanent environmental effects are shown in Table 2. The lowest BIC and AIC values were observed for models fitting a linear effect of age at measurement (model II). Except for the relatively large changes between models I and II, 2eremained unchanged for the remainder of the genetic models compared.
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2p, 2a, and 2pebased on model II are shown in Figure 2.All estimates increased as age at measurement increased. Both 2aand 2pestarted the same and 2aincreased as age at measurement increased from 28 to 63 wk. However, 2peestimates declined until 40 wk of age, followed by a gradual increase until 0.38 was reached at 63 wk of age. In agreement with results from a single-trait analysis, model II estimates of 2pand 2aat 52 wk of age were 0.94 and 0.47%, respectively.
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2pis shown in Figure 3. The 2econtributed up to 40% of the 2pbetween ages 28 to 38 wk. However, the 2pecontribution ranged from 19 to 28% of 2p. Generally, 60 to 70% of the variability in UPFAT of bulls and heifers between ages of 28 to 38 wk was nongenetic.
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Repeatability of UPFAT measures increased from a minimum of 0.60 at ages of 28 to 39 wk to a maximum of 0.80 at ages 61 to 63 wk. Hassen et al. (1999) reported a pooled repeatability of 0.63 for bulls, heifers, and steers averaging 62 wk of age. Steer data were more repeatable (0.73) than those of bulls (0.59) and heifers (0.52). However, their results were based on 144 bulls, heifers, and steers with diverse breed compositions. Furthermore, prediction equations used in current image interpretation software have better R2 and root mean square error values than previous equations (Hassen et al., 2001).
With regard to present results, it could be argued that assuming homogeneous 2emight contribute to the upward trend in genetic parameter estimates for older bulls and heifers. As Meyer (1999) explained, fitting heterogeneous residual variance compensates for insufficient order of fit for direct additive genetic and direct permanent environmental effects, and avoids a possible bias in CF estimates. Huisman et al. (2002), working on pig weights measured at three different time periods, suggested using independent error terms for each measurement date to avoid bias in 2peestimates.
When fitting heterogeneous error variances, grouping of ages into subgroups with relatively uniform 2e is more important than the number of groups specified (Olori et al., 1999). This also was shown to be the case when differences in degree of heterogeneity did not influence 2a and 2pe estimates (Meyer, 1999). Criteria such as stage of lactation (Olori et al., 1999) or seasonal cyclic body weight changes (Meyer, 2000) may be reasonable bases for classifying measurement ages into subcategories. However, the present data provide no clear trend in 2e to justify such subgroups.
In order to study possible changes in genetic parameter estimates due to heterogeneous error variances, estimates from model II were compared with results from another model. The model included the same kAandkRas model II but allowed different error variances at each of the 36 different ages (model k2e36). (Co)variances between random regression coefficients and the corresponding coefficients of the CF based on model II and model k2e36 are shown in Table 3. Generally BIC value for model k2e36 (1,427) suggests no improvement in modeling UPFAT variance compared to model II. However, for both models, individual animal intercepts for direct additive genetic and direct permanent environmental effects were often more variable than the respective individual animal slopes. Similarly, correlations between individual animal slopes and intercepts were stronger for direct additive genetic effect than corresponding values for direct permanent environmental effect.
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and 5 show the general trend in 2a and 2pe for models II, III, IV, V, and k2e36. With the exception of minor differences at earlier ages, fitting heterogeneous 2e did not show an apparent change in 2a estimates for most ages. The similar trend in 2a for models II, III, IV, and V suggests that additional degrees of polynomial fit other than linear may not be necessary to describe the present data.
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2a estimates, model k2e36 showed a higher 2pe at earlier ages than model II until such differences dwindled to zero at 46 wk of age, which was then followed by reranking of estimates. The absolute difference in the 2pe estimate between models II and k2e36 ranged from 0 (at 48 wk) to a maximum of 0.07%2 (at 28 wk). However, problems associated with the use of higher-order polynomials (Kirkpatrick et al., 1994), coupled with lack of an adequate number of observations at extreme ages, may be the reason for the unexpected trend in 2pe for models IV and V.
Heritability and repeatability of UPFAT measurements for all genetic models in the present study are shown in Table 4. Values represent mean heritability and repeatability values by a class interval of 4 wk. Mean heritability estimates based on model II were similar to those of models k2e36, III, IV, and V, across all ages. However, repeatability of UPFAT based on models k2e36 was higher than the mean estimates of models with homogeneous 2e for ages of 28 to 35 wk.
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2a, 2pe, and 2p for the entire measurement period were constant at 0.36, 0.16, and 0.85, respectively. Furthermore, heritability and repeatability of UPFAT were estimated at 0.42 and 0.61, respectively.
Considering the general trend in variance components and genetic correlation estimates based on traditional single- and multiple-trait analysis, present results suggest that the use of a repeatability model may not be an appropriate choice. However, model II seems to be the simplest model able to provide an adequate description of genetic parameters for serially measured UPFAT. Unlike previous recommendations (Olori et al., 1999; Meyer, 2000; Huisman et al., 2002), the use of heterogeneous 2e did not show an apparent change in genetic parameter estimates for most ages. This could be partly due to uniformity in herd management, narrow ranges of scan age, and/or consistent scanning procedures during each of the 3 yr.
Currently, UPFAT scans for breeding bulls are taken at about 1 yr of age and at 395 d of age for developing heifers. These endpoints have been chosen from a practical herd management standpoint, and also because they do allow animals to differentiate themselves genetically more than younger age scans. Present results indicate that heritability and repeatability of UPFAT measures are also at their optimum at approximately 52 wk and also through at least 63 wk of age. This suggests that differences in UPFAT measurements during this period are good measures of differences in marbling genetic potential of Angus cattle. However, it is unknown if this is true for other breeds of beef cattle.
Another important consideration is the genetic correlation of yearling UPFAT with earlier measures. Figure 6 shows the general trend of genetic correlations. In agreement with results of multiple trait analysis, genetic correlations with yearling measurements were positive and generally increased as the gap between ages decreased. Genetic correlation estimates suggest that selecting for UPFAT as early as 28 wk of age would increase yearling UPFAT. However, genetic correlations with yearling UPFAT of 0.90 and above were attained starting at 35 to 36 wk of age.
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2a, heritability, and repeatability values with advancing measurement ages. But, this increase also may be associated with an increase in mean UPFAT levels. Hence, a better understanding of the trend in genetic parameter estimates with age, as well as the possible association with mean UPFAT levels, could be better understood by including data from cattle of diverse biological types. Therefore, similar studies should be conducted to evaluate variance components and genetic parameter estimates on different breeds of beef cattle in the United States. |
Implications |
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TopAbstractIntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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Footnotes |
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Received for publication February 17, 2002. Accepted for publication July 18, 2002.
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Literature Cited |
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TopAbstractIntroductionMaterials and MethodsResults and DiscussionImplicationsLiterature Cited |
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