Relative contribution of effects included in contemporary groups for adjusted and actual 120-day and 210-day weights in Nelore cattle in Brazil

The objective of this research was to estimate the relative magnitude of effects included in contemporary groups (CG) and their interactions with adjusted and actual 120 d and 210 d weights in 72,731 male and female Nelore calves born from 1985 to 2005 in 40 herds from PMGRN (Genetic Improvement Program of Nelore). Ten models with different CG structures were compared. The analyses were done using the general linear models (GLM) procedure run in SAS software. All of the effects included in the CG for each model were significant (p < 0.001) for the four traits analyzed. Inclusion of semester or trimester of birth as part of a CG was more appropriate than its use as an independent effect in the model because it accounted for interactions with the other effects in the CG. Calf sex (CS) and dam age at calving (DAC) had similar effects across the models, which suggested independence from other effects in these models. The corresponding age deviation effect had a larger impact on actual weight at 120 d than any other effect in all of the models tested. The use of actual weights in models with no CS effect in CG provides an alternative that would allow better genetic connectedness among CGs and greater accuracy in genetic evaluations.


Introduction
Contemporary groups (CGs) are used in genetic evaluations to eliminate bias caused by systematic environmental effects such as differences in management, feeding and seasons (Van Vleck, 1987;Van Bebber et al., 1997;Carabaño et al., 2004;Cantet et al., 2005). However, a large number of CG can result in a small number of records per subclass, resulting in an increase in the variance of prediction errors and a reduction in the accuracy of genetic evaluations (Van Vleck, 1987;Van Bebber et al., 1997).
The length of time to identify animals belonging to the same CG within a herd is controversial. A balance between maximum accuracy and reduced bias must be achieved to optimize the definition of CG. The problem with the usual definition of CG is its arbitrary definition of periods of time that do not correspond to criteria for maximum accuracy and minimum bias (Schmitz et al., 1991;Carabaño et al., 2004). In an attempt to resolve this problem several criteria to compare different definitions of CG that consider the estimated intra-CG variance, residual variance and accuracy of genetic evaluations have been proposed (Schmitz et al., 1991;Sivarajasingam, 1993;Van Bebber et al., 1997;Carabaño et al., 2004).
Brazil is known for its environmental diversity, with strong seasonal effects and fluctuations in pasture production that should be considered in the construction of CGs for genetic evaluation models (Fries and Ferraz, 2006). A significant influence in non-genetic effects and their interactions on growth in beef cattle has been widely proven in Brazil (Cardellino and Cardellino, 1984;Pons et al., 1989;Mascioli et al., 1996;Reyes et al., 1998Reyes et al., , 2006Paz et al., 1999;Cardoso et al., 2001;Bocchi et al., 2004).
Several studies have shown that a linear adjustment of weight to a constant age at weaning in beef cattle does not completely remove the effect of age (Rossi et al., 1992;Villalba et al., 2000;Lobo and Martins Filho, 2002;Teixeira and Albuquerque, 2003;Reyes et al., 2004;Torres Júnior and Toral, 2006) because the age of the animal at weighing time influences its average daily gain and consequently its adjusted weight (Toral et al., 2007).
A model for genetic analysis should be preceded by careful study of systematic environmental effects and their interactions. The objective of this study was therefore to estimate and compare the relative magnitudes of effects included in CGs and their interactions on adjusted and actual calf weights at 120 d and 210 d of age in Nelore cattle in Brazil.

Material and Methods
The dataset consisted of adjusted and actual (real) weights at 120 d (AW120, RW120) and 210 d (AW210, RW210) of age from 72,731 male and female Nelore calves born from 1985 to 2005 in 40 herds belonging to PMGRN (Genetic Improvement Program of Nelore). Actual weights were those within 120 ± 60 d of age for RW120 and within 210 ± 60 d of age for RW210, and the corresponding ages were expressed as deviations (CAD -corresponding age deviations) for 120 d and 210 d, respectively. Standardized weights were obtained by interpolation using a weight before and another after the standard age (120 d or 210 d), with a maximum interval of 195 d between them (± 90 d with a tolerance of 15 days because of possible changes in management). If there was no previous weight for AW120, then birth (either measured or the average of the breed: males = 33 kg and females = 31 kg) was used as the first weight for the interpolation. Computations were done in a manner similar to that used by PMGRN (Lôbo, 1996): where AW = adjusted weight at a standardized age (AW120 or AW210), W = nearest actual weight to a standardized age, Wp = previous weight, I = days between W and Wp, A = standardized age (120 d or 210 d) and Aw = age at measurement of W.
The effect of dam age at calving (DAC) was classified into six classes: 1 = 2 yr, 2 = 3 yr, 3 = 4 yr, 4 = 5 yr, 5 = 6-9 yr and 6 = ³ 10 yr old. Five CG structures, with a minimum of five records per subclass, were defined as follows: CG 1 : herd -year of birth -management group at each age. CG 2 : CG 1 -semester of birth. CG 3 : CG 1 -trimester of birth. CG 4 : CG 2 -calf sex. CG 5 : CG 3 -calf sex. The GLM procedure of SAS was used to estimate the relative importance of effects included in CGs and their in-teractions in 10 linear models. The structure of these models (M) was as follows: M 1 : Weight = a + CG 1 + SB + CS + DAC + e M 1A : Weight = a + CG 1 + TB + CS + DAC + e M 1B : Weight = a + CG 1 + CS + DAC + JDB + e M 1C : Weight = a + CG 1 + CS + DAC + JDB(CS) + e M 2 : Weight = a + CG 2 + CS + DAC + e M 3 : Weight = a + CG 3 + CS + DAC + e M 3A : Weight = a + CG 3 + CS + DAC(CS) + e M 3B : Weight = a + CG 3 + CS + DAC + CAD(CS) + e M 4 : Weight = a + CG 4 + DAC + e M 5 : Weight = a + CG 5 + DAC + e where Weight = adjusted or actual weight at 120 d or 210 d of age, a = a constant, CG = contemporary group, SB = semester of calf birth, TB = trimester of calf birth, CS = calf sex, DAC = class of dam age at calving (one of the six classes defined above), JDB = Julian date of calf birth, CAD = calf age deviation (deviation from 120 d or 210 d) and e = a residual. The CAD effect was modeled as a cubic polynomial in all analyses using actual weights (RW120 and RW210).
The adjustability of the models was evaluated using an adjusted coefficient of determination (R 2 A = 1 -[residual mean square / total mean square]) and an estimate of the residual variance. The contribution of each effect to the R 2 coefficient for each model was computed as the ratio of the sum of squares due to each effect (Type I) and the total sum of squares.
Models for adjusted weights (AW120 and AW210) were defined as follows. Models M 1 to M 1C included the effects of CG 1 , calf sex (CS), dam age at calving (DAC), and season of birth defined as semester of birth (SB, M 1 ), trimester of birth (TB, M 1A ) and Julian date of calf birth (cubic polynomial; JDB, M 1B ), and Julian date of calf birth date nested within calf sex (cubic polynomial; JDB(CS), M 1C ). Model M 2 included CG 2 = CG 1 -SB, whereas models M 3 and M 3A contained CG 3 = CG 1 -TB, and these three models included the effects of CS and DAC; DAC was nested within CS in M 3A . Model M 4 tested CG 4 = CG 2 -CS, model M 5 had CG 5 = CG 3 -CS, and both models included DAC. Models for actual weights (RW120 and RW210) contained the same effects as models for adjusted weights plus the effect of calf age at weight expressed as a deviation from 120 d or 210 d of age (CAD) as a cubic polynomial. This model was tested using M 3B , where a cubic polynomial CAD effect was nested within CS. Table 1 shows descriptive statistics for adjusted and actual weights at 120 d and 210 d of age. Larger ranges and greater standard deviations were observed for actual weights compared to standardized weights at both ages because of the effect of calf age on weight measurements. 570 Pascoa et al. Table 2 shows the number of CGs and the mean number of records per CG for the five CG structures defined here. For weight at 120 d the number of subclasses remained constant between the actual and standardized weights and the average size of the five CG structures was similar. On the other hand, for weight at 210 d, CG number and size were slightly larger for actual weights than for standardized weights in all five CG structures, possibly because of management conditions in the herds where the animals were located. A large proportion of animals was weighed before the standard age of 210 d and subsequently at ages beyond the maximum interval of 195 d (maximum interval allowed for standardization), thus explaining the difference between the actual weights and weights standardized to 210 d.

Results and Discussion
The relative contributions of each effect to the coefficient of determination (R 2 ) in each model are summarized in Table 3. All effects were significant (p < 0.001) for the four traits analyzed (AW120, AW210, RW120 and RW210).
The smallest contribution of seasonal effects was for SB (M 1 ), the largest was for JDB (M 1B ), and the effect of TB (M 1A ) was intermediate between SB (M 1 ) and JDB (M 1B ). Maximum R 2 A (%) differences for AW120, AW210, RW120 and RW210 were between those for M 1B and M 1 (0.4, 3.2, 0.2 and 2.5, respectively), and the corresponding maximum reductions in V R (%) were 0.6, 5.4, 0.5 and 5.2. These results clearly indicate that seasonal effects were more important for weight at 210 d of age than at 120 d of age, in agreement with the findings of Reyes et al. (1998) for adjusted weights at 120 d and 240 d of age in Nelore cattle.
The differences in R 2 A (%) between models M 5 and M 1 showed increases of 3.2, 5.03, 1.5 and 3.9, accompanied by reductions in V R (%) of 5.0, 8.9, 4.9 and 8.0 for AW120, AW210, RW120 and RW210, respectively. The differences in R 2 A (%) between models M 2 and M 1 (1.4, 1.7, 0.6 and 1.3 for AW120, AW210, RW120 and RW210, respectively) reflected the contribution of interactions between SB and the other effects in CG. The contribution of interactions between TB and the rest of the effects contained in CG 3 were 2.5, 2.7, 1.2, and 2.1 for the same four traits (M 3 -M 1A ). These values showed that interactions involving SB (M 1 ) and TB (M 1A ) were of similar importance and that inclusion of some seasonal class effects within a CG would be more effective than their inclusion as an independent main effect (including as JDB) or the application of a correction factor for these effects. Similar results were found by Reyes et al. (1998) for adjusted weights at 120 d and 240 d of age in Nelore cattle, and by Reyes et al. (2006) for preweaning growth in a multibreed Nelore x Hereford population.
As shown in Table 2, CG 2 had only 62.9% of CG, but a mean CG size 58.9% larger than CG 4 for AW120; the corresponding values for AW210, RW120 and RW210 were 63.8% and 56.7%, 62.9% and 58.7%, and 63.7% and 57.1%, respectively. Table 2 also shows that GC 3 had 64.5% of CG and a mean CG size 55.2% larger than GC 5 for AW120; the corresponding values for AW210, RW120 and RW210 were 64.8% and 54.4%, 64.5% and 55.1%, and 64.8% and 54.0%, respectively. Significant differences among the CG structures were accompanied by increases in R 2 A (%) between 0.26 (RW120) and 0.84 (AW210), and reductions in V R (%) between 0.83 (RW120) and 1.46 (AW210). These results identified models M 2 (GC 2 with SB) and M 3 (GC 3 with TB), both without CS in their CG but with R 2 A (%) differences between 0.61 (RW120) and 1.98 (RW210), as viable alternatives for use in genetic evaluations of preweaning growth traits.
Estimates of the effects of CS and DAC and their contributions to R 2 were similar for all traits in all models. The estimates for CS(%) were 3.9, 4.7, 1.8 and 3.3 for AW120, AW210, RW120 and RW210, respectively, and for DAC (%) they were 4.1, 1.9, 1.7 and 1.6, respectively. Similar estimates for CS and DAC were obtained for preweaning growth in Nelore x Hereford crosses (Reyes et al., 2006). These results indicated that CS and DAC were independent of the other effects in the models considered here for all four traits, and that, for both adjusted and actual weights, CS was more important than DAC at 210 d of age, Structure of contemporary groups in Nelore cattle 571  whereas the opposite was true at 120 d of age. These results agreed with the expectation of an increase in the importance of the sex effect and a decrease in maternal influence as the animals grow older; they also support the current practice of including maternal effects when evaluating growth in young calves.   ( Differences of 0.6, 0.8, 0.3, and 0.6 in R 2 A (%) between models M 4 and M 2 and reductions in V R (%) of 0.9, 1.5, 0.8 and 1.4, for AW120, AW210, RW120 and RW210, respectively, represented the contribution of interactions between CS and the remaining effects in CG 2 . Similarly, R 2 A (%) differences between models M 5 and M 3 and reductions in V R (%) were attributable to the combined effect of interactions between CS and the other components of CG 3 . The corresponding values were 0.6, 0.9, 0.3 and 0.6 for differences in R 2 A (%) and 1.0, 1.6, 0.9 and 1.4 for reductions in V R (%) for AW120, AW210, RW120 and RW210, respectively. The low interaction between CS and other CG components in CG 2 and CG 3 relative to the main CS effect suggested that CS can be included as a class effect separately from CG, and that this will have a very small impact on the adjustment of records. In addition, an independent CS effect will decrease the number of CGs and increase their size, thereby increasing connectedness and the accuracy of genetic evaluations. These results showed that estimates of CS were similar across models and reconfirmed the results for Nelore x Hereford cattle (Reyes et al., 2006). Although significant, within sex estimates of DAC (M 3A ) and JDB (M 1C ) for all four traits, and of CAD (M 3B ) for actual weights did not show appreciable contributions to the increase in R 2 A (< 0.1%) or to the reduction in V R (< 1 unit), suggesting that these effects would not need to be included in the usual models for genetic evaluation of preweaning growth traits where simple models are required. Reyes et al. (2006) reached a similar conclusion for Nelore x Hereford cattle.
The contribution of the CAD effect was large relative to other effects in the CGs tested here. The CAD contributed most to the increase in R 2 A and the reduction in V R , and was one of the most important effects for weight at 210 d. Figure 1 shows the cubic polynomial regressions of calf actual weights on days of age expressed as deviations from 120 d and 210 d, estimated using models M 2 , M 3 , M 4 and M 5 . The quadratic and cubic terms were significant (p < 0.05) for both traits in all models, reconfirming that the relationship between weight and age is not linear, in agreement with previous findings (Rossi et al., 1992;Lobo and Martins Filho, 2002;Reyes et al., 2004;Torres Júnior and Toral, 2006). Hence, the use of actual weights measured within an interval centered on a pre-established standard age, and inclusion of the effect of calf age in the analysis model provides an advantageous alternative for genetic evaluations.
Structure of contemporary groups in Nelore cattle 573 In conclusion, the independence of calf sex effects from other effects in the CGs tested here suggests that this effect could be modeled separately from CG effects. This independence creates a promising alternative for modeling genetic analyses of preweaning growth traits that would increase the size of CGs and the accuracy of genetic predictions. The inclusion of semester or trimester of birth as part of a CG was more appropriate than independent estimates of these effects because it accounted for interactions with all other components of a CG. Estimates of Julian date of calf birth, dam age at calving, and calf age at weighing within calf sex suggested that genetic evaluation models for preweaning growth traits need not include these effects, which means that simpler models for these traits can be used. The use of actual weights in models that include a season of birth effect within CGs and model calf sex separately constitute alternatives that could improve genetic connectedness among CGs and help increase the accuracy of genetic evaluations.