Economic values

The economic values were obtained by bioeconomic modelling using the Microsoft Excel 2010 computer programme to simulate a complete cycle in Angus–Nellore crossbred production system. In order to obtain the economic selection index for Angus bulls, the used breeding objective was chosen according to economically significant traits and determined according to the methodology described by Ponzoni and Newman (Reference Ponzoni and Newman1989). The adopted breeding objective consisted of the weaning rate and slaughter weight according to the aim of the simulated production system, which was the production of crossbred animals for commercialization at the moment of slaughter.

Information on biological parameters (mortality rate, pre-slaughter mortality, disposal rate, weaning rate, conception rate and weights from birth to slaughter), gathered from technical and scientific literature (Kaps et al., Reference Kaps, Herring and Lamberson2000; Martha et al., Reference Martha, Barioni, Vilela and Barcellos2003; Weber et al., Reference Weber, Rorato, Lopes, Comin, Dornelles and Araújo2009; Valadares Filho et al., Reference Valadares Filho, Marcondes, Chizzotti and Paulino2010) and information from real herds, were used in the simulation of a stabilized herd, obtaining the number of animals per category, which was used to calculate the sources of income and expenses (Anualpec, 2017; Cepea, 2018) in the evaluated system. The model comprised an intensive production system, distributed in pasture areas containing Brachiaria brizantha cv. Marandu, and the herd consisted of 1000 Nellore cows, including 24-month-old heifers, and seven Aberdeen Angus bulls. Calves were weaned on average at 7 months of age and maintained in the pasture with their mothers. After weaning, they were separated into batches by sex, and remained in the pasture until 18 months of age, after which they were transferred to a feedlot until 21 months of age. At the end of the cycle, all of the animals (males and females) were sold for slaughter; disposal cows and bulls had the same destination. The average prices of the expenses and revenue components for the production system are shown in Tables 1 and 2, respectively.

Table 1. Annual expenses of the complete-cycle production system

Table 2. Annual revenues of the complete-cycle production system

The economic values were based on economic and productive assessments, relating the expenses, revenues, biological information and management of the production system, which were calculated for each evaluated trait. The influence on the annual profitability of the production system was verified by simulating 1.0% increase in the performance of a particular trait, maintaining the others traits constant, according to the following equation:

$$EV = \left({\displaystyle{1 \over n}} \right)\times \left({\displaystyle{{MP} \over {GG}}} \right)$$

where: EV economic value; n corresponds to the number of animals in each category; MP represents the marginal profit obtained by the difference between the profit before and after trait improvement, and GG was calculated by the difference between the performance of the trait before and after the improvement (Groen et al., Reference Groen, Steine, Colleau, Pedersen, Pribyl and Reinsch1997). The calculations were based on Brazilian currency (R$) and converted to North American currency (US$) using the average price in 2017 (US$1.00 = R$3.19). The economic value was expressed in American currency (US$) per change in trait unit, based on cow/year. The profit equations can be represented by the following equations:

$$P = ( {P_M + P_F + P_{DC} + P_{DB}} ) \ndash TE$$

$$\eqalignno{P_M & = Nx 0.5 x ( {1-R_{MW}} ) x( {1-R_{M12}} ) x( {1-R_{M18}} ) x( {1-R_{MS}} ) \cr & \quad x ( {FW_Mx US\dollar /@} ) } $$

$$\eqalignno{P_F & = Nx 0.5 x ( {1-R_{MW}} ) x( {1-R_{M12}} ) x( {1-R_{M18}} ) x( {1-R_{MS}} ) \cr & \quad x ( {FW_Fx US\dollar /@} ) }$$

$$P_{DC} = ( {N_C + N_H} ) x ( {1 -R_M} ) + ( {1 -R_{DC}} ) x ( {FW_{DC}x US\dollar /@} ) $$

$$P_{DB} = N_Bx ( {1 -R_{DB}} ) x ( {FW_{DB}x US\dollar /@} ) $$

where P, marginal profit; P_M and P_F, profit from sale of male and female, respectively; P_DC, profit from sale of disposal cows; P_DB, profit from sale of disposal bulls; TE, total expenses; N, number of animals born; R_MW, mortality rate from birth to weaning; R_{M 12}, mortality rate at 12 months; R_{M 18}, mortality rate at 18 months; R_MS, mortality rate at slaughter age; FW_M and FW_F, final weight of male and female, respectively; N_C, number of mature cows; N_H, number of heifers 2 years; R_M, mortality rate of cows; R_DC, discard rate of cows; N_B, number of bulls; R_DB, discard rate of bulls; FW_DC and FW_DB, final weight of disposal cows and bulls, respectively.

Estimation of variance components and genetic parameters

The data regarding performance and pedigree of the animals of the Angus breed were provided by Gensys Consultores Associados S/S Ltda. and PROMEBO (Programa de Melhoramento de Bovinos de Carne - Beef Cattle Breeding Programme) of the National Breeders Association (ANC) ‘Herd-Book Collares’. The employed traits consisted of weaning weight, 18-month weight, scrotal circumference, fat thickness and ribeye area. The 18-month weight was adjusted to 550 days as recommended by BIF (1996), and calculated by applying the following equation:

$$W18_{aj} = \displaystyle{{W18-WW} \over {N_1}} \times 345 + W_{205}$$

where: W18 and WW represent 18-month weight and weaning weight, respectively, expressed in kilograms, and N ₁ corresponds to the number of days from weaning until 18 months of age, and W ₂₀₅ correspond to adjusted 205-day weight calculated as recommended by BIF (1996).

The assembly of the files for analyses was performed using the SAS software (2003) computer programme for data file editing. Four seasons were created with the month of the year (1 = October, November and December; 2 = January, February and March; 3 = April, May and June; 4 = July, August and September) for dates of birth, weighing at weaning and yearling, date of scrotal circumference measurement and date of ultrasound for subcutaneous fat thickness and ribeye area. The contemporary groups were formed for birth weight with animals from the same farm, year, sex and season of birth. For the weaning weight and yearling weight, the contemporary groups contained animals of the same farm, sex, year of birth, year and season at the time of measurement and management group. For scrotal circumference, the contemporary groups were composed of animals from the same year and season of birth, management group and year and season at the time of measurement. For the ribeye area and the subcutaneous fat thickness the contemporary groups included animals of the same sex, year of birth, management group, year and season at the time of ultrasound.

Were deleted records of animals with incomplete information, bulls with less than five offspring, cows with reproductive ages of less than three and greater than 13 years, contemporary groups with less than five animals and observations displaying plus or minus 3.5 standard deviations from the mean of the traits within the contemporary group.

After data editing, a total of 1242 animals remained with information regarding all of the traits considered for analyses. The animal model for all of the traits included the fixed effect of the contemporary group, the random effects of the animals (direct) and the random residual effects. For weaning weight, the age of cow at calving was used as a covariate (linear and quadratic). For scrotal circumference, fat thickness and ribeye area, the age of the animals on the date in which the measurement was taken was considered as a covariate (linear and quadratic). The pedigree file contained 220 045 animals, which were used in the relationship matrix. The genetic parameters were estimated in bivariate analyses, employing the restricted maximum likelihood method using the WOMBAT software (Meyer, Reference Meyer2007). The animal model applied can be written as:

$$\left[{\matrix{ {y_1} \cr {y_2} \cr } } \right] = \left[{\matrix{ {X_1} & 0 \cr 0 & {X_2} \cr } } \right]\ast \;\left[{\matrix{ {\beta_1} \cr {\beta_2} \cr } } \right] + \left[{\matrix{ {Z_1} & 0 \cr 0 & {Z_2} \cr } } \right]\ast \;\left[{\matrix{ {a_1} \cr {a_2} \cr } } \right] + \left[{\matrix{ {M_1} & 0 \cr 0 & {M_2} \cr } } \right]\ast \;\left[{\matrix{ {m_1} \cr {m_2} \cr } } \right] + \left[{\matrix{ {e_1} \cr {e_2} \cr } } \right]$$

where: y ₁ and y ₂ are the vectors of observation for traits 1 and 2; X ₁ and X ₂ represent the incidence matrices relating the elements of trait 1 and 2 to the fixed effects; β ₁ and β ₂ correspond to the vectors of the fixed effects for traits 1 and 2; Z ₁ and Z ₂ are incidence matrices which relate the elements of trait 1 and 2 to the direct effects; a ₁ and a ₂ represent the vectors of the random effects of the animal (direct) for traits 1 and 2; M ₁ and M ₁ are incidence matrices which relate the elements of traits 1 and 2 to the maternal additive genetic; m ₁ and m ₂ represent the vectors of the random maternal genetic effects; and e ₁ and e ₂ are the vectors of the random residual effects for traits 1 and 2.

Development of the economic selection index

The selection index was defined for animals of the Angus breed in order to select potential bulls for the production of crossbred animals (Angus × Nellore). Weaning rate and final weight at slaughter were adopted as the breeding objective for the selection index. In order to achieve the objective, weaning weight, 18-month weight (adjusted to 550 days of age), scrotal circumference, subcutaneous fat thickness and ribeye area were used as selection criteria.

The Angus breed data file did not contain the measurements of the final weight at slaughter. Therefore, in order to construct the index, the final weights were estimated using the 18-month weights and the weight gain from weaning to 18-month. The economic selection index (I) was generated by combining the expected progeny difference (EPD) of the animals for each trait with their respective index coefficients (b) of the selection criteria, according to the following equation:

$$I = ( {b_{1\;} \times EPD_1} ) + ( {b_2 \times \;EPD_2} ) + \cdots + ( {b_n \times \;EPD_n} ) $$

The methodology used for the calculation of regression coefficients of the indices was proposed by Schneerberger et al. (Reference Schneerberger, Barwick, Crow and Hammond1992), where the coefficients are calculated as

$$b = G_{11}^{{-}1} \;\times \;\;G_{12}\;\times \;\;v$$

where b is the vector of selection index coefficients; G ₁₁ represents genetic (co-) variances matrix among the selection criteria in the index; G ₁₂ corresponds to the genetic covariance matrix between the breeding objective and the selection criteria, and v is the vector of the economic values of the breeding objective. The regression coefficients were calculated using the R software (R Core Team, 2016).

Some (co) variance components between the objectives and selection criteria for Aberdeen Angus used in the current study had been estimated previously by Fernandes et al. (Reference Fernandes, Savegnago, El Faro, Roso and Paz2018). The covariance components not found were assumed as zero in the simulation of the current study.

Cluster analyses

Hierarchical and non-hierarchical cluster analyses were performed using predicted breeding values of the traits used as selection criteria (weaning weight, 18-month weight, scrotal circumference, subcutaneous fat thickness and ribeye area) to group animals based on similarities of the genetic values in order to evaluate the genetic profile of the groups within the population. The breeding values were standardized using the normal standard distribution (z scores) before carry out cluster analyses. The hierarchical cluster analysis was used to choose the number of clusters into which the population could be initially divided. The Euclidean distance was applied as a measurement of dissimilarity between the animals, and the employed clustering algorithm for group formation was Ward' method (Ward, Reference Ward1963). After defining the number of clusters, the non-hierarchical analysis using the K-means method was conducted to explore the genetic profile of the groups, based on the breeding values of the evaluated traits. In both analyses, the genetic values of the animals were considered for all the traits used as selection criteria. The PROC CLUSTER procedure of the SAS software (2003) was used for cluster analysis.