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This study aimed to verify if random regression models using linear splines (RRMLS) are suitable for identifying genetic parameters in multiple-breed populations and also to investigate whether an interaction exists between the breeding value (BV) of sires and their progeny breed group. Ten populations were simulated by crossing 2 breeds with distinct genetic variance and nonzero segregation variance. To obtain the genetic parameters, 2 models were used: a multiple-trait model (MULT), in which the trait was considered distinct when evaluated in each group (1/2P1 + 1/2P2, 5/8P1 + 3/8P2, and 3/4P1 + 1/4P2), and a RRMLS with the spline polynomial knots adjusted to these same groups. The genetic parameters estimated through MULT and RRMLS did not differ from the simulated values. The correlations between BV (simulated and estimated) of animals were high and varied from 0.74 to 0.76, which indicates the efficiency of using MULT and RRMLS for predicting BV. Using field data, the traits age at first calving (AFC), first lactation length (LL), and 305-d milk yield (MY-305) from a multiple-breed population of Holstein-Gyr cattle were analyzed. The BV of animals were modeled through RRMLS with 3, 5, and 7 knots, distributed in accordance with the fraction of Holstein breed in each progeny breed group. It was verified that RRMLS with 7 knots for adjusting mean trajectories and genetic effects, with homogeneous residual variance, best fit AFC and LL. For MY-305, the best fit for mean trajectory and genetic effects was the RRMLS with 5 knots and with homogeneous residual variance. The posterior means of heritability varied from 0.21 to 0.48, 0.21 to 0.38, and 0.10 to 0.33 for AFC, LL, and MY-305, respectively. Estimates from genetic parameters obtained by using RRMLS with field data showed that this model is a useful tool for genetic evaluations of populations formed by a great number of breed groups. An interaction occurred between the BV of sires and their progeny breed group, and the genetic parameters for AFC, LL, and MY-305 traits from a multiple-breed population depend on breed composition of the progeny from which the evaluations are based. [ABSTRACT FROM AUTHOR]

• Heritabilities for carcass traits of beef cattle. • Breeding values of carcass traits according to residual feed intake. • Genetic trend of carcass traits in relation to different residual feed intake groups. Our objective was to verify if genetic differences (i.e., additive genetic variation) among animals classified in different residual feed intake adjusted for fat (RFI fat) groups occur, and if selecting for RFI fat impacts carcass traits. Ribeye area, backfat thickness, rump cap (' picanha ' in Brazilian Portuguese) fat thickness, subcutaneous fat thickness, and marbling score were evaluated in relation to the high, medium and low RFI fat groups. Tri-trait analyses were performed using the animal model. The estimated values for heritability were high and no difference was found between the obtained values according to the RFI fat groups, for any of the carcass traits evaluated. These results demonstrate that all traits evaluated in this study have the potential for genetic improvement, regardless of RFI fat classification. The genetic improvement capacity of the herd was confirmed by the genetic trends performed using the breeding value of each RFI fat group, and independently of the group a bull belongs. Therefore, regardless of whether the animals are more or less efficient in terms of RFI fat , it is possible to practice selection for RFI fat in conjunction with carcass traits. [ABSTRACT FROM AUTHOR]

• Random regressions for weight gain in quails. • Legendre polynomials of distinct orders to study in the genotype × environmental interaction. • The genetic group influence the reaction norms behavior. The objective of this study was to use reaction norm models to study genotype × environment interactions of meat-type quails raised on different levels of digestible methionine + cystine. The weight gains of two meat-type quail strains (EV1 and EV2) were measured from 21 to 35 days of age. For EV1 strain the levels of digestible methionine + cystine were 0.60, 0.70, 0.80, 0.90 and 1.00%, for EV2 strain the levels were 0.61, 0.71, 0.81, 0.91 and 1.01%. Reaction norm models with Legendre polynomials (LP) varying from zero to four orders were tested, by using Bayesian methodology. The model of best fit was selected based on the criterions of Deviance Information and Posterior Model Probabilities (PMP). For the EV1 strain, the fourth-order LP model was the best fit for the weight gain description with different levels of digestible methionine + cystine for the mean trajectory, additive genetic effects and five classes of residual variance. For the EV2 strain, the first-order LP model was the best fit for the mean trajectory, fourth-order for additive genetic effects and five classes of residual variance. In both strains, genetic correlation estimates and reaction norm of the genotype in relation to dietary methionine + cystine indicated the existence of a genotype × dietary level of amino acids interaction. For EV1 strain, genetic correlations for weight gain in different levels of digestible methionine + cystine ranged from –0.98 to 0.84, while for EV2 strains these estimates varied from –0.98 to 0.94. Also, in general, for both strains the high density intervals of genetic correlations with 90% of samples included zero, indicating that genetic correlations between the weight gain in different levels of digestible methionine + cystine did not differed from zero. Furthermore, the reaction norms indicated that genotypes were not linearly related to tested dietary levels of amino acids. This absence of linearity implies that to verify the same response to selection in field that was predicted by the genetic evaluation, the nutritional levels used at the herds for selection candidates and their progenies must be the same. [ABSTRACT FROM AUTHOR]

• Different statistical models for analyzing genetic parameters for longitudinal traits. • Simulation processes to validate field data analyzed by single trait model. • Sampling records influence over estimation of genetic parameters. The comprehensive analyses of longitudinal traits under sequential selection could improve genetic parameters estimates and lead to more accurate selection decisions. The objective of this study was to evaluate statistical models for analyzing longitudinal traits under sequential selection. We used single trait (STM), multiple trait (MTM) and random regression model with linear splines polynomials (RRM) to estimate genetic parameters for body weight records of Nellore young bulls. First, we used a complete dataset (DS100) with 60,550 body weight records of 12,110 young bulls. Two additional datasets were also obtained from DS100. They were obtained with a sequential selection of 85% (DS85) and 70% (DS70) of heaviest animals. In addition, some datasets with the same number of records as DS85 and DS70 were also obtained with random sampling of 85% (RS85) and 70% (RS70) of body weight records at each age. Body weights were standardized at 330, 385, 440, 495 and 550 days of age for STM and MTM analysis. In RRM, the knots of linear splines were fitted at 250, 330, 385, 440, 495, 550 and 597 days of age. The estimates of additive genetic, residual and phenotypic variances from STM analysis of DS85 and DS70 were lower than the corresponding estimates from STM analysis of DS100. However, the estimates of genetic and environmental parameters from MTM and RRM analysis of DS100, DS85 and DS70 were similar. The reduction of dataset size with random sampling (RS85 and RS70) did not affect the estimates of genetic and environmental parameters from STM, MTM and RRM analysis. MTM and RRM are adequate for genetic evaluation of the longitudinal traits under sequential selection, but RRM presents some advantages over MTM. RRM with linear splines does not need previous adjustments of the body weights for standard ages and it also provides estimates of genetic and environmental parameters directly at the same points as the corresponding traits in MTM. [ABSTRACT FROM AUTHOR]