Multiple trait and random regression models using linear splines for genetic evaluation of multiple breed populations

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 (1/2P(1) + 1/2P(2), 5/8P(1) + 3/8P(2), and 3/4P(1) + 1/4P(2)), 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 arid 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.