Boligon A A, Baldi F, Mercadante M E Z, Lobo R B, Pereira R J, Albuquerque L G
Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista Júlio de Mesquita Filho, Jaboticabal, SP, Brasil.
Genet Mol Res. 2011 Jun 28;10(2):1227-36. doi: 10.4238/vol10-2gmr1087.
We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.
我们使用基于勒让德多项式和B样条函数的多性状和随机回归模型，对内洛尔牛从出生到成熟体重的预期育种值准确性的潜在提高进行了量化。使用了来自8144头母牛的87712条体重记录，这些记录是从巴西内洛尔计划中从出生到成熟每三个月记录一次的。对于随机回归分析，考虑了从出生到八岁的所有母牛体重记录（数据集I）。从这个总体数据集中创建了一个子集（数据集II），其中仅包括九个体重记录：出生时、断奶时、365天和550天时，以及2、3、4、5和6岁时。使用随机回归和多性状模型对数据集II进行了分析。分析模型包括当代组作为固定效应以及母牛年龄作为线性和二次协变量。在随机回归分析中，使用年龄的正交多项式的三次回归对平均生长趋势进行建模。残差方差通过具有五个类别的阶梯函数进行建模。分别使用四阶和六阶勒让德多项式对直接遗传效应和动物永久环境效应进行建模，而对于母体遗传效应和母体永久环境效应则考虑三阶勒让德多项式。在基于B样条函数的随机回归模型中，使用二次多项式对所有随机效应进行建模。在基于B样条函数的随机回归模型中，直接遗传效应和动物永久环境效应使用三段或五个系数进行建模，遗传母体效应和母体永久环境效应使用一段或三个系数进行建模。对于两个数据集（I和II），根据通过随机回归或多性状模型获得的预期育种值，动物的排名不同。使用随机回归模型时，在体重记录数量较少的年龄获得了最高的准确性提高。结果表明，随机回归模型比传统的有限多性状模型提供了更准确的预期育种值。因此，通过用随机回归模型替代多性状模型进行遗传评估，预计肉牛生长性状将有更高的遗传反应。B样条函数可以作为勒让德多项式的替代方法，用于对从出生到成熟体重的协方差函数进行建模。
