Rates of gain and feed efficiency are important traits in most breeding programs for growing farm animals. The rate of gain (GAIN) is usually expressed over a certain age period and feed efficiency is often expressed as residual feed intake (RFI), defined as observed feed intake (FI) minus expected feed intake based on live weight (WGT) and GAIN. However, the basic traits recorded are always WGT and FI and other traits are derived from these basic records. The aim of this study was to develop a procedure for simultaneous analysis of the basic records and then derive linear traits related to feed efficiency without retorting to any approximation. A bivariate longitudinal random regression model was employed on 13,791 individual longitudinal records of WGT and FI from 2,827 bulls of six different beef breeds tested for their own performance in the period from 7 to 13 mo of age. Genetic and permanent environmental covariance functions for curves of WGT and FI were estimated using Gibbs sampling. Genetic and permanent covariance functions for curves of GAIN were estimated from the first derivative of the function for WGT and finally the covariance functions were extended to curves for RFI, based on the conditional distribution of FI given WGT and GAIN. Furthermore, the covariance functions were extended to include GAIN and RFI defined over different periods of the performance test. These periods included the whole test period as normally used when predicting breeding values for GAIN and RFI for beef bulls. Based on the presented method, breeding values and genetic parameters for derived traits such as GAIN and RFI defined longitudinally or integrated over (parts of) of the test period can be obtained from a joint analysis of the basic records. The resulting covariance functions for WGT, FI, GAIN, and RFI are usually singular but the method presented here does not suffer from the estimation problems associated with defining these traits individually before the genetic analysis. All the results are thus estimated simultaneously, and the set of parameters is consistent.

中文翻译：

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肉牛体重、采食量和剩余采食量曲线遗传参数的同步贝叶斯估计

增重率和饲料效率是大多数农场动物育种计划中的重要特征。增重率 (GAIN) 通常在特定年龄期间表示，饲料效率通常表示为剩余采食量 (RFI)，定义为观察到的采食量 (FI) 减去基于活重 (WGT) 和 GAIN 的预期采食量. 但是，记录的基本性状始终是 WGT 和 FI，其他性状均来自这些基本记录。本研究的目的是开发一种同时分析基本记录的程序，然后得出与饲料效率相关的线性性状，而无需反驳任何近似值。采用双变量纵向随机回归模型对来自 2、6 种不同牛肉品种的 827 头公牛在 7 至 13 月龄期间测试了它们自己的表现。使用 Gibbs 抽样估计 WGT 和 FI 曲线的遗传和永久环境协方差函数。GAIN 曲线的遗传和永久协方差函数是从 WGT 函数的一阶导数估计的，最后根据给定 WGT 和 GAIN 的 FI 条件分布，将协方差函数扩展到 RFI 曲线。此外，协方差函数被扩展为包括在性能测试的不同时期定义的 GAIN 和 RFI。这些时期包括在预测肉牛的 GAIN 和 RFI 育种值时通常使用的整个测试时期。基于所提出的方法，衍生性状的育种值和遗传参数，例如纵向定义或在测试期间（部分）综合定义的 GAIN 和 RFI，可以通过对基本记录的联合分析获得。得到的 WGT、FI、GAIN 和 RFI 的协方差函数通常是奇异的，但这里介绍的方法不会受到与在遗传分析之前单独定义这些特征相关的估计问题的影响。因此，所有结果都是同时估计的，并且参数集是一致的。和 RFI 通常是单数的，但这里介绍的方法不会受到与在遗传分析之前单独定义这些特征相关的估计问题的影响。因此，所有结果都是同时估计的，并且参数集是一致的。和 RFI 通常是单数的，但这里介绍的方法不会受到与在遗传分析之前单独定义这些特征相关的估计问题的影响。因此，所有结果都是同时估计的，并且参数集是一致的。