Equations were developed to predict the equilibrium response to the aggregate genotype in units of genetic standard deviation by using selection index composed of GEBVs. A situation was considered in which four-path selection was executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. In practice, index selection comprising standardized GEBVs is often used for the aggregate genotype in units of genetic standard deviation in accordance with the standardization of the true genetic value in the aggregate genotype. Economic weights of the breeding goal in units of genetic standard deviation are used as the coefficients of the standardized GEBVs of the practical index. However, the variance of GEBV necessary to standardize GEBV changes from generation to generation. It meant that economic weights in the breeding goal corresponding to the practical index changed during generations, although relative economic weights in the breeding goal among the component traits should be the same during generations. The practical index assumes GEBVs as estimates with no prediction errors, although GEBVs are estimates with prediction errors, which resulted in overestimation of the selection accuracy of the practical index. The asymptotic genetic gain from the practical index reacted sharply to the uncertainty in GEBVs compared with the theory-based index. Consequently, especially in practical breeding, the correct aggregate genotype in selection index theory associated with the practically used index must be examined and breeding goal should not include a component related to the uncertainty in GEBVs, because economic weights fluctuate during generations in line with the uncertainty in GEBVs.

通过使用由GEBV组成的选择指数，开发了方程以遗传标准差为单位预测对总基因型的平衡响应。考虑了一种情况，在这种情况下执行四路径选择：父亲育种儿子，父亲育种女儿，大坝育种儿子和大坝育种女儿。实际上，根据总基因型中真实遗传值的标准化，通常以遗传标准偏差为单位将包含标准化GEBV的索引选择用于总基因型。以遗传标准偏差为单位的育种目标的经济权重被用作实用指数的标准化GEBV的系数。但是，标准化GEBV所必需的GEBV的差异一代又一代地变化。这意味着育种目标中与实际指标相对应的经济权重在世代之间发生了变化，尽管各成分性状在育种目标中的相对经济权重在世代之间应相同。实际指数假定GEBV为无预测误差的估计值，尽管GEBV是具有预测误差的估计值，这导致对实际指数选择准确性的过高估计。与基于理论的指数相比，实际指数的渐近遗传增益对GEBVs的不确定性产生了强烈的反应。因此，尤其是在实际育种中，必须检查选择指数理论中与实际使用的指数相关的正确的总基因型，并且育种目标不应包括与GEBV不确定性有关的成分，