Guelph Food Research Centre, Agriculture and Agri-Food Canada, Guelph, Ontario, Canada.
Poult Sci. 2013 Apr;92(4):916-22. doi: 10.3382/ps.2012-02688.
Direct selection on a ratio (R) of 2 traits (x1/x2) does not have a mechanism to accommodate the relative economic values (a1 and a2) between x1 and x2 because selection criteria x1/x2 and a1x1/a2x2 rank animals in the same order. This study presented a procedure to incorporate the economic weights into ratio traits through linear transformation. The partial derivatives of a nonlinear profit function evaluated at the means were widely taken as economic weights in the literature. This study showed that the economic weights derived in this manner were erroneous because they actually contain a mixture of actual economic weights and transformation effects. The ratios 1/2 and 2/4 are considered equal by selection on R, but are treated differently by the linear index. In addition, this study presented a unified approach to compare 4 different selection strategies for genetic improvement of ratio traits: linear index (I), selection on the ratio (R), selection on difference between x1 and x2 (D), and selection on x1 alone. This study considered 3 levels of heritability each for variables x1 and x2 and 2 levels of genetic correlations (γG), 2 ratios of means (µ1/µ2), and 4 ratios of phenotypic variances giving a total of 96 scenarios. Linear index I was the most efficient of the 4 criteria compared in all 96 scenarios studied. The superiority of index I over R, D, and selection on x1 alone are particularly remarkable when x1 and x2 have a large difference in heritability and are highly correlated. Selection on x1 alone is an economically viable alternative to criterion I or R for the improvement of ratio traits particularly when x1 is more heritable than x2 and when x2 is costly to measure. Selection on D is more efficient than direct selection on R or selection on x1 alone when x1 is less heritable than x2 and the difference between µ1 and µ2 is small.
直接对两个性状（x1/x2）的比例（R）进行选择，没有一种机制可以适应 x1 和 x2 之间的相对经济价值（a1 和 a2），因为选择标准 x1/x2 和 a1x1/a2x2 会对动物进行相同的排序。本研究提出了一种通过线性变换将经济权重纳入比例性状的方法。文献中广泛采用非线性利润函数在平均值处的偏导数作为经济权重。本研究表明，以这种方式得出的经济权重是错误的，因为它们实际上包含了实际经济权重和转换效应的混合物。通过对 R 进行选择，1/2 和 2/4 的比例被认为是相等的，但线性指数对它们的处理方式不同。此外，本研究提出了一种统一的方法来比较 4 种不同的选择策略，以遗传改良比例性状：线性指数（I）、对比例（R）进行选择、对 x1 和 x2 之间的差异（D）进行选择、仅对 x1 进行选择。本研究考虑了变量 x1 和 x2 的 3 个遗传力水平和 2 个遗传相关系数（γG）、2 个均值比（µ1/µ2）和 4 个表型方差比，共 96 种情况。在所有 96 种情况下，线性指数 I 都是 4 种比较标准中最有效的一种。当 x1 和 x2 的遗传力差异较大且相关性较高时，指数 I 优于 R、D 和仅对 x1 进行选择的优越性尤为显著。仅对 x1 进行选择是对比例性状进行改良的一种经济可行的替代方案，特别是当 x1 比 x2 更具遗传性且 x2 测量成本较高时。当 x1 的遗传力比 x2 低且µ1 和µ2 之间的差异较小时，D 选择比直接对 R 或仅对 x1 进行选择更有效。
