Abstract
Multistage linear selection indices select individual traits available at different times or stages and are applied mainly in animals and tree breeding, where the traits under consideration become evident at different ages. The main indices are: the unrestricted, the restricted, and the predetermined proportional gain selection index. The restricted and predetermined proportional gain indices allow null and predetermined restrictions to be imposed on the trait expected genetic gain (or multi-trait selection response) values, whereas the rest of the traits remain changed without any restriction. The three indices can use phenotypic, genomic, or both sets of information to predict the unobservable net genetic merit values of the candidates for selection and all of them maximize the selection response, the expected genetic gain for each trait, have maximum accuracy, are the best predictor of the net genetic merit, and provide the breeder with an objective rule for evaluating and selecting several traits simultaneously. The theory of the foregoing indices is based on the independent culling method and on the linear phenotypic selection index, and is described in this chapter in the phenotypic and genomic selection context. Their theoretical results are validated in a two-stage breeding selection scheme using real and simulated data.
Highlights
Multistage linear selection indices select individual traits available at different times or stages and are applied mainly in animals and tree breeding, where the traits under consideration become evident at different ages
In a similar manner to the linear phenotypic selection index (LPSI, Chap. 2), the objectives of the multistage linear phenotypic selection index (MLPSI) are: 1. To predict the net genetic merit H 1⁄4 w0g, where g0 1⁄4 [g1 g2 . . . gt] is the vector of true breeding values of an individual for t traits and w0 1⁄4 1⁄2 w1 w2 . . . wt is the vector of economic weights
9.2.1 The multistage restricted linear phenotypic selection index (MRLPSI) Parameters for Two Stages In Chap. 3, we indicated that vector bR 1⁄4 Kb is a linear transformation of the LPSI vector of coefficients (b) made by the projector matrix K, and that matrix K is idempotent (K 1⁄4 K2) and projects b into a space smaller than the original space of b
Summary
In a similar manner to the linear phenotypic selection index (LPSI, Chap. 2), the objectives of the multistage linear phenotypic selection index (MLPSI) are: 1. To predict the net genetic merit H 1⁄4 w0g, where g0 1⁄4 [g1 g2 . . . gt] is the vector of true breeding values of an individual for t traits and w0 1⁄4 1⁄2 w1 w2 . . . wt is the vector of economic weights. In a similar manner to the linear phenotypic selection index 2), the objectives of the multistage linear phenotypic selection index (MLPSI) are: 1. Gt] is the vector of true breeding values of an individual for t traits and w0 1⁄4 1⁄2 w1 w2 . 3. To maximize the MLPSI selection response and its expected genetic gain per trait. When selection is based on all the individual traits of interest jopinffitffiffilffiyffiffi,ffiffiffithe LPSI vector of coefficients that maximizes the selection response R 1⁄4 k b0Pb and the expected genetic gain per trait E 1⁄4 kpCffiffi0ffibffiffiffiffi is b 1⁄4 PÀ1Cw, where C and P are the b Pb covariance matrices of the true breeding values (g) and trait phenotypic values (y) respectively, and k is the selection intensity. In MLPSI terminology, the LPSI is called a one-stage selection index.
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