Multistage linear selection indices

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 multitrait 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.