Open Access

The plant net genetic merit is a linear combination of trait breeding values weighted by its respective economic weights whereas a linear selection index (LSI) is a linear combination of phenotypic or genomic estimated breeding values (GEBV) which is used to predict the net genetic merit of candidates for selection. Because economic values are difficult to assign, some authors developed economic weight-free LSI. The economic weights LSI are associated with linear regression theory, while the economic weight-free LSI is associated with canonical correlation theory. Both LSI can be unconstrained or constrained. Constrained LSI imposes restrictions on the expected genetic gain per trait to make some traits change their mean values based on a predetermined level, while the rest of the traits change their values without restriction. This work is geared towards plant breeders and researchers interested in LSI theory and practice in the context of wheat breeding. We provide the phenotypic and genomic unconstrained and constrained LSI, which together cover the theoretical and practical cornerstone of the single-stage LSI theory in plant breeding. Our main goal is to offer researchers a starting point for understanding the core tenets of LSI theory in plant selection.

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