Chapter 6. Constrained linear genomic selection indices

Abstract

The constrained linear genomic selection indices are null restricted and predetermined proportional gain linear genomic selection indices (RLGSI and PPG-LGSI respectively), which are a linear combination of genomic estimated breeding values (GEBVs) to predict the net genetic merit. They are the results of a direct application of the restricted and the predetermined proportional gain linear phenotypic selection index theory to the genomic selection context. The RLGSI can be extended to a combined RLGSI (CRLGSI) and the PPG-LGSI can be extended to a combined PPG-LGSI (CPPG-LGSI); the latter indices use phenotypic and GEBV information jointly in the prediction of net genetic merit. The main difference between the RLGSI and PPG-LGSI with respect to the CRLGSI and the CPPG-LGSI is that although the RLGSI and PPG-LGSI are useful in a testing population where there is only marker information, the CRLGSI and CPPG-LGSI can be used only in training populations when there are joint phenotypic and marker information. The RLGSI and CRLGSI allow restrictions equal to zero to be imposed on the expected genetic advance of some traits, whereas the PPG-LGSI and CPPG-LGSI allow predetermined proportional restriction values to be imposed on the expected trait genetic gains to make some traits change their mean values based on a predetermined level. We describe the foregoing four indices and we validated their theoretical results using real and simulated data