Abstract
The linear genomic selection index (LGSI) is a linear combination of genomic estimated breeding values (GEBVs) used to predict the individual net genetic merit and select individual candidates from a nonphenotyped testing population as parents of the next selection cycle. In the LGSI, phenotypic and marker data from the training population are fitted into a statistical model to estimate all individual available genome marker effects; these estimates can then be used in subsequent selection cycles to obtain GEBVs that are predictors of breeding values in a testing population for which there is only marker information. The GEBVs are obtained by multiplying the estimated marker effects in the training population by the coded marker values obtained in the testing population in each selection cycle. Applying the LGSI in plant or animal breeding requires the candidates to be genotyped for selection to obtain the GEBV, and predicting and ranking the net genetic merit of the candidates for selection using the LGSI. We describe the LGSI and show that it is a direct application of the linear phenotypic selection index theory in the genomic selection context; next, we present the combined LGSI (CLGSI), which uses phenotypic and GEBV information jointly to predict the net genetic merit. The CLGSI can be used only in training populations when there are phenotypic and maker information, whereas the LGSI is used in testing populations where there is only marker information. We validate the theoretical results of the LGSI and CLGSI using real and simulated data.
Highlights
The linear genomic selection index (LGSI) is a linear combination of genomic estimated breeding values (GEBVs) used to predict the individual net genetic merit and select individual candidates from a nonphenotyped testing population as parents of the selection cycle
The main advantage of the LGSI over the linear phenotypic selection index (LPSI) lies in the possibility of reducing the intervals between selection cycles (LG) by more than two thirds (Lorenz et al 2011); this parameter should be incorporated into the LGSI selection response and the expected genetic gain per trait to reflect the main advantage of the LGSI over the LPSI and the other indices
Where kI is the standardized selection differential associated with the LGSI, σHIG is the covariance between H 1⁄4 w0g and the LGSI, σ2IG is the variance of the LGSI, σH is the standard deviation of H, ρHIG is the correlation between H and the LGSI, and LG denotes the intervals between selection cycles
Summary
The breeding value (gi) is the average additive effects of the genes an individual receives from both parents; it is a function of the genes transmitted from parents to progeny and is the only component that can be selected and, the main component of interest in breeding programs (Mrode 2005). Basic assumptions for gi and ei are: both gi and ei have normal distribution with expectation equal to zero and variance σ2gi and σ2ei respectively. This means that yi 1⁄4 μi + gi + ei is a linear mixed model (Mrode 2005; Searle et al 2006), where μi is the mean of yi. Equation (5.2) can be extended to the multi-trait phenotypic selection index case, but to predict the net genetic merit (H 1⁄4 w0g, see Chap. 2 for details) it would be necessary to construct linear combinations of the predicted values of gi associated with the traits of interest as was described in the Foreword of this book
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