In genetics, covariance serves a basis for computation of kinship matrix (genetic relationship matrix (GRM)) enabling inference on population structure from sample with no known close relatives as well as inference on estimation of heritability of complex tratis
MTGS assings weights to different traits relative to their economic importance: index selection. Classical index selection only optimizes genetic gain in the next generation and requires optimizing nonlinear breeding objectives.
Formulas (1) to (3) are just to remember the mathematical expressions in
$$ y=\sum_{i}g_ix_i+\sum_{ij}g_ig_jz_{ij}+O(g^3)+noise$$(4)
(4) is the general model for quantitative phenotype where:
Approach maximizing certain traits while keeping others within desirable ranges. LAS = look-ahead selection algorithm LAMS = look-ahead mate selection MTLAS is more effective balancing multiple traits compared with index selection GEBV = genomic estimated breeding values are calculated as the sum of the estimated marker effects Goal 1 Development of models to improve the accuracy of GEBV prediction These studies have been focused on selecting the parents of the next generation by defining new quantitative selection merits Mate selection optimize the contribution of potential parents to the next generation based on maximizing a desired breeding objective The optimization is performed with respect to the next generation LAMS optimize parental contributions with respect to grand-progeny (two generations in the future) ST-GS = single trait genomic selection Pareto efficiency is a state where resources are allocated in the most efficient manner The accuracy of genomic prediction critically depends on the level of relatedness between the training population and the testing population The use of multivariate linear mixed models in genetic evaluations provides a basis for inference about traits' integration
GS using all markers GS using marker selection Use of BLUEs estimates are used with genomic data to estimate marker weights prior to cosntruction of the marker based relationship matrix
PLS-CA: Partial Least Squares Canonical Analysis