Estimation of heritabilities and genetic correlations by time slices using predictivity in large genomic models

Under genomic selection, genetic parameters may change rapidly from generation to generation. Unless genetic parameters used for a selection index are current, the expected genetic gain may be unrealistic, possibly with a decline for antagonistic traits. Existing methods for parameter estimation are computationally unfeasible with large genomic data. We present formulas for estimating heritabilities and genetic correlations applicable for large models with any number of genotyped individuals. Heritabilities are calculated by combining 2 formulas for genomic accuracies: one that relies on predictivity and another that depends on the number of independent chromosome segments. Genetic correlations are calculated from predictivities across traits. We simulated data including 2 traits for 240,000 genotyped and phenotyped animals in 6 generations, namely, production trait with an initial heritability of 0.4 and a fitness trait with a fixed heritability set at 0.1 in each generation. Only the first trait (production) was selected, whereas the second trait (fitness) was constructed so that its genetic correlation with the first trait declined by about 0.1 per generation. Calculations were for 3-generation windows, with the first 2 generations treated as a reference population. Compared with realized values, the estimated heritabilities were within 0.02. Genetic correlations were within 0.15 with predictivity of production phenotype by prediction for fitness and within 0.05 with predictivity of the fitness phenotype by prediction for production. The proposed formulas enable the estimation of heritabilities and genetic correlations by time slices for models in which predictivities can be calculated and genetic evaluation is feasible.