Interplay between heritability,genetic correlation and economic weighting in a selection index with and without genomic information

The availability of genomic information demands proper evaluation on how the kind (phenotypic versus genomic) and the amount of information influences the interplay of heritability (h²), genetic correlation () and economic weighting of traits with regard to the standard deviation of the index (σ_I). As σ_I is directly proportional to response to selection, it was the chosen parameter for comparing the indices. Three selection indices incorporating conventional and genomic information for a two trait (i and j) breeding goal were compared. Information sources were chosen corresponding to pig breeding applications. Index I incorporating an own performance in trait j served as reference scenario. In index II, additional information in both traits was contributed by a varying number of full‐sibs (2, 7, 50). In index III, the conventional own performance in trait j was combined with genomic information for both traits. The number of animals in the reference population (N_P = 1000, 5000, 10 000) and thus the accuracy of GBVs were varied. With more information included in the index, σ_I became more independent of , and relative economic weighting. This applied for index II (more full‐sibs) and for index III (more accurate GBVs). Standard deviations of index II with seven full‐sibs and index III with N_P = 1000 were similar when both traits had the same heritability. If the heritability of trait j was reduced ( = 0.1), σ_I of index III with N_P = 1000 was clearly higher than for index II with seven full‐sibs. When enhancing the relative economic weight of trait j, the decrease in σ_I of the conventional full‐sib index was much stronger than for index III. Our results imply that N_P = 1000 can be considered a minimum size for a reference population in pig breeding. These conclusions also hold for comparing the accuracies of the indices.