RESUMO
Due to consistent increases of inbreeding of on average 0.95% per generation in layer populations, selection tools should consider both genetic gain and genetic relationships in the long term. The optimum genetic contribution theory using official estimated breeding values for egg production was applied for 3 different lines of a layer breeding program to find the optimal allocations of hens and sires. Constraints in different scenarios encompassed restrictions related to additive genetic relationships, the increase of inbreeding, the number of selected sires and hens, and the number of selected offspring per mating. All these constraints enabled higher genetic gain up to 10.9% at the same level of additive genetic relationships or in lower relationships at the same gain when compared with conventional selection schemes ignoring relationships. Increases of inbreeding and genetic gain were associated with the number of selected sires. For the lowest level of the allowed average relationship at 10%, the optimal number of sires was 70 and the estimated breeding value for egg production of the selected group was 127.9. At the highest relationship constraint (16%), the optimal number of sires decreased to 15, and the average genetic value increased to 139.7. Contributions from selected sires and hens were used to develop specific mating plans to minimize inbreeding in the following generation by applying a simulated annealing algorithm. The additional reduction of average additive genetic relationships for matings was up to 44.9%. An innovative deterministic approach to estimate kinship coefficients between and within defined selection groups based on gene flow theory was applied to compare increases of inbreeding from random matings with layer populations undergoing selection. Large differences in rates of inbreeding were found, and they underline the necessity to establish selection tools controlling long-term relationships. Furthermore, it was suggested to use optimum genetic contribution theory for conservation schemes or, for example, the experimental line in our study.