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Background
In recent decades, the widespread use of artificial insemination and other reproductive technologies has resulted in substantial genetic gains in livestock populations. However, another consequence is that only a limited number of animals with high estimated breeding values (EBV) have been intensively used in breeding programs, which can result in increasing rates of inbreeding to undesired levels. A high rate of inbreeding not only leads to considerable reduction in genetic variation but also more deleterious recessive alleles become homozygous, which may threaten the entire future of the population [1]. Thus, there is a conflict between maximizing genetic gain and managing the rate of inbreeding.
Crossbreeding has been demonstrated to be an efficient method to reduce the threat of inbreeding depression and increase the level of genetic diversity [2]. In addition, local breeds are often crossed with breeds of high economic value to improve performance. However, such introgressions of genetic material can be a threat for maintaining local breeds. Amador et al. [3] confirmed that, after several generations without management, even a small introduction of foreign genetic material will rapidly disperse throughout the original population, and that this material is difficult to remove. Therefore, foreign introgressions present a large risk for the conservation of local breeds, which leads to a conflict in current breeding programs between increasing the contribution of foreign genetic material and conserving local breeds.
Optimum contribution selection (OCS) is a selection method that is effective at achieving a balance between rate of inbreeding and genetic gain. This selection process maximizes genetic gain in the next generation while constraining the rate of inbreeding via restriction of relatedness among offspring [4-6]. The superiority of OCS has been demonstrated with both simulated [7, 8] and real data [9-11]. The objective function for OCS has been optimized using Lagrange multipliers [4, 8, 12], evolutionary algorithms [7, 13, 14], and semidefinite programming algorithms [9, 15, 16]. A similar related optimization problem was expressed as a mixed-integer quadratically constrained optimization problem and solved with branch-and-bound algorithms [17]. In this paper, we applied the algorithm described in [18] for solving cone-constrained convex problems by using R package optiSel.
OCS is efficient for controlling the level of kinship among progeny and the rate of inbreeding in future generations and can...