Abstract:Aquatic multi-trait integrated breeding system is an important selective breeding technology to improve economic traits of aquatic animals in China. It has been a vital issue how to select and mate the broodstock candidates to maximize the genetic gain at a defined rate of inbreeding in the breeding system. The optimum contribution theory (OC) has become an effective tool to establish equilibrium between the genetic gain and the inbreeding in the nucleus population. In this review we introduced the establishment and development of optimum contribution theory, the characteristics of different optimization algorithms, and its application in selective breeding of plants and animals. Three algorithms, Lagrange multipliers, Semidefinite programming and Differential evolution, have been used in the calculation of optimum genetic contribution. At equal rates of inbreeding, genetic gains calculated with Lagrange multipliers were 21%–60% greater than that with selection for BLUP-EBV. An improved algorithm based on Lagrange multipliers was invented for the calculation of optimal genetic contributions in the case of large number of candidates in the aquatic animal population. The additive relationship matrix between the selection candidates and the inverse of this matrix was replaced with the relationship matrix between the parents of the selection candidates and its inverse in the calculation of the optimal genetic contribution of the selection candidates to the next generation. Lagrange multipliers did not guarantee that the final solution is the global maximum; on the contrast the SDP method could always find the optimum solution that maximized the genetic gain using the interior point algorithms. The expected gains obtained from the Semidifinite programming were 1.5%–9% greater than that from Lagrange multipliers. Individual selection and mate allocation could be performed using Differential evolution algorithm. Many issues including genetic gain, diversity, progeny inbreeding, connections among farms, multi-stage selection, management of genetic marker, and various types of costs could be contained in the object function and be optimized. Genetic gain and the accuracy of optimum contribution could be increased using the pedigree and genomic information at predefined rate of inbreeding. The inbreeding level of selective breeding population was effectively controlled and genetic gains of object traits were 17%–30% greater than that of selection for BLUP-EBV in the livestock and forest breeding. New progress on the OC theory based on genomic information was also reviewed. The prospect of application of optimum contribution theory in aquatic selective breeding was analyzed in order to provide reference and guidance in aquatic animal breeding.
