Technical note: Constrained optimization of breed composition in composite populations to balance net merit and risk.

We developed a method to derive optimum composite genotypes when the proportion of a specific breed (or combination of breeds) in the composite is constrained to a desired level. The method allows development of composites that balance net merit according to available parameters and reflects the production system and(or) risk preference, particularly when traits in the breeding objective do not represent all traits important for production. The method can also be used to evaluate the cost of constraining breed use. For example, when the true optimal composite is difficult to obtain in the time frame available to the producer, the predicted merit of the composite with breed proportion restricted to those that are obtainable in practice can be compared with the predicted merit of the true optimum composite. In a case study the method is used to optimize a tropical composite using Brahman, Charolais, and Belmont Red breeds. The proportion of Charolais is to be constrained to 50%. Using growth parameters from a tropical crossbreeding experiment, the unconstrained optimum composite was 32.5% Brahman, 11.1% Belmont Red, and 56.3% Charolais. When the proportion of Charolais in the composite was constrained to 50%, optimum proportions of Brahman and Belmont Red were 33.9% and 16.1% respectively. In the case study net merit (annualized profit per cow exposed, $), as defined by the growth parameters, was .2% less than that of the unconstrained optimum composite.