Optimum designs for breeding programmes under mass selection with an application in fish breeding

Abstract

AbstractA procedure for maximizing genetic gain (after a number of generations of selection) for a given rate of inbreeding or for a given coefficient of variation of response is presented. An infinitesimal genetic model is assumed. Mass selection is practised for a number of discrete generations. With constraints on inbreeding, expected rates of genetic progress (ΔG) are combined with expeced rates of inbreeding (ΔF) in a linear objective function (Ω = ΔG - μΔF). In addition, an expression to approximate the rate of gain at any generation accounting for changes in genetic parameters due to linkage disequilibrium and due to inbreeding is derived. Predicted gain is in general within 5% of that obtained from simulation. Thus, both ΔG and ΔF are obtained from simple analytical formulae. An equivalent function is used when the coefficient of variation of response (CV) is the parameter restricted (Ω = ΔG -μCV). Maximization of the objective function Ω for appropriate values of μ gives the optimum number of sires and dams selected when specific constraints on the level of inbreeding or the coefficient of variation of response are imposed. The method is applied to a practical situation in fish breeding. Optimum mating ratios and optimum numbers of sires selected are obtained for different scored population sizes and heritabilities. Results obtained with this procedure agree very well with results from simulation studies. The optimum number of sires increases with the size of the scheme and with more severe restrictions on risk. In the schemes considered, the optimum mating ratio is equal to 2 unless the constraint on the rate of inbreeding is severe, the size of the scheme is small and the heritability is low. In these situations the optimum mating ratio is equal to 1. The procedure is general in terms of generations of selection considered and in terms of parameters to be constrained. A large amount of computer processor unit time is saved with this method in comparison with simulation procedures.