OPTIMUM DESIGNS FOR BREEDING PROGRAMS UNDER MASS SELECTION WITH AN APPLICATION IN FISH BREEDING

A procedure for maximizing genetic gain (after a number of generations of selection) for a given rate of inbreeding or for a given coefficie nt of variation of response is presented. An infinitesimal genetic mod el is assumed. Mass selection is practised for a number of discrete ge nerations. With constraints on inbreeding, expected rates of genetic p rogress (Delta G) are combined with expeced rates of inbreeding (Delta F) in a linear objective function (phi=Delta G-lambda Delta F). In ad dition, an expression to approximate the rate of gain at any generatio n accounting for changes in genetic parameters due to linkage disequil ibrium and due to inbreeding is derived. Predicted gain is in general within 5% of that obtained from simulation. Thus, both Delta G and Del ta F are obtained from simple analytical formulae. An equivalent funct ion is used when the coefficient of variation of response (CV) is the parameter restricted (phi=Delta G-lambda CV). Maximization of the obje ctive function phi for appropriate values of lambda gives the optimum number of sires and darns selected when specific constraints on the le vel of inbreeding or the coefficient of variation of response ave impo sed. The method is applied to a practical situation in fish breeding. Optimum mating ratios and optimum numbers of sires selected are obtain ed for different scored population sizes and heritabilities. Results o btained with this procedure agree very well with results from simulati on studies. The optimum number of sires increases with the size of the scheme and with more severe restrictions on risk. In the schemes cons idered, the optimum mating ratio is equal to 2 unless the constraint o n the rate of inbreeding is severe, the size of the scheme is small an d the heritability is low. In these situations the optimum mating rati o is equal to 1. The procedure is general in terms of generations of s election considered and in terms of parameters to be constrained. A la rge amount of computer processor unit time is saved with this method i n comparison with simulation procedures.