Optimum designs for fish breeding programmes with constrained inbreeding Mass selection for a normally distributed trait

Abstract

Optimum designs for fish breeding programmes to achieve maximum genetic gain whilst constraining the rate of inbreeding are studied through stochastic simulation. Mass selection is carried out for 15 discrete generations for a trait recorded in both sexes. Schemes are optimized for the number of males selected. Different but fixed numbers of scored individuals, heritabilities and mating ratios are analyzed. Genetic gains averaged over the last ten years of selection obtained when imposing specific constraints on the rate of inbreeding are compared. Variability of response is also considered. For a fixed mating ratio, the optimum number of sires increases with the size of the scheme, the heritability and with more severe restrictions on the rate of inbreeding. The effects of the size of the scheme and the heritability on the optimum number of selected individuals are larger when more severe constraints on inbreeding are imposed. Increasing the mating ratio leads to lower genetic gains and to a considerable higher number of fullsib groups. However, the effect of mating ratio on genetic gain is very small. The increase in genetic progress obtained by increasing the size of the scheme is higher with more severe restrictions on inbreeding and with higher mating ratios. In percentage, the loss in gain by restricting inbreeding to different levels is very similar for different heritabilities and is larger for the smaller schemes. The reduction in genetic progress by decreasing the rate of inbreeding from 2% to 0.25% ranged from around 10% (largest scheme) to around 40% (smallest schemes). The extra genetic progress obtained by increasing the size of the scheme was larger for the smaller schemes, the higher heritabilities, the higher mating ratios and under the more severe restrictions on inbreeding. The variance of genetic gain decreased with more severe restrictions on inbreeding and with the heritability and remained approximately constant for schemes of different size and for different mating ratios. The implications of the results for fish breeding programmes that apply mass selection are discussed.