Computer simulation of directional selection in large populations. I. The programme, the additive and the dominance models.

I N the prediction of genetic progress by directional selection, the most important parameter involved is the heritability ( hz ) of the character under selection, which is defined as the ratio of the additive genetic variance to the phenotypic variance ( uZp) of the population. Several experiments on directional selection (CLAYTON, MORRIS and ROBERTSON 1957; CHANG and CHAPMAN 1958; MARTIN and BELL 1960; SHELDON 1963 and others) have been reported and the ability of the heritability estimates to predict long term genetic changes has varied from experiment to experiment. Several factors could have contributed to this variation; many quantitative traits may be governed by complex epistatic systems, the heritability estimates may have been associated with large sampling errors, the effective population sizes in some experiments may have been small, as is often the case, or the real value of heritability may have changed quickly from generation to generation. Any one or more of these or other factors could have made estimates of heritability poor predictors. Two important factors in the formulation of selection plans and in the interpretation of selection results are the predictive value of the heritability estimate, and the rate of change of heritability under selection. An understanding of the predictive value of heritability and the rate of change of h' under selection can be obtained if sufficient numbers of selection experiments of suitable size can be carried out and if h' is estimated in every generation. This is often impracticable because of the cost and time involved. Also, while it is possible to predict theoretically the change in the population mean from one generation to the next according to the estimate of hz, theoretical prediction for the rate of change of heritability under selection has so far defied mathematical analysis because of the complexities of different genetic models, involving the effect of linkage and recombination, and of environment on quantitative traits. Some insight into both the predictive value of hz and the rate of change in uZA under selection, however, may be gained by using Monte-Carlo methods on a high speed computer. This approach was first used in genetical problems by FRASER (1957). It is true that any answers derived by this approach are likely to be specific, as only a limited number of situations can be investigated at a time, but some approximation can be obtained if sufficient numbers of studies are made. TWO reports on the simulation of genetic systems relevant to directional selec-