Optimal Strategies for Varietal Selection

Varietal selection programmes for agricultural and horticultural crops are generally constructed to achieve one of two main objectives. These are firstly the selection of a fixed number of varieties in such a way as to achieve a maximum expected mean yield for the selected varieties and secondly the selection of sufficient varieties to achieve some minimum or expected probability that a specified number of the ‘best’ varieties are among those selected. The two approaches are contrasted by assuming that the varieties being assessed are a random sample of varieties whose true yielding capacities are normally distributed. The approach meeting the second objective gives rise to an unpredictable number of selected varieties. By choosing the parameters of the selection procedure to give an expected number selected equal to the number selected in the approach for the first objective, comparisons can be made. Our paper shows that, with the normal distribution assumption, the approaches give approximately the same expected probability of selecting one of the best varieties as well as approximately the same expected gains in yield. The approach for the first objective is favoured because of the practical advantages of selecting a predefined number of varieties. The advantages of maximizing expected mean yield over achieving stated probabilities of correct selection are stressed. Also considered in this paper is the optimal number of varieties to carry forward to a final stage of selection so that the probability that the best variety statistically significantly outyields a control variety in the final stage is maximized.