Predictions of non-linear responses to selection for forage yield under competition.

The expected response of a population of competing genotypes to selection of high yielding individuals is expressed in terms of a regression model of a type similar to that used to describe genotype-environment interactions (Perkins and Jinks 1968). It is shown that response to selection on the basis of the yielding ability of genotypes (direct effects) can also cause changes in the magnitude of their effects on their neighbours (indirect effects) and on the interactions of direct and indirect effects. Thus, if yij = μ + gi aj + γjgi + sij, where yij is the expected yield of the ith genotype in competition with the jth, gi is the direct effect of the ith genotype, aj the indirect effect of the jth, and γj the regression onto direct effects of interactions involving the jth associate, it follows that response is R(g) = g(1+b(a/g) + bγ/gg), where g is the change in average direct effect of the population brought about by selection, and b represents a regression coefficient. If b(γ/g) is important, then response to selection will be non-linear over a range of genotypes, and where it is negative, then selection will become progressively less effective as it proceeds until a plateau is reached, beyond which it will be detrimental.Estimates of the above parameters were made from nine sets of data from diallel arrangements of binary mixtures. Although a degree of uncertainly was induced in these estimates by the need to reparametrize the model describing competition within and between binary components to cater only for inter-genotypic effects, the consistency of the prediction of non-linearity of response induces some confidence in the results. Predicted optima are as low as 8 pc abovethe mean inthe case of closely related material. Other deficiencies and implications of this selection model are discussed.