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The contribution of two of the major causes of non-normality in the distribution nf pure-breeding lines derivable by single seed descent from an F2, namely, linear epistasis and genotype x micro-environment interaction, are examined theoretically by algebraic models and computer simulations. It is shown that all the parameters required for predicting the distribution of the pure-breeding lines including the sign and magnitude of the coefficients of skewness and kurtosis which measure the deviation from normality, can be estimated from the basic set of P1, P5, F1, F2, B5 and B, generations and an F, triple test cross. These predictions are shown to be satisfactory in practice for nine characters in the generations and families derived from the cross between varieties I and 5 of .J'Iieotiana rzutiea. Although the distributions of 80 F15 families derived by single seed descent from this cross display non-normality which is attributable to epistasis and genotype x environment interaction, predictions of their properties which assume normality are satisfactory providing that we make a correction to the expected means of the distributions equal to the epistatic component [ij. This cnrrectinn accounts for considerably more of the discrepancies between observations and predictions than all other causes including non-normality. In practice, therefore, it appears to be the only correction that needs to be made for data of the kind we have analysed in which there are moderate levels of epistasis and medium to high heritabilities.

SUMMARYEvidence is presented which shows that self-incompatibility in diploid Lolium perenne is determined, as in other self-incompatible grasses that have been investigated, by two multi-allelic genes and that control of the pollen phenotype is gametophytic.The present results are compared with those of others which have led to a different conclusion concerning the genetical control or expression of selfincompatibility in this species. The importance of the materials and methods used in investigations of this kind are discussed.

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