The causes and consequences of non-normality in predicting the properties of recombinant inbred lines

Summary

The contribution of two of the major causes of non-normality in the distribution of pure-breeding lines derivable by single seed descent from an F₂, namely, linear epistasis and genotype × 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, P₂, F₁ F₂, B₁ and B₂ generations and an F₂ 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 1 and 5 of Nicotiana rustica. Although the distributions of 80 F₁₁ families derived by single seed descent from this cross display non-normality which is attributable to epistasis and genotype × 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 [i]. This correction 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.