Phenotypic Stability of Mixtures – Relations Between the Stability Parameters of a Mixture and Its Components

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Abstract
For each of the two stability parameters (‘regression coefficient’ and ‘sum of squared deviations from the regression’) of the common regression approach (= regression of the yield of population i in environment j on the environmental index of this evironment j which often has been estimated by the mean of all tested populations in this environment j) the phenotypic stability of a mixture and it's components have been analysed theoretically. It can be shown that in practical applications (for example: variety testing) the regression coefficient of a mixture often can be sufficiently approximated by the arithmetic mean of the regression coefficients of the components grown singly. This simple relation between a mixture and it's components don't hold for the second stability parameter ‘sum of squared deviations from the regression’. The exact relation has been deduced and useful and clear approximations are discussed. All the theoretical results are demonstrated and applied using the well‐known experimental barley data of Sandfaer (1970).