Studies on the optimal numbers of components in mixtures of clones or lines
1984
Huehn, M. (Kiel Univ. (Germany). Inst. of Crop Science and Plant Breeding)
Theoretical studies on the optimal number of components in multiclonal varieties or mixtures of lines have been performed according to phenotypic yield stability (measured by the parameter variance). For each component a parameter has been introduced reflecting the different survival and yielding ability of the clones or lines. For the character 'total yield' the phenotypic variance V can be explicitly expressed dependent on 1) the number n of components in the mixture, 2) the mean variance, 3) the variance of the parameter, 4) and 5) the ratios of the variance and the variance of the means to the mean of the paramter. According to the dependence of the phenotypic stability on these factors some conclusions can be easily derived from this V-formula. Furthermore, two different approaches for a calculation of necessary or optimal numbers of components using the phenotypic variance V are discussed: A. Determination of 'optimal' numbers in the sense that a continued increase of the number of components brings about no further significant effect according to stability. B. A reduction of the number of components but nevertheless an unchanged stability can be realized by an increase of the mean parameter by 1%. Numerical results on n (from A) and 1 (from B) are given. Computing the coefficient of variation v for the character 'total yield' and solving for the number n of components one obtains an explicit expression for n dependent on v and the factors 2. - 5. mentioned above. In the special case of equal variances, the number n depends on v, x = ratio variance of parameter means to mean and y = variance of the parameter to its mean. For x1 and y1 one obtains n
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