Stability Analysis of Winter-rape (Brassica napus L.) by Using Plant Density and Mean Yield per Plant

The yield F per area can be expressed multiplicatively by using yield components. For the most simple case of including only two yield components one obtains: F = X₁− X₂ with X₁= number of plants per area (= plant density) and X₂= mean yield per plant.
For normal variables X₁ and X₂ the phenotypic yield stability of F, which has been measured quantitatively by the variance V(F) of F, can be explicitly expressed dependent on 1) the component means, 2) the component variances and 3) the correlation between the two components. V(F), therefore, depends on 5 parameters.
For many applications the use of the coefficient of variation v of F instead of the variance itself may be advantageous, v can be explicitly expressed dependent on 1) the coefficients of variation of the yield components and 2) the correlation between the components, v, therefore, depends on 3 parameters.
The different conditions leading to the same phenotypic yield stability can be investigated by using these explicit expressions for V(F) and v.
The main purpose of the present paper is the application of these theoretical models and results to the data of an extensive field trial with winter-rape, which has been performed for 5 years with 4 plant densities and 3 row distances.
For the lowest plant density (40 plants/m²) there results a very good agreement between the theoretically expected and the experimentally obtained values for the phenotypic stability of yield per area. But, for the higher plant densities this result don't hold true. Possible causes and explanations are discussed in detail.