A general approach to determine the effect of accuracy of sowing technique on yield per area

Caused by nonperfect seed placement accuracy of sowing machines as well as by many other abiotic and biotic factors the resulting plant stands exhibit nonregular plant distributions. Based on several simplifying assumptions a stochastic approach provides a quantitative determination of the effects of accuracy of sowing technique on yield per area. In this approach, two random variables are assigned to each individual plant: single plant yield E and single plant area A, which is calculated in this paper by the construction and quadrature of the so-called Thiessen-polygons. The yield per area F is calculated as the expectation of the ratio E/A. By assuming a deterministic mathematical relationship between E and A, the calculation of F reduces to the calculation of the expectation of a function of only one random variable A. A simple approximation with sufficient accuracy for many applications only depends on the mean and on the variance of the areas of the individual plants. For demonstration purposes, the theoretical approaches and results have been finally applied to three data sets for drilled seeds of winter oilseed rape (plant density: 60 plants/m(2) and distance between rows: 10 cm). These data sets exhibit different accuracies of the longitudinal distributions within rows which have been quantitatively measured by the coefficient of variation for the distances between plants within rows: Yield depression increases with an increasing variability of plant distances within rows.