Note on the Effect of Non-regular Spatial Patterns of Plants on Yield per Area Based on a Logarithmic Relationship between Single Plant Yield and Individual Area

Abstract

Based on several simplifying assumptions, a previously developed stochastic approach allows an estimation of the effects of non-regular spatial patterns of the distribution of individual plants on yield per area (F). In this approach, two random variables were attached to each plant: single plant yield (E) and individual space per plant (A). The latter was estimated by the area of Thiessen-polygons. Yield per area was calculated theoretically by the expectation of the ratio E/A. Based on a logarithmic relationship between E and A the expectation of E/A can be expressed by an approximation which depends on the mean and on the variance of the individual plant spaces. An improvement of this approximation can be easily obtained by including skewness and kurtosis of the distribution of individual plant areas. Finally, all theoretical concepts and results were applied to an experimental data set of winter oilseed rape (Brassica napus L.).