Theoretical Results on the Effects of Nonregular Spatial Patterns of Plants on Yield per Area

Abstract

Caused by the necessarily imperfect seed placement accuracy of sowing machines and, additionally, caused by many other biotic and abiotic factors, the resulting plant stands exhibit nonregular spatial distributions of its plants. Based on several simplifying assumptions, a stochastic approach is developed which allows an estimation of the effects of nonregular spatial patterns on yield per area. In this approach, two random variables are attached to each plant: single plant yield E and individual space A. The latter is estimated by the area of Thiessen polygons. Yield per area, calculated by the expectation of the ratio E/A, can be approximately expressed dependent on the means (Ē and Ā) and coefficients of variation (vE and vA) of E and A and their correlation (rEA). In relation to the commonly used estimate Ē/Ā for yield per area, one obtains yield decreases if vA/vE < rEA. This inequality, however, will be usually valid in the field of applications. The theoretical approaches and results were applied to three experimental data sets for drilled seeds of winter oilseed rape (Brassica napus L.) (plant density: 60 plants m−2, row distance: 10 cm). These data sets are characterized by different accuracies of longitudinal distributions within rows (58 %, 101 %, 150 %): yield depression increases with an increasing variability of plant distances within rows.