Effects of Nonregular Spatial Distribution of Plants on Yield per Area: A Theoretical Approach with Applications to Winter Oilseed Rape (Brassica napus L.)

Abstract

In this study a stochastic approach, based on several simplifying assumptions, is developed that allows an estimation of the effects of nonregular spatial patterns of the distribution of individual plants on yield per area. In this approach, two random variables were attached to each individual plant: single plant yield and individual space per plant. The latter can be estimated, for example, by the area of Thiessen polygons. Yield per area is calculated theoretically by the expectation (=mean) of the ratio between individual yield and area. Based on the logarithmic relationship between single plant yield and individual space per plant, yield per area can be broken down into three additive terms: the first term depends only on the mean of individual plant areas, while the second depends on their mean and variance simultaneously. This second term is the product of the variance and a factor which depends only on the mean. The third term is a function of the mean and of higher order (≥ 3) central moments of a fractional linear transformation of individual plant area. Finally, these theoretical concepts were applied to 17 experimental data sets of three cultivars of winter oilseed rape (Brassica napus L.) with measurements for single plant yields and individual areas for the Thiessen polygon tesselations. Since yield per area is theoretically defined by the expectation of the ratio between individual yield and area, it is estimated by the arithmetic mean of the individual yield/area‐ratios. The agreement between this estimate and the sum of the estimated terms from the aforementioned additive decomposition of yield per area is particularly good. For the 17 data sets, percentages for these additive terms of approximately 71.4 % up to 98.4 % (mean: 89.0 %) for the first term, 1.6 % up to 20.0 % (mean: 9.8 %) for the second term and 0 % up to 8.7 % (mean: 1.2 %) for the third term are obtained. As a consequence it may be concluded, that yield per area can be explained mainly by dependencies on the means of individual plant areas while the variance of individual plant spaces is of only minor importance. The effect of the third term is insignificant. These results clearly indicate an answer to the main issue raised in the paper, namely the importance of seeding density as opposed to seeding accuracy/uniformity: nonuniformity is of limited influence and seeding density is the main correlate of yield/area. Seed placement accuracy of seeding technology therefore plays an only minor role.