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Estimating yield depression caused by nonuniformity of spatial plant patterns

Inst. of Crop Science and Plant Breeding, Christian-Albrechts Univ., Am Botanischen Garten 1-9, D-24118 Kiel, Germany

* Corresponding author (mhuehn{at}plantbreeding.uni-kiel.de)

Agricultural plant stands at harvest are characterized by more or less irregular spatial distributions of their individual plants. The objective of this study was to quantify the yield depression caused by nonuniformity of spatial plant patterns. On the basis of several assumptions, a stochastic approach is proposed that allows an estimation of the effects of irregular spatial patterns of the distribution of individual plants on yield (Y). The variables, single plant yield (S) and individual area per plant (A) estimated by the area of Thiessen polygons, were evaluated. Yield was calculated theoretically by the expectation of the ratio S/A. On the basis of a nonlinear relationship between single plant yield and individual area per plant, yield can be represented by two additive terms. The first term depends on the mean of individual plant areas. The second term is negative, depends on the mean and variance simultaneously, is proportional to the variance of individual plant areas, and can be interpreted as the effect of variable individual plant areas on yield. This provides the amount of yield depression caused by nonuniformity of spatial distribution of plants across the area. Theoretical concepts and results were applied to an experimental yield data set of winter oilseed rape. The amount of yield depression was 5.3%.