State‐Space Approach to Spatial Variability of Crop Yield

Spatial crop yield variability complicates interpretation of field experiments if there is no information available about the spatial variability structure of the soil. Our objective was to determine, using a state‐space approach, the underlying process in a soil that caused spatial yield variability of a N 2 ‐fixing crop and a nonfixing crop. On a heterogeneous soil, ryegrass ( Lolium multiflorum L.) and alfalfa ( Medicago sativa L.) were cropped on neighboring transects. Dinitrogen fixation, calculated with either the difference method or the 15 N isotope dilution method and averaged across the transects, did not differ. But, as we examined locations along the transect, differences in amount of fixed N calculated by each method became apparent. Yields of both crops showed different variability structures along the transects. Local effective soil N content was related to local N uptake from soil and to soil symbiotic N 2 fixation of alfalfa. In order to conclude this, the spatial distribution of the soil volume taken by stones in this partially rocky soil had to be considered. In stochastic (state‐space) models based on spatial dependence between observations, crop yield, effective soil N, and N 2 fixation were identified as first‐order autoregressive processes moving through the transect. In other cases, state‐space models were useful tools for spatial interpolation of plant yield, except for large yield alterations between neighboring plots along a transect. This study showed that the spatial variability structure of yields could be explained from located field observations combined with state‐space models.