Describing the spatial pattern of crop plants with special reference to crop–weed competition studies

The spatial distribution of individual crop plants in the field is important for crop growth, yield production, and crop–weed interactions, but the role of spatial pattern has not been appreciated in agricultural research. A quantitative measure of degree of spatial uniformity/aggregation of individual plants would be very useful in this context. We digitized photographs of field plots of weed-infested spring wheat sown in uniform, random and normal row patterns at three densities (204, 449 and 721 seeds m−2), and described the locations of individual wheat seedling as x- and y-coordinates. We analyzed the spatial pattern of these plant locations in two ways. One approach is based on Voronoi or Thiessen polygons (also called tessellations or tiles), which delimit the area closer to each individual than to any other individual. The relative variation (coefficient of variation) in polygon area and the mean shape ratio (ratio between the circumference of the polygon and that of a circle of the same area) of the polygons are measures of spatial aggregation. The other approach was Morisita's index of dispersion, which is based on the mean and variance in number of individuals in sampling units (quadrats). The CV of polygon area, the mean shape ratio of these polygons and Morisita's index of dispersion, all performed well as descriptions of the degree of spatial aggregation of crop plants. Models using one of these measures of uniformity and sowing density as explanatory variables accounted for 74–80% of the variation in crop biomass production. Despite its simplicity, models with Morisita's index performed slightly better than models using polygon parameters, accounting for 80–86% of the variation in weed biomass. Simple spatial analyses of individuals have much to offer agricultural research.