Describing the spatial pattern of crop plants with special reference to crop–weed competition studies L. Kristensen a , J. Olsen a , J. Weiner a, * , H.W. Griepentrog b , M. Nørremark b a Department of Ecology, Royal Veterinary and Agricultural University, DK-1958 Frederiksberg, Denmark b Department of Agricultural Sciences, Royal Veterinary and Agricultural University, DK-2630 Taastrup, Denmark Received 30 June 2005; accepted 2 July 2005 Abstract 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 twoways. 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 CVof 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. # 2005 Elsevier B.V. All rights reserved. Keywords: Individual plants; Morisita’s index; Spatial analysis; Voronoi polygons 1. Introduction Agricultural production is the result of the growth, development and yield of individual plants in the field. The spatial distribution of crop plants is important for these processes, but the role of crop spatial pattern remains poorly investigated. In a series of recent studies, we have shown that a highly uniform pattern of crop plants suppresses weeds 30% better on average than plants distributed in standard 12 cm rows, and that further improvements in weed suppression can be achieved by also increasing crop density (Weiner et al., 2001; Olsen et al., 2005, in press). But it is not clear what degree of uniformity is necessary to achieve major improvements in weed suppression (Olsen et al., 2005). Addressing this question requires a meaningful and useful measurement of the degree of spatial uniformity of individual plants. Spatial analysis of individuals is an important tool in plant ecology (Tilman and Kareiva, 1998; Dieckmann et al., 2000) but not yet in agricultural research, where the underlying spatial patterns of individual crop (or weed) plants are usually described in very general categories. More detailed information on the pattern of individual plants in the field and appropriate analytical methods are needed if we are to understand and evaluate the effects of spatial pattern on crop performance. Here we ask the following question: is it possible to describe the degree of spatial aggregation/ uniformity with a simple quantitative measure, which can then be used to compare different spatial crop patterns? A wide range of methods is available for quantifying spatial patterns (e.g. Ripley, 1981; Krebs, 1989; Cressie, www.elsevier.com/locate/fcr Field Crops Research 96 (2006) 207–215 * Corresponding author. Tel.: +45 3528 2822; fax: +45 3528 2821. E-mail address: jw@kvl.dk (J. Weiner). 0378-4290/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fcr.2005.07.004