Spatial pattern model of herbaceous plant mass at species level

Individual plant species distribute according to their own spatial pattern in a community. In this study, we proposed an index for measuring the spatial heterogeneity in mass (dry weight) of individual plant species. First, we showed that the frequency distributions for mass of individual plant species per quadrat in a plant community are expressed using the gamma distribution with two parameters of λ (mean) and p. The parameter p is a measure indicating the level of spatial heterogeneity of plant mass as follows: (1) when p = 1, the plant mass per quadrat has a random pattern; (2) when p > 1, the plant mass has a spatial pattern with a lower heterogeneity than would be expected in the random pattern; and (3) when p < 1, the plant mass has a spatial pattern with a higher heterogeneity than would be expected in the random pattern. The p value for a given species can easily be calculated by the following equation if we use the moment method: (mean plant mass among quadrats)2 / (variance of plant mass among quadrats). The scatter diagram of (λ, p) for individual plant species, exhibits the spatial characteristics of each species in the community. We illustrated two examples of the (λ, p) diagram from data for individual species composing actual communities in a semi-natural grassland and a weedy grassland. Frequency distributions for the plant mass of individual species per quadrat followed the gamma distribution, and indi vidual species exhibited an inherent level of spatial heterogeneity.