Improving the effectiveness of angular dispersion in plant neighbourhood models

Spatial arrangement can be an important factor affecting competition among plants. We evaluated three ways to improve the effectiveness of angulardispersion (AD) for describing spatial arrangement in plantneighbourhoodmodels. First, we modified Zar's (1974) AD formula by weighting each neighbour by its competitive influence. We calculated this using two different competition indices to derive an AD of competitive influence, rather than of equally weighted plant locations, around a subject plant. Secondly, we constrained the effect of AD on the neighbourhoodmodel using an optimised parameter that defines the minimum value that AD can adopt. Thirdly, we included the direction in which competition is concentrated (the mean azimuth of the weighted AD) in the growth models. These developments were evaluated within a radial growth model of Scots pine and birch growing in semi-natural, spatially heterogeneous forest. Weighted AD resulted in significant improvements in predicted radial growth of target trees over the traditional measure of AD. The optimised parameter that defines the minimum value of AD consistently evolved values significantly higher than zero. This suggests that clumped and dispersed neighbourhoods do not differ in their negative effects on a subject tree as much as expected. The inclusion of directional components of the weighted AD did not improve the accuracy of the growth models. Weighting of the angulardispersion of neighbours improved the performance of local competition models.