Point process modelling of root distribution in pure stands of Fagus sylvatica and Picea abies

A previous study by Schmid and Kazda (L Schmid and M. Kazda. 2001. Can. J. For. Res. 31: 539-548) evaluated the vertical distribution and radial growth of coarse roots greater than 2 mm diameter in pure and mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.). The vertical distribution of roots of Norway spruce was fitted by an exponential function, while the root distribution of European beech was approximated by a gamma distribution. Now, in the present paper, planar point process models have been applied to investigate the spatial (two-dimensional) distribution of data for roots between 2 and 5 mm diameter. After a homogenization with respect to the vertical axis, the pair correlation function and the L function were estimated to fit Matern-cluster point process models to the given root data. The models were finally vertically retransformed to provide information on the inhomogeneous spatial patterns of small roots as well as on the original shape and size of the root clusters. All models based on vertically transformed data confirmed that the root distribution patterns are not completely random, as they indicated root clustering for both species, with different degrees of exploitation intensity (clustering) between the two species. According to the Matern-cluster models, Norway spruce had stronger clustering in smaller cluster regions, while roots of European beech formed weaker clusters in larger cluster regions. Furthermore, beech root clusters seemed to avoid overlapping. Together with previous studies on the root system of both species, the present study indicates more intensive belowground intraspecific competition for spruce than for beech. On the other hand, the clustering characteristics described indicate that European beech has a more sophisticated rooting system than Norway spruce. The spatial distribution of the inhomogeneous raw data is characterized by the clustering properties analysed in the present paper and by the vertical distribution previously studied.