Modelling the spatial and space-time structure of forest stands: How to model asymmetric interaction between neighbouring trees

Spatial relationships between trees play an important role in forest ecosystem and its dynamics. These relationships determine how much of the common resources are available for an individual tree and influence the growth and mortality of the tree through a competition process. The way how plants share the available resources determines the mode of competition. In the case where a tree influences another tree but not vice versa we speak about asymmetric competition, otherwise competition is symmetric. When modelling interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. Thus, in general there are both kind of interaction between trees: symmetric and asymmetric. We take an approach to quantify the strength of the competition process between the trees which is based on the hierarchy of trees. The space-time model considered here is based on a spatial point process with time-dependent marks where the asymmetric competition is incorporated into the model by interaction kernels.