Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

Abstract

A stochastic model is applied to describethe spatial structure of a forest stand. We aim at quantifying thestrength of the competition process between the trees in terms ofinteraction within and between different size classes of trees usingmultivariate Gibbs point processes with hierarchical interactionsintroduced by H\uf6gmander and S\ue4rkk\ue4 (1999). The new modelovercomes the main limitation of the traditional use of the Gibbsmodels allowing to describe systems with non-symmetric interactionsbetween different objects. When analyzing interactions betweenneighbouring trees it is natural to assume that the size of a treedetermines its hierarchical level: the largest trees are notinfluenced by any other trees than the trees in the same size class,while trees in the other size classes are influenced by the othertrees in the same class as well as by all larger trees. In thispaper, we describe a wide range of Gibbs models with bothhierarchical and non-hierarchical interactions as well as asimulation algorithm and a parameter estimation procedure for thehierarchical models. We apply the hierarchical interaction model tothe analysis of forest data consisting of locations and diameters oftree stems