Spatial dependence and individual-tree growth models: I. Characterising spatial dependence

Spatial dependence in individual-tree diameter, and growth model residuals was characterised for an even-aged Eucalyptus pilularis (Smith) experiment in New South Wales, Australia. The magnitude of spatial dependence changed as the dominance of competitive mechanisms and micro-site influences changed through stand development. Examination of spatial dependence at several spatial scales revealed a consistent structure of initially significant positive spatial dependence declining over larger inter-tree distances. This structure was attributed to the influence of micro-site variation, whereby neighbours are subject to similar environmental conditions, but the confounding influence of competition was also observed over small inter-tree distances. This structure was prevalent among individual-tree diameters, and residuals from an individual-tree growth model. The finding of a significant and consistent spatial dependence in growth model residuals violates the assumption of independent residuals thus threatening estimation efficiency and model inference. Improved individual-tree growth modelling methodologies need to be developed capable of incorporating this observed spatial dependence.