Spatial dependence and individual-tree growth models: II. Modelling spatial dependence

Abstract

An individual-tree growth modelling methodology capable of explicitly modelling observed spatial dependence was sought using growth data for even-aged Eucalyptus pilularis (Smith.) in New South Wales, Australia. Candidate methodologies included the moving average autoregression, the directly specified Gaussian covariance function, and the Papadakis method. The directly specified Gaussian covariance function and the Papadakis method adequately modelled positive spatial dependence attributable to micro-site influences, but failed to model the negative spatial dependence attributable to competitive influences. The moving average autoregression was the only model which facilitated the simultaneous modelling of spatial dependence attributable to confounded competitive and micro-site influences. Consequently, the moving average autoregression was identified as the best methodology for explicitly modelling the spatial dependence prevalent among the individual trees of forests. Benefits from this new methodology for estimating individual-tree growth models include valid parameter estimates and inferences, improved estimation efficiency and a strengthened theoretical basis for the model. Furthermore, the moving average autoregression provides a definition of the dispersion matrix which can be used to generate more realistic stochastic predictions of individual-tree growth. The results detailed here apply to an even-aged eucalypt stand, and their generality need to be explored further in different forest structures, particularly irregular natural forests. Practical application of the methodology is discussed.