Problems with models assessing influences of tree size and inter-tree competitive processes on individual tree growth: a cautionary tale

In forest growing at any one site, the growth rate of an individual tree is determined principally by its size, which reflects its metabolic capacity, and by competition from neighboring trees. Competitive effects of a tree may be proportional to its size; such competition is termed ‘symmetric’ and generally involves competition below ground for nutrients and water from the soil. Competition may also be ‘asymmetric’, where its effects are disproportionate to the size of the tree; this generally involves competition above ground for sunlight, when larger trees shade smaller, but the reverse cannot occur. This work examines three model systems often seen as exemplars relating individual tree growth rates to tree size and both competitive processes. Data of tree stem basal area growth rates in plots of even-aged, monoculture forest of blackbutt (Eucalyptus pilularis Smith) growing in sub-tropical eastern Australia were used to test these systems. It was found that none could distinguish between size and competitive effects at any time in any one stand and, thus, allow quantification of the contribution of each to explaining tree growth rates. They were prevented from doing so both by collinearity between the terms used to describe each of the effects and technical problems involved in the use of nonlinear least-squares regression to fit the models to any one data set. It is concluded that quite new approaches need to be devised if the effects on tree growth of tree size and competitive processes are to be quantified and modelled successfully.