Evaluating a single tree-based growth model for even-aged stands against the maximum size–density relationship: Some insights from balsam fir stands in Quebec, Canada

Abstract

In this study, we addressed the issue of model evaluation when long-term monitoring data are unavailable or inappropriate. More specifically, we fitted a single tree-based growth model for pure even-aged balsam fir stands and we compared stochastic predictions with an existing maximum size–density relationship (MSDR). Growth trajectories for plots of different initial densities and diameter distributions were simulated over a 70-year period using 500 realizations for each combination of initial density-diameter distribution. Long-term predictions were consistent with the existing MSDR. The model properly reproduced the senescence phase in which the trajectories diverge from the MSDR. This phase was initiated when the average tree volume reached 0.2-0.3 m3 per tree, which roughly corresponded to a DBH (diameter at breast height, 1.3 m from the ground) between 19 and 23 cm. Although it cannot be generalized, our case study shows that a simple single tree-based growth model with a distance-independent competition index and no stand density index can reproduce an existing MSDR. The match between long-term predictions and an existing MSDR strengthens the confidence in the biological behaviour of the model.