Modelling Diameter at Breast Height Distribution for Eight Commercial Species in Natural-Origin Mixed Forests of Ontario, Canada

Diameter at breast height (DBH) is a unique attribute used to characterize forest growth and development for forest management planning and to understand forest ecology. Forest managers require an array of DBHs of forest stands, which can be reconstructed using selected probability distribution functions (PDFs). However, there is a lack of practices that fit PDFs of sub-dominating species grown in natural mixed forests. This study aimed to fit PDFs and develop predictive models for PDF parameters, so that the predicted distribution would represent dynamic forest structures and compositions in mixed forest stands. We fitted three of the simplest forms of PDFs, log-normal, gamma, and Weibull, for the DBH of eight tree species, namely balsam fir (Abies balsamea [L.] Mill.), eastern white pine (Pinus strobus L.), paper birch (Betula papyrifera Marshall), red maple (Acer rubrum L.), red pine (Pinus resinosa Aiton), trembling aspen (Populus tremuloides Michx), and white spruce (Picea glauca [Moench] Voss), all grown in natural-origin mixed forests in Ontario province, Canada. We estimated the parameters of the PDFs as a function of DBH mean and standard deviation for these species. Our results showed that log-normal fit the best among the three PDFs. We demonstrated that the predictive model could estimate the recovered parameters unbiasedly for all species, which can be used to reconstruct the DBH distributions of these tree species. In addition to prediction, the cross-validated R2 for the DBH mean ranged between 0.76 for red maple and 0.92 for red pine. However, the R2 for the regression of the standard deviation ranged between 0.00 for red pine and 0.69 for sugar maple, although it produced unbiased predictions and a small mean absolute bias. As these mean and standard deviations are regressed with dynamic covariates (such as stem density and stand basal area), in addition to climate and static geographic variables, the predicted DBH distribution can reflect change over time in response to management or any type of disturbance in the regime of the given geography. The predictive model-based DBH distributions can be applied to the design of appropriate silviculture systems for forest management planning.