Modelling diameter at breast height distribution of jack pine and black spruce natural stands in eastern Canada

Abstract

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce (Picea mariana (Mill) B.S.P.) and jack pine (Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH.

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

“…These results correspond to previous pieces of work that showed that geography and climate can substantially impact DBH growth [20,49]. When dendrometric variables have a strong relationship with the response variables, like DBH, the bioclimatic variables may come to be insignificant [32], even though these variables are always important in forest growth and development.…”

“…A reason for the opposite behaviors of the stem density and basal area could be due to the fact that the stands were dominated by small-sized trees [63]. Such a parametric relationship with the response variable, DBH mean, was consistent with an earlier study for two dominant species: black spruce and jack pine, in the same study area [32].…”

“…The PDF (f) of X is as given in Equation (1) below. For simplicity, Equations (1)-( 9) are reproduced here from Rijal and Sharma [32].…”

“…There have been a few studies on the development of diameter distribution models for jack pine and black spruce grown in Ontario [22,[30][31][32]. However, these models are not available for many other commercially important tree species which are less common or sub-dominating in terms of abundancy in Ontario.…”