Twenty nonlinear height–diameter functions were fitted and evaluated for major Alberta species based on a data set consisting of 13 489 felled trees for 16 different species. All functions were fitted using weighted nonlinear least squares regression (wi = 1/DBHi) because of the problem of unequal error variance. The examination and comparison of the weighted mean squared errors, the asymptotic t-statistics for the parameters, and the plots of studentized residuals against the predicted height show that many concave and sigmoidal functions can be used to describe the height–diameter relationships. The sigmoidal functions such as the Weibull-type function, the modified logistic function, the Chapman–Richards function, and the Schnute function generally gave the most satisfactory results.

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A generalized logistic model of individual tree mortality was developed for trembling aspen (Populus tremuloides Michx.), white spruce (Picea glauca (Moench) Voss), and lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia Engelm.) in Alberta boreal mixedwood forests based on an empirical data base of permanent sample plots. The model is suitable for observations from unequal remeasurement intervals. The maximum likelihood estimation was used to fit the model, the likelihood ratio test was combined with our understanding of mortality process to select the important variables, and the Hosmer-Lemeshow goodness-of-fit test was conducted to evaluate the fit. The fitted model predicts the survival probability of an individual tree based on the tree diameter at breast height, annual diameter increment, stand basal area, species composition, and site productivity.

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A site productivity measure based on the relationship between total tree height and diameter at breast height of dominant and codominant trees was presented for four major tree species (white spruce (Piceaglauca (Moench) Voss), lodgepole pine (Pinuscontorta Dougl.), trembling aspen (Populustremuloides Michx.), and black spruce (Piceamariana (Mill.) B.S.P.)) growing in boreal mixed-species stands in Alberta. The measure is based on a three-parameter modified Weibull function fitted to growth data from permanent sample plots using the difference-equation method; R2-values ranged from 0.90 to 0.97. The measure has many logical properties similar to those of the site-index approach and produces curves that are polymorphic and reference-diameter invariant. It can be used as a simple and quick method of quantifying site productivity for uneven-aged and (or) mixed-species stands.

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Based on a data set from 164 permanent sample plots, an age-independent individual tree diameter increment model is presented for white spruce (Piceaglauca (Moench) Voss) grown in the boreal mixed-species stands in Alberta. The model is age independent in that it does not explicitly require tree or stand age as input variables. Periodic diameter increment is modelled as a function of tree diameter at breast height, total tree height, relative competitiveness of the tree in the stand, species composition, stand density, and site productivity. Because data from permanent sample plots are considered time series and cross sectional, diagnostic techniques were applied to identify the model's error structure. Appropriate fit based on the identified error structure was accomplished using weighted nonlinear least squares with a first-order autoregressive process. Results show that (1) all model parameters are significant at α = 0.05 level, and (2) the plot of studentized residuals against predicted diameter increment shows no consistent underestimate or overestimate for diameter increment. The model was also tested on an independent data set representing the population on which it is to be used. Results show that the average prediction biases are not significant at α = 0.05 level, indicating that the model appropriately describes the data and performs well when predictions are made.

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