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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Tree mortality, growth, and recruitment are essential components of forest dynamics and resiliency, for which there is great concern as climate change progresses at high latitudes. Tree mortality has been observed to increase over the past decades in many regions, but the causes of this increase are not well understood, and we know even less about long-term changes in growth and recruitment rates. Using a dataset of long-term (1958-2009) observations on 1,680 permanent sample plots from undisturbed natural forests in western Canada, we found that tree demographic rates have changed markedly over the last five decades. We observed a widespread, significant increase in tree mortality, a significant decrease in tree growth, and a similar but weaker trend of decreasing recruitment. However, these changes varied widely across tree size, forest age, ecozones, and species. We found that competition was the primary factor causing the long-term changes in tree mortality, growth, and recruitment. Regional climate had a weaker yet still significant effect on tree mortality, but little effect on tree growth and recruitment. This finding suggests that internal communitylevel processes-more so than external climatic factors-are driving forest dynamics.boreal forest | climate change | forest dynamics | tree demographic rates | tree competition F orests provide fundamental ecosystem services for sustaining the global environment, such as storing carbon and maintaining biodiversity. These services, however, are at risk for decline as evidence has increasingly shown that forests in many parts of the world are undergoing rapid changes (1-4). Climate at the regional or global scale is often presumed to be responsible for these changes (5-14), with surprisingly little attention being paid to the possible effects of endogenous processes despite the fact that competition is often an important force driving stand dynamics and succession (15-18). How climate change and competition interplay to affect the long-term change of demographic rates and what are their relative contributions to the change are unanswered questions (19,20).We addressed these questions by compiling data from 1,680 permanent sample plots (PSPs) that are located in undisturbed natural forests across western Canada (Fig. 1). The trees in these plots, which cover a wide geographic region spanning 32°of longitude and 10°of latitude primarily in the boreal zone, were censused over a period from 1958 to 2009 (Fig. 1). Within each plot, all standing trees with diameter at breast height (DBH) ≥ 9 cm were tagged, recorded, and remeasured at irregular time intervals (mean = 10 y) (SI Appendix, Fig. S1). Plot sizes ranged from 0.04 ha to 0.81 ha (mean = 0.14 ha). To reduce possible impact of plot sizes on our analyses, only the plots with at least 50 trees at their first census were selected. The plots have been censused three to eight times (mean of four times). In total, these plots contained 320,878 living trees over the study period (SI Appendix, Table S1).We analyzed the ...

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Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within-and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance-covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating treespecific predictions of diameter inside bark, whole tree volume, and sectioned log volume.

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Model validation is an important part of model development. It is performed to increase the credibility and gain sufficient confidence about a model. This paper evaluated the usefulness of 10 statistical tests, five parametric and five nonparametric, in validating forest biometric models. The five parametric tests are the paired t test, the Χ2 test, the separate t test, the simultaneous F test, and the novel test. The five nonparametric tests are the Brown-Mood test, the Kolmogorov–Smirnov test, the modified Kolmogorov–Smirnov test, the sign test, and the Wilcoxon signed-rank test. Nine benchmark data sets were selected to evaluate the behavior of these tests in model validation; three were collected from Alberta and six were published elsewhere. It was shown that the usefulness of statistical tests in model validation is very limited. None of the tests seems to be generic enough to work well across a wide range of models and data. Each model passed one or more tests, but not all of them. Because of this, caution should be exercised when choosing a statistical test or several tests together to try to validate a model. It is important to reduce and remove any potential personal bias in selecting a favorite test, which can influence the outcome of the results.

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.