Models are abstractions of reality. In order to be useful, models must include essential elements of the real world system that are to be mimicked to meet some specified modelling objective. The pattern in a data set can often be described with a relatively simple model. Models of forests have been constructed for numerous management and research objectives. To determine an appropriate modelling unit (e.g. cell, organ, tree, stand, landscape), one must define the modelling objective and the forecasting time frame. Often the level of modelling detail possible is dictated by the data available. However, there are guiding principles that can aid in selecting an appropriate level for modelling. These principles include: (i) developing as parsimonious a model as possible; and (ii) adjusting the number of state variables for the forecasting period involved. The application of these principles is discussed within the framework of forest growth and yield models. As an illustration of the relationship between model accuracy and complexity, data from a loblolly pine [Pinus taeda] spacing trial in Virginia, USA, were used to predict stand volume.

In this study, we compared individual-tree mortality models for peatland Scots pine (Pinus sylvestris) in Finland constructed using different estimation methods. We applied standard logistic regression with the maximum likelihood (ML) method by ignoring the data structure, and alternatively accounted for the data hierarchy using generalized linear mixed models with either the marginal quasi-likelihood (MQL) or penalized quasi-likelihood (PQL) estimation method. We evaluated the models on the basis of traditional logistic regression goodness-of-fit criteria including the χ2 test, sensitivity, specificity, rate of correct classification, bias and the receiver operating characteristic (ROC) curves with subsequent R2. The interpretation of the fit measures appeared to be complicated. The ML and MQL methods resulted in models with high sensitivity, a high rate of correct classification and low bias. Despite the good fit measures, the Hosmer-Lemeshow test suggested rejection of the models. The graphical expression of the models' ROC curves did not give additional information to make a selection between any of the models, but the R2 showed that the models obtained with the ML and MQL methods were slightly better than that obtained with the PQL method.

Cork oak (Quercus suber) stands (montados) are the most common forest system in southern Portugal. Actual modifications in the management of this agroforestry system have reduced its resilience, compromising sustainability. Simulation results, obtained with a spatial single-tree growth model, were used to test the influence of different strategies of regeneration and management on the sustainability of the system. Crown cover, stand structure and cork production were the variables used to build a sustainability evaluation method.

In many timber species, height growth of dominant trees (100 largest trees per hectare) in even-aged stands is usually assumed to remain unchanged over a wide range of stand density. This assumption allows us to use the stand dominant height (mean height of the 100 largest trees per hectare) at a specified reference age as an index of site quality. A tree-distance independent growth model was developed for Corsican pine (Pinus nigra subsp. laricio) in France to describe individual growth and mortality according to tree size (diameter at breast height) but not to tree location within the stand, silviculture (modifying stand density and structure) and site quality. The five relationships were: stand dominant height growth, tree diameter growth (potential × modifiers form), mortality, stem profile and a static height-diameter function. Data analyses evidenced the density-dependence of height growth even for dominant trees. Therefore, the dominant height growth relationship supports an original feature: a stand density effect was included in addition to age at breast height and site index effects. This result was then evaluated using a wider range of experimental stands, namely 27 experimental plots of Corsican pines planted in the region 'Centre' (France) and managed with different thinning regimes. Annual height increments since planting were measured (non-destructive method) for each tree that had been dominant at least once since thinning (plots had been measured every 2 years). This independent data set allowed us to: (1) determine more precisely the influence of stand density on the dominant tree population; and (2) improve the density-related function for dominant height growth. Lastly, we suggest the use of a potential dominant height increment (i.e. corrected for stand density effect) as the potential growth component in the diameter growth function.

We demonstrate the methods and results for broad-scale mapping of forest site productivity for the Canadian province of Alberta. Site index (SI) data were observed for lodgepole pine (Pinus contorta var. latifolia) based on stem analysis (observed height at an index breast height age of 50 years). A total of 2624 trees at nearly 1000 site locations were available for the analysis. Mapping methods were based on ANUSPLIN, Hutchinson's thin-plate smoothing spline in four dimensions (latitude, longitude, elevation, site index). Although this approach is most often used for modelling climatic surfaces, the high density of the site productivity network in Alberta made this an appropriate application of the method. Maps are presented for lodgepole pine, the major forest species of Alberta. Although map patterns were highly complex, predicted SI decreased regularly and continuously as elevation increased from the parklands, through the foothills, to the mountains, conforming to field observations and a shorter growing season. In the high mountains, SI predictions were the lowest (<10 m), again conforming to field observations. Thus, the map correctly represents the inverse relationship between SI and elevation exhibited in the data. Analysis of residuals revealed no bias in the predictions. Furthermore, residuals were homogeneous and had no apparent pattern. The standard deviation of the observed site index values was 3.23 m, and the root mean squared error of the spline surface predictions was 1.16 m.