Abstract Data from a large, long-term loblolly pine (Pinus taeda L.) plantation study including 186 permanent sample plots were used to evaluate four dynamic site equations derived with the ...generalized algebraic difference approach (GADA). All of the equations are base-age invariant and directly estimate height and site index from any height and age. The fittings were done in one stage using the base–age invariant dummy variables method. A first-order autoregressive error structure was used to correct the serial correlation of the longitudinal data used in this study. Cieszewski’s model (Cieszewski, C.J. 2002. Comparing fixed- and variable-base–age site equations having single versus multiple asymptotes. For. Sci. 48:7–23) best described the data.
Tree height is a key variable in forest monitoring studies and for forest management. However, tree height measurement is time consuming, and the recommended procedure is to use estimates from ...height-diameter models. Here, we compare height-diameter model forms and approaches for predicting tree height (h) as a function of tree diameter at breast height (d) and additional stand level covariates. Four model forms were evaluated: (i) basic models (which only used d as predictor variable); (ii) generalized models (which used d and stand-level predictor variables); (iii) a mixed-effects model based on the best basic model; and (iv) a mixed-effects model based on the best generalized model. Several alternatives aimed at minimizing height measurement effort were tested in terms of accuracy and applicability. From a practical point of view, the selected generalized model is recommended for estimating the height of maritime pine in Portugal. The results also show that a calibrated basic mixed model provides more accurate results than a basic model locally fitted when the number of h-d observations is limited.
Site index is the most common measure of forest site productivity used worldwide, serving as an important baseline for forest-level planning and helping to formulate silviculture strategies. Site ...index is usually obtained through measurement of dominant height and stand age. However, age is not available in many cases, such as in most national forest inventories or when it is not a main determinant of growth. Age-independent methods have been developed to overcome this problem, allowing modelling of the dominant height growth and estimation of site index in the absence of age data. The purpose of this study was to compare the most widely used age-dependent method and several age-independent alternatives, namely the growth intercept method, the age-independent difference equation method and an iterative method proposed in this study. We used stem analysis and permanent sample plot data from Pinus pinaster Ait. stands in Asturias, Spain, to test the alternative methods. It was found that for site index estimation, a 7-year growth intercept was the most accurate method. However, for prediction of dominant height growth, an age-independent equation that depends on climatic factors performed best, even better than the traditional age-dependent site quality curves. The iterative method proposed in this study proved to be the least accurate alternative, although it performed well in predicting height growth for long intervals starting from low heights. Finally, we provide recommendations regarding when the different methods should be used.
A compatible volume system for the major pine species in El Salto, Durango (Mexico) was developed from data corresponding to 1930 destructively sampled trees. Several well-known taper functions were ...evaluated and compared against the model selected in a previous study of these pine species in the same area. Appropriate statistical procedures were used in model fitting to account for the problems of autocorrelation and multicollinearity that are associated with the construction of taper functions. A compatible segmented model best described the experimental data and was found to be better than the previously selected model. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the five species analyzed. The non-linear extra sum of squares method indicated differences in species-specific taper functions. A different taper function should therefore be used for each pine species.
We used data from Pinus pinaster Ait. and Pinus sylvestris L. trees growing in single-species even-aged stands in northwestern Spain to develop crown profile models. Such models are key components of ...growth and yield models, and they are also important for assessing competitive level, microclimate, tree vigour, mechanical stability, biological diversity, fire susceptibility and behaviour under wind stress, amongst other features. The equations used in crown profile estimation (i.e. those including crown radius, largest crown radius, height to the largest crown radius and height to the base of the live foliage) were fitted simultaneously to take into account correlations between the different variables. The fitting technique also enabled us to consider an autocorrelated, heteroscedastic error structure and to use a different number of observations for the different variables involved in the fitting process. The fitted models explained between 66 and 94 per cent of the variability in crown radius, with a mean error between 0.15 and 0.64 m. The crown profile models developed can be used to estimate the crown profile when only diameter at breast height, total tree height and height to the base of the live foliage are measured. Inclusion of more variables (such as largest crown radius) provides more accurate results.
A model for predicting the height growth of radiata pine plantations in Galicia (north-western Spain) was developed. Data from stem analysis of 161 trees were used for model construction. Seven ...dynamic site equations derived with the generalized algebraic difference approach (GADA) were tested, which constitute compatible site index and height models in one common equation. All of the equations directly estimate height and site index from any other height and age, and are base-age invariant. To obtain unbiased parameter estimates the base-age invariant dummy variables method was used, which recognizes that each measurement is made with error and, thus, fits a curve to the observed individual trends in the data by considering one parameter to be site-specific and the remaining parameters common for all individuals. A second-order continuous-time autoregressive error structure was used to correct the inherent autocorrelation of the longitudinal data used in this study, which allows the model to be applied to irregularly spaced, unbalanced data. The GADA formulation derived on the basis of the Bertalanffy–Richards model by considering the asymptote and the initial pattern parameters as related to site productivity resulted in the best compromise between biological and statistical considerations, producing the most adequate site curves. This model showed superior behavior when compared to the model currently in use. It is, therefore, recommended for height growth prediction and site classification of radiata pine plantations in Galicia.
This study develops some components to complete a management-oriented dynamic model system for simulating current and future volume and biomass of even-aged stands of managed downy birch (Betula ...pubescens Ehrh.) in Galicia (NW Spain). The specific components developed are a mortality equation, a basal area growth equation, a diameter distribution prediction system and equations for total and component biomass prediction. Functions to predict decreases in number of trees per hectare and basal area growth were simultaneously fitted using Nonlinear Seemingly Unrelated Regression (NSUR) and a base-age invariant dummy variable method; critical errors of 19 and 16 per cent were obtained, respectively, when projections were made. The Weibull function modelled successfully all but four of the 198 diameter distributions examined, using the parameter recovery method through moments. To predict components and total aboveground biomass, a system of additive equations was simultaneously fitted using the generalized method of moments (GMM), which takes into account heteroscedasticity and inherent correlations among the biomass components. A two-step fitting procedure was used because of the different number of observations for the components considered. The biomass equations explained more than 85 per cent of the observed variability. The Galician birch stands which were surveyed were found to have grown by 3–10 m3 ha−1 year−1 in volume and by 2–8 Mg ha−1 year−1 in aboveground total biomass, with rotations between 30 and 60 years. The model system now forms an accessible decision support system for forest management and land development in the region.
The ability to precisely describe forest spatial structures, and their modifications through timber harvesting, is of prime importance for sustainable management of complex forest ecosystems, ...especially regarding uneven-aged, multi-species forests. For this purpose, forest managers require statistical indices that are meaningful descriptors of the spatial structure of a given forest ecosystem. This paper presents a new sensitive permutation test of spatial randomness for solving the classification problem of three nearest neighbour-based indices. The test enables a categorisation of a spatial pattern as a whole into one of three groups: regular, random or cluster, with a sensitivity comparable to that of Ripley's L test, at finer scales. The examples illustrate how the Clark and Evans, the uniform angle, and the mean directional indices can be used for precise detection of departure from spatial randomness. The results show that these three indices should be used simultaneously because they are sensitive to slightly different types of processes.
In this study we developed a dynamic growth model for Scots pine (
Pinus sylvestris L.) plantations in Galicia (north-western Spain). The data used to develop the model were obtained from a network ...of permanent plots, of between 10 and 55-year-old, which the
Unidade de Xestión Forestal Sostible (Sustainable Forest Management Unit) of the University of Santiago de Compostela has set up in pure plantations of this species of pine in its area of distribution in Galicia. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate stand volume, classified by commercial classes, for a given projection age. The model uses three transition functions expressed as algebraic difference equations of the three corresponding state variables used to project the stand state at any point in time. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. This alternative should only be used when the stand is not yet established or when no inventory data are available. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class, by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution (arithmetic mean diameter and variance, respectively). By using a generalized height–diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume.
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