Algebraic Difference Approach Research Articles

Site index curves using the generalized algebraic difference approach – Gada in planted forests of Pinus taeda L. in the midwest of Santa Catarina, Brazil

One of the most widely used tools for assessing the productive potential of planted Pinus taeda L. forests is to generate site index curves. Site index is a measure of the productive potential of forests and is influenced by various factors such as soil, water, light, among others, representing the relationship between the dominant height of trees and age at a specific location. This relationship produces a curve and can be used for site classification, consequently estimating the productivity of the forest stand. The objective of this study was to evaluate the performance of dynamic equations, the Algebraic Difference Approach (ADA), and its generalization (GADA). The data were obtained from permanent plots of Continuous Forest Inventory (CFI), collected in forest stands, through a sequence of annual remeasurements from 5 to 17 years of age. Dominant height was estimated as a function of age using nonlinear equations, and subsequently, the ADA and GADA methods were applied using the Chapman-Richards basic equation. The results of the GADA method provided a substantial reduction in the root mean square error (RMSE), less than half when compared to the traditional guide curve method, and an increase from 0.95 to 0.99 in R2adj. Therefore, the GADA methodology proved to be suitable and efficient for site index classification, with noticeable flexibility and reliability on its estimates.

Modeling dominant height growth of teak plantations in the Caribbean region of Colombia

Identifying sites with adequate biological productivity is a critical factor in ensuring timber production and the profitability of forest-based investments. The productivity of forest sites is influenced by climatic, edaphic and topographic variables, as well as by silvicultural practices. Site index is a phytocentric method widely used to assess site productivity and its estimation is based on dominant height growth modeling. Teak is the fifth most planted forest species in Colombia, and its importance is associated with high economic returns and profitability. This study aims to model dominant height growth using the generalized algebraic difference approach for teak plantations established in the Caribbean region of Colombia. The Lundqvist-Korf model, in which the correlation of the residuals was handled with a continuous autoregressive specification of the first order, resulted in a satisfactory statistical estimation of the dominant height growth. The results indicate that in the Caribbean region of Colombia, productive sites for the establishment of teak plantations can be found as productive as in some tropical American countries and better than some sites in Asian countries. This suggests a potential for the expansion of teak plantations and forest-based investments in Colombia.

Dynamic Height Growth Equations and Site Index-Based Biomass Models for Young Native Species Afforestations in Spain

The expansion of forested areas through afforestation and reforestation is widely recognized as a highly effective natural solution for mitigating climate change. Accurately assessing the potential carbon uptake capacity of newly afforested areas requires modelling tools to estimate biomass stocks, including site index curves and biomass models. Given the unique conditions in terms of tree size, uniform spacing, and tree allometries observed in young afforestations compared to natural stands, specific tools are necessary. In Spain, over 800,000 ha has been afforested with native forest species since 1992, but specific modelling tools for these plantations are lacking. Using data from 370 stem analyses collected across an extensive network of plots in young afforestations, we developed dynamic height growth and site index models for the main native species (five pines and five oaks) commonly used in afforestation in Spain. We compared various nonlinear models, such as ADA (algebraic difference approach) and GADA (generalized algebraic difference approach) expansions. The developed site index models were then used to predict the total biomass stored in the afforestation. Our results underscore the necessity for specific site index models tailored to afforestations, as well as the potential of the established site index in predicting biomass and carbon fixation capacity in these young forests.

Dynamic height growth models for highly productive pedunculate oak (Quercus robur L.) stands: explicit mapping of site index classification in Serbia

Key messageWe applied the generalized algebraic difference approach (GADA) to develop dynamic models of height growth for pedunculate oak (Quercus robur L.) in Serbia. According to the dominant heights, the studied region comprises some of Europe’s most productive sites for pedunculate oak. Therein, we have generated a map showing the current site index class of stands. Such a map could be used to enhance forest management and evaluate climate change impacts.ContextAlthough sustainable forest management requires reliable prediction of forest site productivity, such indicators are currently unavailable for pedunculate oak sites in Serbia. The site index (SI) curves represent the most commonly used indirect scale for site productivity classification. The dynamic equations derived by the Generalized Algebraic Difference Approach (GADA) are the state-of-the-art approach in growth modeling, but they have not been widely applied for studying the height dynamics of pedunculate oak.AimsThe main objectives of this study were to develop the first dynamic site index curves for pedunculate oak in Serbia and subsequently to provide stand-level maps with predicted site indices.MethodsWe have tested five flexible polymorphic equations with variable asymptotes derived by the GADA approach. Models were calibrated using artificially established growth trajectories obtained from 3636 detailed temporary sample plots. The selection of the most suitable model was accomplished according to (1) quantitative measures of goodness of fit, (2) the analysis of residual scattering, and (3) the biological plausibility of obtained height growth curves.ResultsAfter correcting the error terms with a continuous first-order autoregressive structure and conducting a three-stage performance analysis, the GADA dynamic site index model derived from the Hossfeld base equation shows the best overall properties. Insight into the oscillations of relative error suggested that 100 years is the most suitable age for site index referencing. Comparison with existing height growth models revealed greater flexibility and a considerably better representation of the height growth dynamic of pedunculate oak in the studied region. Additionally, we have produced a spatially explicit map showing the expected SI100 for 1907 stands with pedunculate oak within 22 management units.ConclusionDynamic SI-curves based on GADA will serve forest practitioners to update management plans and serve as a reference point for benchmarking the impact of climate change and for developing adaptation strategies. The utilized approach allowed unbiased estimation of SI100 across all age classes so that the results could be mapped at a broader scale. This study provides the second known application of the dynamic model for pedunculate oak in Europe but the first that includes some of the most productive sites in the species distribution range.

Analysis of Height Growth Suggests Moderate Growth of Tilia cordata and Acer platanoides at the Native Hemiboreal Stands in Latvia

In the Eastern Baltics, climatic changes are expected to alter forest composition favouring broadleaved species. The height growth of trees influences the productivity of stands and the competitiveness of species, particularly in mixed sites, thus emphasising the necessity for accurate projections. Accordingly, height models are paramount for projecting productivity and yields of stands. As tree height growth dynamics vary regionally, regional or even local models are needed. Based upon 214 National Forest Inventory plots and 510 individual canopy trees, dominant height growth for small-leaved lime (Tilia cordata Mill.) and Norway maple (Acer platanoides L.) in Latvia were analysed. Height growth was modelled using a generalised algebraic difference approach, testing several non-linear equations. The Sloboda (for lime) and Hossfeld I (for maple) models showed the best fit and were the most realistic, predicting slower initial and middle-age (maturing period) growth, yet also displayed higher asymptotes compared to Western Europe. The predicted height at the age of 80 years was 14–33 m and 13–34 m for lime and maple, accordingly. A longer establishment period and later growth culmination suggest longer rotation, highlighting the assessment of long-term risks. In this case, supplementation of the models with climatic effects appears advantageous.

Height growth patterns of genetically improved Scots pine and silver birch

Abstract The breeding of forest tree species in the Baltic region has notably contributed to wood production for the bioeconomy. Growth modelling is used for long-term estimates of forest development. However, usually based on data from unimproved stands, they may underestimate the growth of improved trees. Accordingly, it is important to identify and integrate the altered stand dynamics associated with improved planting stock into existing growth models to accurately capture the resulting gains or, alternatively, develop new functions specifically designed for improved trees. We used the generalized algebraic difference approach to model and analyze height growth patterns of Scots pine and silver birch with different genetic improvement levels (improved forest reproductive material categories ‘qualified’ and ‘tested’). Modelling was based on 14 260 and 55 926 height–age series from open-pollinated progeny trials in Latvia and Lithuania with an age range of 3–46 and 5–22 years for pine and birch, respectively. Dynamic generalized algebraic difference approach forms of commonly applied height growth functions with forest reproductive material-category-specific sets of coefficients were tested. The dynamic form of the Chapman–Richards and King–Prodan equations had the best fit for Scots pine and silver birch, respectively. The expected height growth of the category ‘tested’ was slightly better than the one for ‘qualified’, with more distinct differences in silver birch. The model with forest reproductive material-category-specific coefficients reflected the actual growth of improved trees; however, such application is limited to sites with medium and high site indices, where improved planting stock is typically used. We recommend the model for young stands up to the age of 20 and 40 years for pine and birch, respectively, considering the empirical data cover on which the functions are based. A unified dynamic height model with the same functional form but category-specific parameterization for different improvement levels allows a practical applicability and effective communication amongst diverse users, thereby promoting the utilization of the model amongst forest owners and managers who possess information regarding the origin of planting stock.

Site Quality Evaluation Model of Chinese Fir Plantations for Machine Learning and Site Factors

Site quality evaluation is an important foundation for decision-making and planning in forest management and provides scientific decision support and guidance for the sustainable development of forests and commercial plantations. Site index and site form models were constructed and subsequently compared utilizing fir (Cunninghamia lanceolata) plantations in Nanping City, Fujian Province, China. This papers aim was to construct a site quality classification model, conduct further analysis on the effects of different site factors on the quality of the site, and achieve an assessment of site quality for Chinese fir plantations. An algebraic difference approach was used to establish a site index model and a site form model for Chinese fir in Fujian Province. The suitability of the two models was compared using model accuracy analysis and partial correlation, and the optimal model was chosen for classifying the site quality of the stands. On this basis, a site quality classification model was established using the random forest algorithm, and the importance of each site factor was determined through importance ranking in terms of their impact on site quality. Within the study area, the R2 of the site index model results was 0.581, and the R2 values of the five site form models based on different reference breast diameters, ranked from high to low, were 0.894, 0.886, 0.884, 0.880, and 0.865. The bias correlation coefficient between site form and stand volume was 0.71, and the bias correlation coefficient between site index and stand volume was 0.52. The results confirmed that the site form model is better suited for evaluating the site quality of Chinese fir plantations. The random forest-based site form classification model had a high classification accuracy with a generalization accuracy of 0.87. The factors that had the greatest impact on site form were altitude, canopy closure, and slope gradient, whereas landform had the smallest impact on site form. These results can provide a reference for the evaluation of the site quality of plantations and natural forests in southern China to ensure the long-term sustainable use of forest resources.

A state-space growth model for Eucalyptus pilularis in subtropical Australia, fitted with and without seemingly unrelated regression

ABSTRACT Inventory data from even-aged, monoculture blackbutt (Eucalyptus pilularis) forests in subtropical eastern Australia were used with the algebraic difference approach to construct a state-space model that predicted stand growth with age for each of quadratic mean diameter, basal area and dominant height, given some initial measurement of the stand. Conventional regression analysis was used to fit each part of the model separately and seemingly unrelated regression (SUR) was used to fit them jointly. Although using SUR resulted in slightly more efficient parameter estimators than when the models were fitted separately, there was no evidence that its use provided any appreciably better fit to the data or precision of estimates of future sizes. Other work in forest science that has used SUR is reviewed briefly and appears to have gained little advantage from its use.

Site Index Models for Loblolly Pine Forests in the Southern United States Developed with Forest Inventory and Analysis Data

Abstract Accurate productivity estimates are essential to assess the overall sustainability of forest resources. Site index (SI) models for loblolly pine (Pinus taeda L.) in plantation and natural forests of the southeastern United States were developed using the Forest Inventory and Analysis (FIA) database. We extracted short (~20 years), unbalanced panel data from the FIA database. Ten different nonlinear models derived from the base models using the algebraic difference approach (ADA) or the generalized algebraic difference approach (GADA) were fitted to the extracted data. The performance of the models was ranked based on a variety of fit and evaluation statistics. The results showed that all top three models were derived using the GADA approach. The best model for loblolly pine plantation and natural forest stands was derived from the Hossfeld model and the Chapman–Richards model, respectively. The best-fitted models for planted forests were also compared with previously developed models. This study demonstrated that base-age invariant and polymorphic SI models could be developed using short panel data extracted from FIA data. The SI models presented here can be used as a height growth model component in forest growth and yield model systems. Study Implications: Improved site index equations for assessing the site quality of loblolly pine plantation and natural stands are now available to stakeholders at the policy, management, and operational levels. Activities such as forest management, restoration, and wildlife management, which require site quality data, will benefit from the new models. Furthermore, the approach of deriving panel data based on Forest Inventory and Analysis data offers information on developing and updating models for other species. Finally, the approach of this study, to use permanent plot measurement data in developing growth and yield models, is cost-effective and time-efficient.

Laurel Regeneration Management by Smallholders to Generate Agroforestry Systems in the Ecuadorian Amazon Upper Basin: Growth and Yield Models

Laurel (Cordia alliodora Ruiz & Pav. Oken) is a Neotropical native tree that is easily regenerated in the secondary forest within the Amazon region. Amazonian smallholders use this tree regeneration to obtain a homogeneous forest cover when developing local agroforestry systems, which do not depend on nursery seedling production for tree planting. The objective of the present investigation was to develop growth and yield models for Laurel within the local agroforestry systems. A total of 226 sampling plots were measured between 2010–2011 and 2014–2015. Chapman- Richard, Hosslfeld II, and the generalized algebraic difference approach (GADA) form of the Chapman-Richard’s function was used for modeling height-age and diameter-age relationships. Eight volume models were tested to describe total stem volume. The GADA method was suited to describe the Laurel height and diameter-age growth. The cutting cycle for agroforestry systems with a density of 300 trees ha−1 at the best site index (SI) (22 m) produced 13.9 m3 ha−1 year−1 and a total wood yield of 195.1 m3 ha−1 at age 14. In the worst SI (14 m), the average annual yield was 3.5 m3 ha−1, with a total yield of 83.3 m3 ha−1 at age 24 years. The Spurr potential model was the best fit to describe the volume of the Laurel according to the Akaike information criteria. The Laurel biological (optimal) rotation age suggests that the minimum cutting diameter should be lowered from 30 cm of DBH in the research zone. Management of the natural regeneration of secondary forests by smallholders is a local agroforestry practice that should be given greater attention, especially within protected forest areas.

Site classification for Eucalyptus sp. in a tropical region of Brazil.

The aim was to determine the productive capacity of a forest site by applying different methods of fitting, combined with geostatistical techniques, to stands of Eucalyptus sp. in a tropical region of Brazil. Data were collected from 845 plots of a continuous forest inventory over four years. The classification of local production capacity was performed using growth curves obtained by the guide curve (GC) method, algebraic difference approach (ADA) and generalized algebraic difference approach (GADA) methods and ordinary kriging through the spherical, exponential, and Gaussian models to determine the spatial dependence of the variables site, geographical boundaries of site index classes, and their respective areas for each hectare in an annual production unit (APU). The modified Chapman-Richards model, fitted by the generalized difference approach method (GADA), provided the best statistical results, an improvement of 12.23% and 39.80% on the ADA and GC methods, respectively. The exponential model selected to express the spatial distribution of dominant height showed a high degree of spatial dependence.

Development of a site form equation for predicting and mapping site quality. A case study of unmanaged beech forests in the Cantabrian range (NW Spain)

Site form (SF), expressed as the dominant height of a stand at a reference dominant diameter, is used less often than site index (SI) to estimate forest site quality. However, it has the advantage that it is age-independent and can therefore be applied in a wider set of situations in forestry practice. Like SI, elaboration of SF has traditionally required stem analysis or repeated measurements in permanent plots; however, Airborne Laser Scanning (ALS) can nowadays be used to generate site quality practical maps, thereby simplifying the method. The aims of this study were to fit a dynamic equation to stem analysis data in order estimate SF in natural beech forests in NW Spain, as well as to compare the performance of SF for site quality estimation and to analyze the possibility of using ALS data for site quality prediction in these forests. The Algebraic Difference Approach formulation of the Bertalanffy-Richards model provided the best results and defined four curves for dominant heights of 5, 10, 15 and 20 m at a reference dominant diameter of 20 cm. A significant relationship between SF and SI was observed, and we therefore believe that SF is a good approach for site quality estimation. These results can be used directly at inventory plot level for establishing site quality classes without the need to know the stand age, either in terms of SF or translated into SI. On the other hand, ALS data allowed estimation of both dominant height and dominant diameter, although better results were obtained with the former. Applying the SF dynamic model to both data sets enabled prediction of SF at 25x25 m/pixel (and SI using the SI-SF relationship). The overall accuracy of the relationship between the observed SI and that predicted from ALS metrics yielded a coefficient of determination of 0.456 without bias, heteroscedasticity or absence of normality. The results of this unbiased raster model were considered rather good, as predictions were obtained for a pixel size of 25x25 m (0.0625 ha). Prediction of mean SI value for one hectare would thus be necessary to average the values obtained in 16 pixels with an expected error compensation. Use of the raster model based on ALS metrics will enable site quality estimation for current beech stands at high spatial resolution without the need for fieldwork, providing very valuable information for forest managers and researchers.

Forecasting production in thinned clonal stands of Tectona grandis in Eastern Amazonia

Aim of the study: We investigated the most suitable thinning ages and intensities to maximize productivity and minimize the rotation age of Tectona grandis clonal plantations in the Brazilian Eastern Amazon.
 Area of study: Capitão Poço, State of Pará, Eastern Amazonia, Brazil.
 Materials and methods: We used diameter, height, and volume data from 72 permanent plots measured on nine occasions. We determined the classification of forest sites using the generalized algebraic difference approach (GADA). Clutter’s segmented model was used to simulate different intensities of basal area reduction, determining the technical ages according to the projected increments.
 Main results: The polymorphic site curves generated by the GADA method revealed that there were sites with different productive characteristics. The Clutter model produced compatible projections of basal area and volume that followed the behavior of the productivity classes. The final production was maximized when three thinning intensities (basal area reductions) were applied: 1st thinning (50%), between the ages of 3.5 to 4.2 years; 2nd thinning (50%), between the ages of 6.1 to 7.3 years; and 3rd thinning (25%), between the ages of 10.6 to 12.8 years. Projected rotation ages ranged from 13.9 to 16.6 years earlier than seminal plantings. The simulations increased the net volume by 8.3%, on average, compared to no thinning.
 Research highlights: Simulations with three thinnings maximized production compared to the no thinning scenario. The time interval between thinnings was less than five years. The research results can help forest management decision-making and reveal production increases of T. grandis clonal stands in a shorter time.

A Dynamical Model Based on the Chapman–Richards Growth Equation for Fitting Growth Curves for Four Pine Species in Northern Mexico

Tree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid growth function: (i) the upper asymptote (θ1), which is the maximal yield indicated by a final dimension (such as the maximal stem diameter); (ii) the maximum specific growth rate (θ2), defined as the slope of the tangent at the inflexion point; and (iii) the time elapsed (θ3), defined by the intercept of this tangent with the abscissas. To the best of our knowledge, however, associations between the three parameters have not been documented for tree species. Using diameter growth data from pine trees located in typical mixed and uneven-aged pine-oak forests in the Sierra Madre Occidental, Mexico, our study aims were: (i) to quantify the putative associations between the three growth parameters and (ii) to test the accuracy of a proposed Hybrid Chapman-Richards growth model based on associations between the three growth parameters, but including only one single parameter, relative to the widely used Generalized Algebraic Difference Approach (GADA) based on the Chapman-Richards, Lundqvist and Hossfeld models and the Hybrid Weibull Model. For statistical comparison of the quality of the models, we used the mean relative percentage error, root mean square error, coefficient of determination and Akaike information criterion to assess the quality of the fit. Although the quality of the five growth models studied was similar, from a practical point of view, the proposed Hybrid Chapman-Richards Model (CR-H) is easier to apply than the other models and has a lower data collection and computational cost. The parameter of CR-H can be easily obtained, by measuring just the dominant trees, especially in coniferous forests with irregular ages. Moreover, in contrast to the Chapman-Richards-GADA factor χ0, when θ2 is assumed to be site-specific, the CR-H has always a closed-form solution.

Nueva ecuación dinámica de altura dominante e índice de sitio para Pinus chiapensis (Martínez) Andresen en Puebla y Veracruz, México

Introduction: Pinus chiapensis (Martínez) Andresen lacks in many areas of site index (SI) models to classify timber productivity. Objective: To develop a dynamic SI equation, using the generalized algebraic difference approach (GADA) to describe the dominant height growth pattern and classify the productivity of natural stands of P. chiapensis in Puebla and Veracruz, Mexico. Materials and methods: Four theoretical growth models were used to derive six equations in GADA, fitted to dominant height-age observations from stem analyses of 31 trees. Fitting was performed using the Dummy variable method, which is invariant to the base age; autocorrelation and heteroscedasticity were corrected. Results and discussion: Quantitative evaluation, graphical analysis of residuals and growth trends of equations allowed the selection of an equation derived from the Levakovic II model with higher predictive capacity. With this equation and a base age of 50 years, polymorphic SI curves with variable asymptotes were constructed to classify productivity into low, medium and high, corresponding to SI of 25, 32 and 39 m, respectively. The maximum mean annual increase for the SI of 32 m was 1.07 m∙yr-1 and occurred at 11.08 years. The equation exhibited better performance relative to a previously reported polymorphic equation. Conclusions: It is recommended to use the developed equation to predict dominant height growth and SI of P. chiapensis stands in Puebla and Veracruz, Mexico.

Long-term term effect of bedding and vegetation control on dominant height of slash pine plantations in the southeastern United States

The long-term effect of bedding and vegetation control on dominant height in slash pine (Pinus elliottii Engelm) was evaluated using data from a site preparation study established in 1979 by the Plantation Management Research Cooperative (PMRC) at the University of Georgia in the southeastern United States. The experimental design corresponded to a 2 × 2 factorial with replications over 16 different locations, distributed over the natural range of slash pine. Our results show sustained gains in dominant height, reaching a peak increment around age 11, with values of 1.0, 2.2, and 2.9 m of average gain for the bedding, vegetation control, and combined (Bed + Veg.) treatments, respectively. At age 31, an approximate rotation age, these gains were no longer present for the bedding treatment, whose dominant height trajectory converged to the values of the untreated control and decreased to 1.9 m for both treatments involving competing vegetation control. These results are similar to previously reported results in the literature for these two treatments in slash pine. We proposed a modified Chapman-Richards type model to describe these trends. In this modeling approach, the base equation was modified using a set of dummy variables in the form of power functions to reflect the treatment effect. Both treated and untreated plots were simultaneously fitted in this model, and contrarily to the most common approach of adding an independent factor to a base model to account for the treatment response, our model does not assume the control plot to be error free. The flexibility of the proposed model allows practitioners to include observed gains in dominant height from these treatments. A slash pine site index model using the algebraic difference approach (ADA) was also derived.

Site Quality Classification Models of Cunninghamia Lanceolata Plantations Using Rough Set and Random Forest West of Zhejiang Province, China

The site quality evaluation of plantations has consistently been the focus in matching tree species with sites. This paper studied the site quality of Chinese fir (Cunninghamia lanceolata) plantations in Lin’an District, Zhejiang Province, China. The site quality model was constructed using the algebraic difference approach (ADA) to classify the site quality grades. The rough set algorithm was used to screen out the key site factors affecting the site rank of Chinese fir plantations. Site quality classification models based on random forest were established, and the importance of key site factors was evaluated. The results are as follows. The random forest model based on the rough set algorithm had small scale and low complexity, and the training and testing accuracies of the model were 92.47% and 78.46%, respectively, which were better than the model without attribute reduction. The most important factors affecting Chinese fir growth in the study area were the slope aspect, slope grade, and canopy closure. The least important factors were the humus layer thickness, soil layer thickness, naturalness, and stand origin. The attribute reduction method proposed in this study overcame the subjectivity of traditional site factor selection, and the site quality classification model constructed improved the model accuracy and reduced the complexity of the algorithm. The methods used in this study can be extended to other tree species to provide a basis for matching tree species with sites and to improve the level of forest management in the future.

Age-independent diameter increment models for mixed mountain forests

Mixed mountain forests with an uneven-aged structure are characterized by a high tree-growth variability making traditional age-dependent growth models inapplicable. Estimating site productivity is yet another impediment for modelling tree growth in such forests. Uneven-aged mixed-stand forests are known for their high resilience, resistance and productivity, and are being promoted as a suitable alternative to even-aged, pure plantations for climate change adaptation and mitigation. However, their growth must be accurately measured and predicted, but diameter at the breast height (dbh) increment models specifically designed for uneven-aged mixed mountain forests are still rare. Using permanent sampling network data and 465 increment cores, we built two age-independent dbh increment ({i}_{d}) models for the main species of the study area, namely Norway spruce (Picea abies (L.) Karst.), silver fir (Abies alba Mill.) and European beech (Fagus sylvatica L.). Mixed effects models and the algebraic difference approach were employed to develop {i}_{d} models based on empirical and commonly used theoretical growth functions. A past growth index was further developed and introduced in the model in order to explain the {i}_{d} variability. Several mixed effects calibration strategies were assessed in order to obtain the most accurate localized curve for new plots. Tree size, competition and biogeoclimatic variables were found to explain the {i}_{d} through the empirical growth function, while the growth index significantly improved the theoretical growth function for Norway spruce. The optimization of the calibration strategy for the mixed effects modelling framework enables the growth index implementation in forest practice as an accurate method for estimating site productivity. The accuracy of the two {i}_{d} models was similar: the root mean squared error of the empirical growth function varied between 0.940 and 1.042 cm for spruce, beech and fir, while the root mean squared error obtained through the theoretical growth function for spruce only was 1.105 cm. The basal area increment prediction at the plot level based on the theoretical growth function reached a root mean squared error of 0.043 m2 while using the empirical growth function the root mean squared error is 0.047 m2. The high accuracy obtained using age-independent models underlines their suitability for predicting growth in mixed uneven-aged forests. The developed models can be easily integrated into forest practice to accurately obtain {i}_{d} estimates.

Climatic and Topographic Variables Improve Estimation Accuracy of Patula Pine Forest Site Productivity in Southern Mexico

Sustainable forest management requires accurate biometric tools to estimate forest site quality. This is particularly relevant for prescribing adequate silvicultural treatments of forest management planning. The aim of this research was to incorporate topographic and climatic variables into dominant height growth models of patula pine stands to improve the estimation of forest stand productivity. Three generalized algebraic difference approach (GADA) models were fit to a dataset from 66 permanent sampling plots, with six re-measurements and 77 temporary inventory sampling plots established on forest stands of patula pine. The nested iterative approach was used to fit the GADA models, and goodness-of-fit statistics such as the root mean square error, Akaike’s Information Criterion, and Bias were used to assess their performance. A Hossfeld IV GADA equation type that includes altitude, slope percentage, mean annual precipitation, and mean annual minimum temperature produced the best fit and estimation. Forest site productivity was negatively affected by altitude, while increasing the mean annual minimum temperature suggested the fastest-growing rates for dominant tree height.

Shortleaf Pine (Pinus echinata) Site Index Equation for the Cumberland Plateau, USA

Abstract Shortleaf pine site index on the Cumberland Plateau is one of the least studied silvics of the species. To obtain site index information, practitioners must use site index curves from outside the region. This research proposes a novel approach to using USDA Forest Service, Forest Inventory and Analysis data to develop a shortleaf pine site index equation specific to the Plateau. Shortleaf pine site trees (n = 410) were grown forward or backward until base age of 50 years, using site specific, mixed-model parameters. Over thirty height models were then fit using traditional methods and the algebraic difference approach (ADA). Fit and cross-validation statistics, along with examinations of model behavior, showed that a derivation of the Lundqvist-Korf model provided the best estimates. The model was rearranged to directly estimate site index, and a traditional site index graph is provided. Site index estimates had average validation results nearly four times better than the currently recommended site index curve developed off the Plateau. Forest practitioners now have access to improved site index estimation for restoring and managing shortleaf pine on the Cumberland Plateau.