Polymorphic Site Index Curves Research Articles

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.

Two subject specific modelling approaches to construct base-age invariant polymorphic site index curves with varying asymptotes

For constructing growth and yield models the concept of site index as measure of productivity is crucial. Here, we use nonlinear mixed-effects models (NLME) with random individual effects and nonlinear models with dummy variables as fixed individual effects (NLFE) to fit mechanistic growth functions to stem analysis data of the economically most important tree species in Zhongtiaoshan forest region, China. The Richards and Lundqvist function are formulated into five dynamic equations (R1, R2, L1, L2 and L3) applying the generalized algebraic difference approach (GADA), which inherit polymorphism, varying asymptotes and base-age invariance. According to Akaike information criterion the R1 model as NLFE fits height growth data of Carrière, Franch., Koidz., Blume and Sukaczev best, while for Blume R2 as NLFE fits height growth data best. For Mayr L1 as NLME has been selected as best model, as R1 and R2 both as NLFE and NLME are not extrapolating the comparably short length of height growth data well enough. However, according to the root mean square error and bias differences between model fits of both the selected equation and the chosen model fitting approach are not so clear. Presented families of height growth curves serve as planning tools to identify site index and therefore assess productivity of forest stands in the studied region. A direct comparison of the productivity of forest stands of the same tree species is possible due to base-age invariance of the selected models.Pinus tabuliformisPinus armandiiQuercus liaotungensisQuercus alienaBetula platyphyllaQuercus variabilisLarix principis-rupprechtii

Polymorphic site index curves for Beech (Fagus sylvatica L.) in Central and Eastern Serbia

This study was mainly aimed at constructing polymorphic site index curves for beech in the central (Rudnik mountain – RU, about 15,000 ha) and eastern (Žagubica – ŽA, about 7,000 ha) part of its distribution in Serbia. To obtain suitable height-age data and evaluate the best-fit growth model we used 107 felled dominant beech trees. The Korf, Korsun and Chapman-Richards growth functions per site class were first parameterized and then mutually compared with respect to residual statistics and the significance of their parameters. They were additionally parameterized in line with empirical data on the value and age of the culmination of current annual height increment (CAI<sub>h</sub>). The obtained results indicated that the Chapman-Richards growth function showed the best results both by statistical (residuals standard error, significance of the parameters, distribution of residuals, and homoscedasticity) and by empirical criteria (the CAI<sub>h</sub> culmination time, the maximal values of the CAI<sub>h</sub>, and the attained height of trees at a certain age) of the height-age beech modelling in the analyzed regions. The obtained polymorphic site index curves which classify sites with regard to their productivity can be very helpful in planning appropriate silvicultural treatments, and for decision-making in forest management planning, forest policy and ecology and, consequently, in the sustainable management of beech forests in Serbia and some neighbouring countries with a similar forestry sector development.

Índice de sitio para bosques naturales de Pinus teocote Schlecht. & Cham. en el oriente del estado de Hidalgo


 
 
 La estimación de la productividad de los sitios forestales es indispensable para el manejo sostenible de los bosques y el índice de sitio constituye la metodología más utilizada en el mundo para este fin. Sin embargo, uno de los problemas más graves en el manejo forestal es la falta de ordenamiento de los rodales en función a su productividad, lo que propicia sobreexplotación de los recursos en algunos casos y la subexplotación en otros. Por ello, el objetivo del presente estudio fue estimar el índice de sitio y comparar la factibilidad de emplear las curvas anamórficas y polimórficas para bosques naturales de Pinus teocote en la región oriente del estado de Hidalgo. Se manejaron 345 pares de valores edad-altura de árboles dominantes y codominantes evaluados en rodales puros de este taxon; se ajustó el modelo de crecimiento de Schumacher que de acuerdo al bajo valor del Cuadrado Medio del Error, el alto valor de Pseudo R2 ajustada y la correcta distribución de residuales mostró un ajuste adecuado a los datos, para determinar la curva guía y la construcción de las familias de curvas anamórficas y polimórficas de índice de sitio. Se establecieron calidades de estación de I, II, III, IV y V, en los valores de 27, 23, 19,15 y 1 m, respectivamente, a una edad base de 50 años.
 
 

Dynamic base-age invariant site index models for Tectona grandis in peninsular India

Data from 27 remeasured sample plots were used to evaluate dynamic base-age invariant site index models for teak (Tectona grandis) forests in Karnataka, India. The data were obtained in observational field studies covering a wide range of sites in Karnataka and provided up to three interval measurements per plot. All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The model evaluation criteria were bias, root mean square error and the adjusted coefficient of determination. The best results were obtained with the generalised algebraic difference equations derived from the Korf base model. The selected model accounted for 99.8% of the total variance in height–age relationships in dominant trees. The dynamic base-age invariant site index model proved to be effective and accurate in presenting polymorphic site index curves with multiple asymptotes. The new dynamic base-age invariant site index models based on generalised algebraic difference approach (GADA) methodology can be recommended for dominant height prediction and forest site quality evaluations in the teak forests in Karnataka, India.

Dynamic base-age invariant site index models based on generalized algebraic difference approach for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands

Data from stem analysis of 397 dominant trees (198 Scots pine and 199 Oriental beech) were used to evaluate dynamic base-age invariant site index models derived from Bertalanffy-Richards, Hossfeld, and Lundqvist-Korf functions with the generalized algebraic difference approach (GADA) for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands. These functions were compared with respect to residuals of these models; specifically, the evaluation criteria were bias (E), root mean square error (RMSE), absolute mean error (AME), adjusted coefficient of determination (R2adj), and Akaike information criterion. The best results were obtained with generalized algebraic difference equations derived from the base models of Bertalanffy-Richards for Oriental beech and Hossfeld for Scots pine. These selected models accounted for 95%-96% of the total variance in height-age relationships in dominant trees with bias of 0.049841 and 0.00171, RMSE of 1.55624 and 1.353736, AME of 0.940128 and 0.884034, and AIC of 723.55 and 1250.78 for Scots pine and Oriental beech, respectively. These dynamic base-age invariant site index models for the 2 tree species presented more effective and accurate polymorphic site index curves with multiple asymptotes than earlier site index models for Oriental beech and Scots pine. The important differences of height growth trend between developed base-age invariant site index models in this study and earlier site curves were determined by graphical comparisons for site index predictions. Therefore, the new dynamic base-age invariant site index models developed based on GADA methodology can be recommended for dominant height prediction and forest site quality evaluations in the mixed stands of these 2 species.

Aplicação da função hiperbólica na construção de curvas de índice de local

Neste estudo foi avaliada a eficiência da função hiperbólica, para geração de curvas anamórficas e polimórficas de índices de local. As curvas de índice de local foram construídas utilizando os métodos: da curva-guia, da equação das diferenças, da predição de parâmetros, de Hammer e dos índices de local definidos preliminarmente. Para aplicação desses métodos foram utilizados dados de parcelas permanentes de povoamentos de eucalipto. A eficiência foi confirmada, sendo a função indicada para descrever tendências polimórficas e anamórficas, podendo ser utilizada na classificação da capacidade produtiva de povoamentos de eucalipto.

Comparison of height growth and growth intercept models of jack pine plantations and natural stands in northern Ontario

Accurate estimates of forest productivity are required for sustainable forest management. Sixty-five jack pine (Pinus banksiana Lamb.) plantations (<50 years of age) were sampled to develop height growth and variable growth intercept (GI) models for jack pine plantations in northern Ontario, Canada. Based on the residual plots and model-fitting statistics, these models can be recommended for estimating site index (SI) of young (<40 years) jack pine plantations. To compare SI of plantations with that of natural stands, we used stem-analysis data from 383 plots of natural jack pine stands (aged 50–157 years) from the same geographic region to develop the GI models for natural stands. Also, polymorphic SI curves were developed for young (<40 years) plantations in northern Ontario. These SI curves were different from those for natural stands. Jack pine plantations had a higher site quality (SI) than did the original natural stands on the similar sites. The SI curves developed from natural stands should not be used to predict growth and yield of jack pine plantations before they are calibrated for jack pine plantations. These GI models will be used to estimate SI for silviculture and forest-management planning.

Polymorphic site index curves for black spruce and trembling aspen in northwest Ontario

Site index curves were developed using stem-analysis data from dominant and codominant trees in 230 black spruce and 194 trembling aspen plots located in mature, well-stocked, even-aged stands. Black spruce plots were in five separate and independent data sets located on mineral and organic soils; trembling aspen plots were in three separate and independent data sets located on mineral soils. Computations showed that the Newnham nonlinear regression model was slightly more precise than other models commonly used for developing site index curves. This model accurately expresses polymorphic height growth for a wide range of site index and age and constrains predicted height to agree with specified 50-year tree height (site index). Computations showed that height-growth curves were similar for each of the five black spruce data sets; likewise, curves for each of the three trembling aspen data sets were similar. Therefore, the five black spruce and the three trembling aspen data sets were combined for computing a single set of black spruce and a single set of trembling aspen site index curves for Northwest Ontario. Comparisons between our Northwest Ontario site index curves and other black spruce and trembling aspen curves showed large differences in height-growth patterns for older ages. Reasons for these differences are uncertain but in many instances these could be artifacts related to study methods involving various amounts and kind of data and variations in analytical techniques. In some cases differences in climate, soil and topography may also be related to variations in these site curves. Key words: site quality evaluation, polymorphic height growth, site index curve comparisons

Growth models and yield tables for Pinus radiata D. Don in Galicia (northwest of Spain)

In this paper, growth models and yield tables for Pinus radiata D. in Galicia (northwest of Spain) are shown. These models were obtained from the measurement of 175 permanent sample plots, stem analyses of dominant trees and index trees. Polymorphic site index curves and three different types of yield tables corresponding to other three possible stand density evolutions are obtained. Optimal biomass rotations range from 28 to 44 years, and mean annual increment varies from 8.1 to 19.8 m3 ha–1year–1 at 30 years, depending on site index. Wood productions to different standard diameters are estimated, and alternative silvicultural regimes are discussed.

Development of top height model and site index curves for Azadirachta indica A. juss

This paper describes the development of top height model for stands of Azadirachta indica. The algebraic difference form of the Chapman–Richards equation is first fitted to the interval data of height–age data pairs resulting in an anamorphic system. Polymorphic site index curves were also developed using Ek’s extension of the Chapman–Richards function. Secondly, some commonly used models were compared for their goodness-of-fit and predictive ability in describing allometric relationships between volume, diameter and age. It has been observed that, in general, Chapman–Richards function may be used to model the relationships between these growth parameters.

Polymorphic site index curves for jack pine in Northern Ontario

Stem-analysis data from dominant and codominant trees were collected from 383 plots located in fully stocked, even-aged, undisturbed mature jack pine stands. Separate site index curves were independently formulated for four regions of northern Ontario using the Newnham constrained nonlinear regression model; these formulations were used for comparing regional site index curves at three levels of site index (10 m, 15 m and 20 m).Comparisons showed that no significant differences existed between the four regional curves as well as with previously published site index curves for the North Central Region. Each of the four regions had similar polymorphic height-growth patterns; therefore, data for the four regions were combined and a single formulation was used to develop a polymorphic set of site index curves for all of northern Ontario. We found that poor sites in each region had almost linear height growth up to 100 years breast-height age, but for each region height growth became more curvilinear with increasing site index. The recommended site index curves for northern Ontario are based on a formulation using only data from plots 100 years and less but this formulation was not significantly different from a formulation using only data from plots 80 years and less, or a formulation that included all data from plots older than 100 years breast-height age.Comparisons were made between our northern Ontario curves and other jack pine site index curves for Ontario as well as curves for other areas of Canada and the United States. These comparisons generally showed considerable older age differences. Reasons for these differences are uncertain but could be due to differences in the amount and kind of data used for these other curves, could be due to differences in analytical methods, or could be due to regional differences in climate, soil and topography. Key words: site quality evaluation, polymorphic height growth, regional site index curves, site index prediction equations, comparisons among site index curves.

Site Index of Balsam Poplar/Western Black Cottonwood in Interior and Southcentral Alaska

Abstract Stem analysis data were obtained from 268 balsam poplar (Populus balsamifera L.) and black cottonwood (P. trichocarpa Torr. & Gray) trees on 67 sites in interior and southcentral Alaska during 1988-1990 for the purpose of height and volume growth analysis. A modified form of the Chapman-Richards growth model was used to produce polymorphic site index curves. Wide variations in curve shape, which were evident in region-to-region comparisons, required stratification of the data. Site index curves for balsam poplar north of the Alaska Range were produced using one equation and data from 35 sites. The remaining 32 sites, located south of the Range, were divided by landform (fluvial vs. upland). Sites on the middle and upper Susitna and Chulitna Rivers were placed in a separate fluvial class, giving three equations for sites south of the Range. The four equations produce the first polymorphic site index curves for poplars in Alaska. North. J. Appl. For. 15(4):174-181.

A New Height Growth Model for Dominant and Codominant Trees

Abstract A model was developed to predict height growth for dominant and codominant trees, using asymptotic tree height, and tree height at the age of maximum height growth as principal characteristics to express the influence of site on tree height. The proposed model has many desirable attributes: it (1) produces polymorphic site-index curves, (2) contains an inflection point, (3) asymptotically approaches maximum tree height as age increases, (4) is mathematically defined at the point of origin, and (5) has a theoretical base (pipe model theory) for height growth. Model performance was evaluated with stem analysis data taken from naturally regenerated forest stands of mature to overmature balsam fir (Abies balsamea [L.] Mill.) and black spruce (Picea mariana Mill.) growing in two separate regions within New Brunswick, Canada. The model was also evaluated by analyzing its ability to reproduce existing site index curves for red pine (Pinus resinosa Ait.). The results indicate that the proposed model performs slightly better than an existing 5-parameter model based on the Richards' growth function. For. Sci. 43(3):348-354.

Height growth–elevation relationships in subalpine forests of interior British Columbia

Stem analysis data from even-aged Engelmann spruce (Picea engelmannii Parry ex Engelm.) and subalpine fir [Abies lasiocarpa (Hook.) Nutt.] stands on zonal sites in the Engelmann Spruce—Subalpine Fir biogeoclimatic zone of British Columbia were used to examine the relationships of site index and height growth and elevation, latitude, and longitude. Elevation and latitude were found to be strongly negatively correlated with site index of both study species. Spruce site index (bh age 50) was predicted to decrease 2.9 m and fir site index 2.5 m with every 100 m and 1° increase in elevation and latitude, respectively; however, (i) site index of both species appeared to decline faster with increasing latitude than elevation, and (ii) decrease appeared to be faster for spruce than for fir. Comparison of height growth curves for stands on zonal and azonal sites with similar site index from different elevations and latitudes suggested that there are probably inconsequential differences between the shape of curves for either species. These findings imply that (i) subalpine fir is better adapted to subalpine boreal climates than Engelmann spruce and (ii) development of polymorphic site index curves for estimating site index of both species may be appropriate. Key words: elevation, latitude, longitude, site index, height growth, Abies lasiocarpa, Picea engelmannii, Engelmann Spruce—Subalpine Fir zone

Base-Age Invariant Polymorphic Site Index Curves for Black Spruce and Balsam Fir Within Central Newfoundland

Abstract Increasing management intensity within Newfoundland requires that regional site index equations be species-specific and base-age invariant. Accordingly, base-age invariant polymorphic site index curves for black spruce and balsam fir were developed for use on upland mineral sites within central insular Newfoundland. Specifically, employing mean dominant height and breast-height age data derived from 129, 0.081 ha permanent sample plots situated in pure black spruce (n = 71) and mixed black spruce/balsam fir (n = 58) stands, site index equations were calibrated by species and stand type. In addition, given the approximate numeric equivalence of the resultant parameter estimates, data for both species and stand types were combined and a pooled equation calibrated. The equations were evaluated on their bias and predictive ability over 10-, 20-, and 30-year projection periods. Results indicated that the predictions were positively biased averaging +1.29 m, +2.36 m, and +3.15 m for 10-, 20-, and 30-year projection periods, respectively. Corresponding 95% prediction error intervals for these periods were -0.56 to +3.14 m, -0.88 to +5.44 m, and -1.27 to +6.56 m. These biases and prediction errors are within acceptable limits for site-class designations; however, explicit use of the site-index equations with growth and yield models would depend on error tolerances specified by individual users. North. J. Appl. For. 9(1):18-22

Site Index Curves for Eastern Cottonwood Plantations in the Lower Mississippi Delta

Abstract A site index equation was developed based on stem-analysis data collected from 30 sites of an eastern cottonwood (Populus deltoides Bartr.) plantation in the lower Mississippi Delta. The Bailey and Clutter (1974) equation form was selected for stand height prediction. Polymorphic site index curves (base age 10 years) were presented based on this equation. These curves should be applicable to cottonwood plantations up to 11 years old in and near the Mississippi River Delta. South. J. Appl. For. 15(1):28-30.