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Este trabalho teve como objetivo desenvolver um Diagrama de Manejo da Densidade (DMD) para definir momentos ótimos para aplicação de desbastes e corte final em povoamentos de Pinus taeda L., no estado do Paraná. A base de dados utilizada no estudo é oriunda de plantios de Pinus taeda estabelecidos no estado do Paraná, nas regiões Centro-Oeste, Sul e Campos Gerais, além de dados coletados na Floresta Nacional de Irati (FLONA de Irati) e em um experimento com diferentes espaçamentos existente no Campus da UNICENTRO (Universidade Estadual do Centro-Oeste), no município de Irati. Foram utilizadas 1.023 parcelas sem desbastes, com idades variando de 7 a 44 anos. Foi ajustado o modelo de densidade de Reineke (1933) para obter o Índice de Densidade de Reineke (IDR), construindo-se então, o DMD similarmente à metodologia proposta por McCarter e Long (1986) e Dean e Baldwin (1993), o qual tem como componentes básicos o IDR e um sistema de equações que relacionam o diâmetro médio quadrático (dg) e o volume do povoamento (V) com a densidade (N), altura dominante (hdom) e o diâmetro médio quadrático. O sistema de equações ajustado para a construção do DMD apresentou estatísticas adequadas de ajuste e precisão, possibilitando a definição das densidades iniciais para atingir um dado diâmetro de tamanho desejado no corte final, bem como conhecer as idades em que devem ser realizadas as intervenções e a prognose da produção de cada colheita.

We predict stand basal area (BA) from small footprint LiDAR data in 129 one-ha tropical forest plots across four sites in French Guiana and encompassing a great diversity of forest structures resulting from natural (soil and geological substrate) and anthropogenic effects (unlogged and logged forests). We use predictors extracted from the Canopy Height Model to compare models of varying complexity: single or multiple regressions and nested models that predict BA by independent estimates of stem density and quadratic mean diameter. Direct multiple regression was the most accurate, giving a 9.6% Root Mean Squared Error of Prediction (RMSEP). The magnitude of the various errors introduced during the data collection stage is evaluated and their contribution to MSEP is analyzed. It was found that these errors accounted for less than 10% of model MSEP, suggesting that there is considerable scope for model improvement. Although site-specific models showed lower MSEP than global models, stratification by site may not be the optimal solution. The key to future improvement would appear to lie in a stratification that captures variations in relations between LiDAR and forest structure.

International audience; Introduction The self-thinning relationship established by Reineke in 1933 assumes a relationship between the number of stems and the quadratic mean diameter in fully stocked pure stands. This rule is extensively used for management purposes, but it has been initially calibrated for pure, even-aged stands for relatively few species. Objectives Here, we extend this relationship to mixed-species and mixed-size forests through a generalized modeling approach. Reineke's rule can be seen as a particular case of this generalized approach. Resource sharing is taken as a starting point; thus, both site fertility and diameter heterogeneity are taken into account. Discussion Calibration on actual inventories is made on a dataset of 82 French stands. The theoretical relationship is successfully adjusted for species in which enough data were available, namely, common beech (Fagus sylvatica L.), oak (Quercus petraea [Mattuschka] Liebl and Quercus robur L.), and Norway spruce (Picea abies [L.] Karst). Conclusion Self-thinning exponents obtained for beech and oak (1.86 and 1.76, respectively) can be used in the mixed-species equation that we developed. These results encourage calibrating the parameters for other species if appropriate data are available. Resource sharing is taken as a starting point; thus, both site fertility and diameter heterogeneity are taken into account. Discussion Calibration on actual inventories is made on a dataset of 82 French stands. The theoretical relationship is successfully adjusted for species in which enough data were available, namely, common beech ( Fagus sylvatica L.), oak ( Quercus petraea [Mattuschka] Liebl and Quercus robur L.), and Norway spruce ( Picea abies [L.] Karst). Conclusion: Self-thinning exponents obtained for beech and oak (1.86 and 1.76, respectively) can be used in the mixed-species equation that we developed. These results encourage calibrating the parameters for other species if appropriate data are available

Introduction In pure and even-aged stands, the allometry between mean tree size and maximum stand density-or self-thinning relationship-has long been considered a constant among tree species. Although the self-thinning allometric coefficient has been shown to be species-dependent, estimates available for a given species also differ. Whether this coefficient truly varies across species thus remains an open issue. A potential cause of variation in the coefficient may lie in a departure from the allometric assumption in the self-thinning relationship. Methods We analysed the species dependence of the self-thinning relationship for 11 temperate and Mediterranean tree species growing in pure and even-aged stands in France based on the French National Forest Inventory (NFI) data. Self-thinning relationships were fitted using a 'stochastic frontier' technique. Pairwise comparison tests of the self-thinning allometric coefficients were implemented. We also investigated the allometric nature of the relationship by testing a linear and a curvilinear model of log density against the log quadratic mean diameter. Results Self-thinning relationships were clearly evidenced from the NFI data and displayed significant differences between species. The curvilinear model was significantly more accurate for 7 out of 11 species and depicted a concave relationship, suggesting a decrease in self-tolerance over ontogeny. Conclusion As a major finding, the self-thinning relationship significantly varies across species. We emphasise the need to consider a high number of species to show such specific variations in the self-thinning relationship. Another important outcome is that the self-tolerance depends on the developmental stage.

Changes in tree form and taper over time, as affected by changes in tree, stand, and site factors for interior lodgepole pine (Pinuscontorta var. latifolia Engelm.) were investigated using detailed stem analysis data from interior British Columbia. It was found that tree shape and taper change along the stem at one time and over time with changes in tree and stand factors, particularly the diameter at breast height to total tree height ratio, crown length, and crown ratio, and with predicted quadratic mean diameter at age 50 years, a stand density measure. At young ages, the trees were parabolic in shape from ground to top. However, as they increased in size over time, different portions of the stem took different shapes because of unequal growth in diameter along the stem. Changes in tree shape and taper over time were closely related to the crown size, which is related to stand density.

Height-age and height-diameter models for plantations of young Douglas-fir ( Pseudotsuga menziesii [Mirb.] Franco var. menziesii ) were examined in relation to vegetation management treatments. The models were developed from 10 years of measurements in a competition release study installed on six sites in the Coast Ranges of Oregon and Washington. Analysis of height growth patterns for dominant trees indicated significant differences between the total vegetation control treatment and operational release treatments or no treatment. The resulting height-age function depicted exponential growth patterns for the total vegetation control treatment and nearly linear patterns for the operational release treatment and no treatment. The height-diameter function was compatible with dominant height growth and quadratic mean diameter prediction functions. Different height-diameter curve shapes were associated with total vegetation control and the operational release and no treatments. The resulting function implied that Douglas-fir trees of a given diameter and age were slightly taller when under interspecific competition, especially for trees with smaller diameters. The height-age and height-diameter functions may be used in conjunction with diameter distribution or stand table projection models developed for those data to predict dynamics and stand structure in young Douglas-fir plantations.

A stand table projection system based on individual-tree and stand-level models for young Douglas-fir ( Pseudotsuga menziesii (Mirb.) Franco var. menziesii ) plantations was developed from and evaluated with remeasurement data from sites in the Siskiyou Mountains of southwestern Oregon and in the Coast Ranges of Oregon and Washington. A projection equation was developed for relative tree size, defined as the ratio of individual-tree diameter at 15 or 30 cm above ground level (depending on the study location) to quadratic mean diameter. The relative size projection equation for the Coast Ranges study included the effect of total vegetation control, which indicated that diameters of Douglas-fir receiving total vegetation control tended to become more uniform over time in the Coast Ranges. An additional equation was developed to project quadratic mean diameter so that individual-tree diameters could be estimated from projected relative size. The effect of vegetation management treatments on projected quadratic mean diameters in the Siskiyou study was expressed as an interaction between proportion of cover removed by treatments (intensity) and dominant height of Douglas-fir at time of treatment relative to current dominant height. In 1- and 2-year projection periods, the stand table projection system performed similarly to a diameter distribution prediction system based on a Weibull distribution function. However, the difference between projected and predicted diameter distributions became more pronounced as the projection period increased to 5 years.

Crown class, site class, and breast-height age were incorporated into Kozak's variable-exponent taper equation (A. Kozak. 1988. Can. J. For. Res. 18: 1363–1368) for three species: Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco), western red cedar (Thujaplicata Donn), and aspen (Populustremuloides Michx.). For lodgepole pine (Pinuscontorta Dougl.), crown ratio, breast-height age, and quadratic mean diameter were incorporated into Kozak's taper equation. The effects of adding these variables to the exponent part of the taper equation on the prediction abilities of the taper model were assessed for prediction of diameter inside bark along the stem, total tree volume, and tree merchantable height. It was found that apart from the use of crown ratio for lodgepole pine, the additional variables resulted in only marginal improvements to the published version of Kozak's taper function. Therefore, the cost of measuring these additional variables is not justifiable.

A stand density management diagram for managed black spruce (Picea mariana (Mill.) B.S.P.) stands was developed using data derived from 37 variable-size temporary and permanent sample plots, and 257 open-grown sample trees. The plots were situated within 15 plantations and 4 precommercially thinned stands located throughout central and western Newfoundland, north-western New Brunswick and northern Ontario. The basic components of the diagram included: (1) an approximate crown closure line (2) the self-thinning rule (3) expected size-density trajectories and (4) isolines for dominant height, relative density index, quadratic mean diameter and merchantability ratio. The utility of the diagram was demonstrated by deriving yields for various initial spacings by site class and subsequently evaluating various outcomes in terms of operability criteria. In addition, the potential of estimating the time of crown closure by initial spacing and site class is discussed in relation to minimizing the adverse effects of Kalmia angustifolia (L.) on black spruce growth and development. Key words: stand density management diagram, initial spacing, black spruce, operability, Kalmia angustifolia (L.)

In Washington State, USA, mountain goats (Oreamnos americanus) have experienced a long-term population decline. To assist management, we created annual and seasonal (summer and winter) habitat models based on 2 years of data collected from 38 GPS-collared (GPS plus collar v6, Vectronic-Aerospace GmbH, Berlin, Germany) mountain goats in the western Cascades. To address GPS bias of position acquisition, we evaluated habitat and physiographic effects on GPS collar performance at 543 sites in the Cascades. In the western Cascades, total vegetation cover and the quadratic mean diameter of trees were shown to effect GPS performance. In the eastern Cascades, aspect and total vegetation cover were found to influence GPS performance. To evaluate the influence of bias correction on the analysis of habitat selection, we created resource selection functions with and without bias correction for mountain goats in the western Cascades. We examined how well the resultant habitat models performed with reserved data (25% of fixes from 38 study animals) and with data from 9 other GPS-collared mountain goats that were both temporally and spatially independent. The statistical properties of our GPS bias correction model were similar to those previously reported explaining between 20 and 30% of the variation, however, application of bias correction improved the accuracy of the mountain goat habitat model by only 1–2% on average and did not alter parameter estimates in a meaningful, or consistent manner. Despite statistical limitations, our habitat models, most notably during the winter, provided the widest extent and most detailed models of the distribution of mountain goat habitat in the Cascades yet developed.

Este trabajo resume la respuesta de Pachira quinata (Jacq.) W.S. Alverson, a tres intensidades de aclareo, hasta 25 años de edad, en Nicoya, Guanacaste, Costa Rica, con 19 años de registros. Se aplicó la metodología de parcelas permanentes de aclareo y rendimiento, bajo un diseño de bloques completos, con cuatro tratamientos y cuatro repeticiones. Los tratamientos se fijaron dejando un área basal remanente de 14, 17 y 20 m²/ha (aclareos fuerte, moderado y leve, respectivamente) y un tratamiento testigo. Se realizaron cuatro aclareos a las edades de 5, 7, 10 y 13 años. Los aclareos fuertes y moderados favorecieron los crecimientos en diámetro y en área basal, en contraste con los aclareos leves y las parcelas testigo (raleadas a los 13 años). Con los primeros se obtuvo un diámetro medio cuadrático (dg) seis centímetros mayor que con el testigo y los aclareos leves. El área basal máxima que limitó el crecimiento en altura se observó en las parcelas testigo entre los años 10 y 13, cuando estas alcanzaron 34 m2/ha. El área basal que limitó el crecimiento diamétrico se presentó cuando la plantación alcanzó un área basal de 24 m2/ha. Después del segundo aclareo se detectó una mayor diferenciación entre los tratamientos con respecto al crecimiento en diámetro y área basal. Los mayores incrementos se presentaron entre los 5 y los 7 años de edad. Se recomienda realizar tres aclareos a las edades de 7, 12 y 16 años, manteniendo el área basal entre 14 y 17 m2/ha. This paper presents the response of Pachira quinata (Jacq.) W.S. Alverson, to three thinning regimes, until 25 years of age, in Nicoya, Guanacaste, Costa Rica, for a period of 19 years. The methodology of permanent plots of thinning and yield was applied, with a complete block design with four treatments and four replications. The treatments were set, leaving a residual basal area of 14, 17 and 20 m²/ha, (as strong, moderate and light thinning, respectively) plus a control treatment. A total of four thinnings were carried out at the ages of 5, 7, 10 and 13. The strong and moderate thinnings helped the growth in diameter and basal area of P. quinata, in contrast to light thinning and the control plots (thinned at 13 years of age). With the first oneswe obtained a mean diameter (dg) six centimeters greater than with the control and light thinnings. The maximum basal area that limited the growth in height, was measured between years 10 and 13, in control plots, when these reached 34 m2/ha. The basal area that limited the growth in diameter occurred in the plantation when it reached 24 m2/ha in basal area. After the second thinning, a clear differentiation between treatments, in relation to diameter and basal area growth was observed.The largest increments occurredin the early years of planting, between 5 and 7 years. We recommend three thinnings, at ages 7, 12 and 16 years, maintaining the basal area between 14 and 17 m2/ha. 131-146 echaves@una.ac.cr fmora@una.ac.cr semestral

This contribution presents an approach to model individual tree height–diameter relationships for Scots pine (Pinus sylvestris) in multi-size and mixed-species stands in Estonia using the Estonian Permanent Forest Research Plot Network. The dataset includes 22,347 trees. The main focus of the study was to use an approach that is spatially explicit allowing for high accuracy prediction from a minimum set of predictor variables that can be easily derived. Consequently, the height–diameter relationship is modeled as a function of only the stand quadratic mean diameter (dg) and the plot geographical coordinates. A specific generalized additive model gam is employed that allows for the integration of a varying coefficient term and 2-dimensional surface estimators representing a spatial trend and a spatially varying coefficient term. The high flexibility of the model is needed due to the very few predictor variables that subsume a variety of potential influential factors. Subsequently, a linear mixed model is used that quantifies the random variation between plots and between measurement occasions within plots, respectively. Hence, our model is based on the theory of structured additive regression models (Fahrmeir et al. 2007) and separates a structured (correlated) spatial effect from an unstructured (uncorrelated) spatial effect. Additionally, the linear mixed model allows for calibration of the model using height measurements as pre-information. Model bias is small, despite the somewhat irregular distribution of experimental areas within the country. The overall model shows some similarity with earlier applications in Finland. However, there are important differences involving the model form, the predictors and the method of parameter estimation. peerReviewed

A stand density management diagram for black spruce (Picea mariana (Mill.) B.S.P.) was developed using data derived from 49 0.081-ha permanent sample plots and 257 open-grown sample trees located throughout central insular Newfoundland. The diagram illustrated the reciprocal equation of the competition-density effect, self-thinning rule, approximate crown closure line, zone of imminent competition-mortality, and isolines for relative density, quadratic mean diameter and merchantability ratio. Mean prediction error for natural stand trajectories over a 30-projection period were 2.5 dm3 for mean volume, 306 stems/ha for density, 16.1 m3/ha for merchantable volume, 14.3 m3/ha for total volume, and 1.9 m2/ha for basal area. Implementation procedures using a combination of monoareal and polyareal sampling methods were described and the potential application of the diagram for evaluating thinning alternatives was demonstrated. Limitations of the diagram and future research directions were identified. Key words: stand density management diagram, black spruce, natural stands, central Newfoundland

In this paper, a two stage ingrowth model is presented for predicting periodic, 10 years ingrowth for pyrenean oak (Quercus pyrenaica Willd.) grown in medium to fully stocked coppice stands in north-western Spain. Data from the Spanish National Forest Inventory was used to develop the model, extracting the information from two inventories taken in 222 permanent plots. The first stage of the model predicts the probability of ingrowth occurrence, and in the second stage, the number of recruits is predicted using a conditional model. Both models were biologically realistic and presented logical behaviour. The ingrowth occurrence probability model was dependent on quadratic mean diameter and average height. The recruitment quantification model included stand density and average diameter as explanatory variables. Although the occurrence probability of ingrowth was predicted correctly in 71.7% of cases, the predictions of the number of recruitment are poorer, yielding a coefficient of determination of 0.358. The evaluation criteria included qualitative and quantitative examinations and a testing with independent data from another region. The proposed ingrowth model is the first to be developed for mediterranean oak species in Spain and is an essential feature in any stand growth system. © 2010 Springer-Verlag.

The probability of survival for an individual tree was modeled. A variable screening algorithm, screen, was used to find the best set of predictor variables. Stepwise procedures in SAS and BMDP were also used, and results were compared with those obtained from the SCREEN algorithm. The logistic model, with independent variables that were found to be significant through the SCREEN algorithm, was fitted to the data. The fitted models were validated by splitting the data and applying equations fitted to the estimation set to the data in the testing set. Two methods of data splitting were applied: (i) according to time period and (ii) at random. Validation statistics were similar for both cases. The final distance-dependent logistic model for the unthinned plots included the following independent variables: crown ratio (CR), total height/average height of dominant and codominant trees (HH), and competition index (CI). The logistic model with CR, HH, and quadratic mean diameter/DBH (DD) was used as the distance-independent model of survival for the unthinned plots. The final distance-dependent logistic model for the thinned plots included as predictor variables HH, CI, and CR1.5. For the thinned plots the final distance-independent model used DD, CI, and CR1.5 as independent variables. The logistic models of survival obtained in this study were compared with survival models developed previously for distance-dependent and distance-independent stand simulators. Only slight improvement is shown by the logistic models.

A parameter recovery procedure for the Weibull distribution function, based on diameter percentiles, was modified to incorporate the effects of interfering vegetation in young Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco var. menziesii) plantations. The applicability of the system was tested by using data from sites in the Coast Ranges of Oregon and Washington and in the Siskiyou Mountains of southwestern Oregon. Four percentiles (0, 25th, 50th, 95th) of the cumulative probability distribution were predicted as functions of quadratic mean diameter and age. In the Siskiyou study, cover and total vegetation control affected quadratic mean diameter and all four percentiles; intensity of the vegetation treatments affected the 0 and 25th percentiles, and the interaction between intensity and timing of treatment affected quadratic mean diameter. In the Coast Ranges study, only quadratic mean diameter was affected by cover of woody vegetation, while quadratic mean diameter and the 25th percentile were significantly affected by total vegetation control. The predicted distributions showed decreasing variance with increasing cover, particularly in the Siskiyou Mountains. In the Coast Ranges study, the coefficient of variation increased with increasing cover, indicating that the variance of stem diameters was affected by average size. On xeric sites in the Siskiyou Mountains, high diameter variability in plots with total vegetation control suggests that interspecific competition may inhibit the expression of microsite variation.

Quadratic mean diameter is the measure of average tree diameter conventionally used in forestry, rather than arithmetic mean diameter. The historical and practical reasons for this convention are reviewed. West. J. Appl. For. 15(3):137-139.

A static stand density management diagram was constructed for Douglas fir (Pseudotsuga menziesii [Mirb.] Franco) plantations in Spain on the basis of 3 equations that were fitted simultaneously by the full information maximum likelihood procedure to data derived from 172 plots measured across the Cantabrian and pre-Pyrenean ranges. The first equation relates quadratic mean diameter to the number of stems per hectare and dominant height. The other 2 equations relate stand volume and stand aboveground biomass to quadratic mean diameter, number of stems per hectare, and dominant height. An estimation of the average slenderness coefficient for the 250 largest trees per hectare and the canopy bulk density were included. The stand density management diagram outlined here enables rapid, straightforward comparisons among different thinning schedules for forest plantations in mountain regions, in which timber production, risk of crown fire, and the risk of damage from wind or snow are considered. Funding for this research was provided by the Spanish Ministry of Science and Technology through project 1FD97-0585-C03-03 SI

A nonlinear mixed-effects modelling approach was used to model the individual tree height-diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height-diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height-diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis-Jones test. Height-diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model. © 2008 Elsevier B.V. All rights reserved.

The effect of different thinning intensities on growth and yield was studied in Pinus sylvestris L. stands at the south-western limit of its distribution area (Central Spain), using five long-term thinning trials. Data were analysed collectively considering several factors (trial, block, plot and period) as random effects. Total volume and volume increment decreased with thinning intensity, this loss being more significant in the case of moderate and heavy thinning. No difference was found among treatments for total basal area or the increment in basal area. The results revealed an optimum basal area (Assmann's definition) between 85 and 100% of the basal area in unthinned plots. Volume growth loss associated with heavy thinnings (reduction of 18% in volume increment) was smaller than that reported in Central and Northern European regions (greater than 25%). Height increment was not influenced by thinning, whereas dominant and quadratic mean diameter increments increased with the thinning intensity. The response of diameter growth to thinning was greater at younger ages (less than 50 y) and in medium-sized trees. © 2008 INRA EDP Sciences.

Cavity trees contribute to diverse forest structure and wildlife habitat. For a given stand, the size and density of cavity trees indicate its diversity, complexity, and suitability for wildlife habitat. Size and density of cavity trees vary with stand age, density, and structure. Using Forest Inventory and Analysis (FIA) data collected in western Oregon and western Washington, we applied correlation analysis and graphical approaches to examine relationships between cavity tree abundance and stand characteristics. Cavity tree abundance was negatively correlated with site index and percent composition of conifers, but positively correlated with stand density, quadratic mean diameter, and percent composition of hardwoods. Using FIA data, we examined the performance of Most Similar Neighbor (MSN), k nearest neighbor, and weighted MSN imputation with three variable transformations (regular, square root, and logarithmic) and Classification and Regression Tree with MSN imputation to estimate cavity tree abundance from stand attributes. There was a large reduction in mean root mean square error from 20% to 50% reference sets, but very little reduction in using the 80% reference sets, corresponding to the decreases in mean distances. The MSN imputation using square root transformation provided better estimates of cavity tree abundance for western Oregon and western Washington forests. We found that cavity trees were only 0.25 percent of live trees and 13.8 percent of dead trees in the forests of western Oregon and western Washington, thus rarer and more difficult to predict than many other forest attributes. Potential applications of MSN imputation include selecting and modeling wildlife habitat to support forest planning efforts, regional inventories, and evaluation of different management scenarios.

A yield model for irrigated, high-density plantations of Acacia nilotica in Pakistan was constructed from data collected on 65 temporary plots, distributed across the existing range in age and stand density. Plantation development is simulated by projecting changes in quadratic mean diameter and number of stems ha−1. Stands are assumed to asymptotically approach an empirical size/density limit by a self-thinning process. Rates of self-thinning and change in mean diameter are controlled by rate of height growth. Parameters of the Weibull probability density function are recovered from whole-stand attributes to facilitate estimation of diameter distributions. Model output includes the biomass of four tree fractions, defined by diameter outside bark (Dob): fodder (leaves and succulent twigs), fine woody material (

Based on data from an experience in a Pinus taeda plantation, including ages between 4 and 7 years old, multiple linear regressions were adjusted to obtain stand yield functions including regression variables associated with prunes intensity and opportunity, besides age, stand density and site index. The response variables analyzed were quadratic mean diameter, basal area and volume per hectare. The results show that it was possible to improve the prediction quality and accuracy of models of basal area when prune variables are considered, with respect to equations without these variables and with statistical significance. Improvements of 9.19% of the standard residual error and 8.99% of the statistics indicator employed to compare the prediction capacity were obtained. The utilization of some of those functions like sub-models inside equations of quadratic mean diameter and volume by hectare, simple and with good statistics, gives results that are sensitive to prune. These functions could be employed in spreadsheets to decide when and how many green branches to prune in relation to the production objective. The obtained models appear interesting for developing new local growth simulation programs of Pinus taeda that include prunes applied in intensive silvicultural systems of forest production., Con datos de un ensayo de Pinus taeda, con edades entre 4 y 7 años, se ajustaron a través de regresión lineal múltiple, modelos de producción estáticos de rodal completo, incluyendo variables regresoras asociadas con la intensidad y oportunidad de podas, además de la edad, la densidad y el índice de sitio. Las variables respuestas analizadas fueron el diámetro medio cuadrático, el área basal y el volumen por hectárea. Respecto del área basal fue posible obtener modelos sensibles a las podas realizadas, de mejor calidad de ajuste y de capacidad de predicción que ecuaciones sin variables vinculadas con las podas, que tuvieron excelentes comportamientos estadísticos. Se lograron mejoras de hasta 9,19% de error estándar residual y de 8,99% del estadístico usado para comparar la capacidad de predicción. La utilización de algunas de esas funciones como submodelos dentro de ecuaciones predictivas de diámetro medio cuadrático y volumen por hectárea, relativamente sencillos y con confiabilidad estadística, produjo resultados sensibles a las podas realizadas. Las funciones obtenidas pueden ser usadas como herramientas de cálculo para decidir cuánto y cuándo podar ramas fotosintéticamente activas de acuerdo a los objetivos de producción. Estos modelos son promisorios para el desarrollo de nuevos programas locales de simulación de crecimiento y producción regionales de P. taeda que contemplen a las podas realizadas en los sistemas de producción intensivos.

A logistic model for determining the probability of survival in the next 5-year period of two of the main species in the Mediterranean area in Spain, Mediterranean maritime pine (Pinus pinaster Ait.) and Scots pine (Pinus sylvestris L.), is presented. Data were supplied by the Forest Research Centre of the National Institute of Agricultural and Food Research (INIA) of Spain, consisting of a Permanent Sample Plot network (PSP) covering different stand conditions. In this study, 84 plots for Mediterranean maritime pine and 74 plots for Scots pine were used. Several models were tested. Variables concerning tree size, competition and social position of the tree were introduced in stepwise selection. The ratio diameter at breast height versus quadratic mean diameter and the interaction basal area-site index resulted as the most significant variables in the case of Mediterranean maritime pine. For Scots pine, the most significant variables were site index, DBH-1 and the interaction between basal area of larger trees and the coefficient of variation of the DBH distribution as a surrogate of structure. Results indicate that competition, tree size and social position within the stand are present in the survival process of both species. One-sided competition in highly structured stands for Scots pine and two-sided competition for Mediterranean maritime pine, are shown to be also important. Model evaluation has been done with data from the PSP not used in the fitting process. The area under the Receiver Operating Characteristic curve is 0.86 for Mediterranean maritime pine and 0.85 for Scots pine. The overall predicted rates of survival and mortality are shown for different cut-off points, indicating that the use of random uniform numbers yields better results. Afterwards, the performance of the model in thinned stands is tested for both species. Results for Mediterranean maritime pine show that it is appropriate to use the same model both for unthinned and thinned stands. However, a new model should be fitted for thinned Scots pine stands. © 2005 Elsevier B.V. All rights reserved.

Upland oak-hickory forests in Arkansas, Missouri, and Oklahoma experienced oak decline in the late 1990s and early 2000s during an unprecedented outbreak of a native beetle, the red oak borer (ROB), Enaphalodes rufulus (Haldeman). Although remote sensing supports fre- quent monitoring of continuously changing forests, comparable in situ observations are critical for developing an understanding of past and potential ROB damage in the Ozark Mountains. We categorized forest change using a normalized difference water index (NDWI) applied to multi- temporal Landsat TM and ETM+ imagery (1990, 2001, and 2006). Levels of decline or growth were categorized using simple statistical thresholds of change in the NDWI over time. Corre- sponding decline and growth areas were then observed in situ where tree diameter, age, crown condition, and species composition were measured withinvariable radius plots. Using a machine learning decision tree classifier, remote sensing-derived decline and growth was characterized in terms of in situ observation. Plots with tree quadratic mean diameter at breast height ≥21.5 cm were categorized remotely as in severe decline. Landsat TM/ETM+-based NDWI derivatives reveal forest decline and regrowth in post-ROB outbreak surveys. Historical and future Landsat-based canopy change detection should be incorporated with existing landscape-based prediction of ROB hazard. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10

A dimensionally compatible system of equations for stand basal area, volume, and basal area and volume growth was derived using dimensional analysis. These equations are analytically and numerically consistent with dimensionally compatible individual tree volume and taper equations and share parameters with them. Parameters for the system can be estimated by fitting individual tree taper and volume equations or by fitting stand level basal area and volume equations. In either case the parameters are nearly identical. Therefore, parameters for the system can be estimated at the tree or stand level without changing the results. Data from a thinning study in loblolly pine (Pinus taeda L.) plantations established on cutover site-prepared lands were used to estimate the parameters. However, the developed system of equations is general and can be applied to other tree species in other locales. Ph. D.

Growth and yield of a direct-seeded eastern white pine (finus sfrobus L.) plantation established in 1959 on a broad undulating sandstone upland (Landtype 1) are summarized. Average heights of dominant and codominant pines were 35,56, 65, and 76 ft at ages 15,25, 30, and 34 years, respectively. Equivalent site indices (base age 25 years from seed) were 56,56,58, and 63 at those respective ages. At age 34, there were 418 pines per acre, which represents a survival rate of 25 percent based on a stocking of 1,650 stems at age 4. Other stand parameters at age 34 were quadratic mean diameter, 8.3 inches; basal area, 157 ft2/acre; and merchantable yield (outside bark to a 3.0-inch top o.b., all trees 23.6 inches in d.b.h.), 5,229 ft3/acre. Also 319 pines per acre were 23.6 inches in d.b.h., and 127 pines were 29.6 inches in d.b.h.. Hardwoods (20.6 inches in d.b.h.) numbered 254 and accounted for an additional 37 ft2 of basal area. Dominant and codominant yellow-poplars (Liriodendron tulipifera L.), black cherries (Prunus serotina Ehrh.), and chestnut oaks (Quercus prinus L.) comprised 25 ft2 of the hardwood basal area. Cubic yield of this direct-seeded white pine plantation on the Mid-Cumberland Plateau has been less than the average yield of planted plantations in the Southern Appalachians, and this study plantation has not grown as well as a nearby planted plantation. But site index is apparently at least 8 ft taller than the estimate for Landtype 1 in the regional forest site classification guide.

Aim of study: The aim of this work was to model diameter distributions of Quercus suber stands. The ultimate goal was to construct models enabling the development of more affordable forest inventory methods. This is the first study of this type on cork oak forests in the area.Area of study: The area of study is “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain).Material and methods: The diameter distributions of 100 permanent plots were modelled with the two-parameter Weibull function. Distribution parameters were fitted with the non-linear regression, maximum likelihood, moment and percentile-based methods. Goodness of fit with the different methods was compared in terms of number of plots rejected by the Kolmogorov-Smirnov test, bias, mean square error and mean absolute error. The scale and shape parameters in the Weibull function were related to the stand variables by using the parameter prediction model.Main results: The best fitting was obtained with the non-linear regression approach, using as initial values those obtained by maximum likelihood method, the percentage of rejections by the Kolmogorov-Smirnov test was 2% of the total number of cases. The scale parameter (b) was successfully modelled in terms of the quadratic mean diameter under cork (R2 adj = 0.99). The shape parameter (c) was modelled by using maximum diameter, minimum diameter and plot elevation (R2 adj = 0.40).Research highlights: The proposed model diameter distribution can be a highly useful tool for the inventorying and management of cork oak forests.Key words: maximum likelihood method; moment method; non linear regression approach; parameter prediction model; percentile method; scale parameter; shape parameter.

International audience; The Reineke Stand density rule relating stem numbers to the quadratic mean diameter is generally used as a reference for modelling maximal stand density.* The linearity of this relationship after double logarithmic transformation is generally assumed, but it must be questioned for untouched stands and stands with a conventional thinning regime. Curvilinearity is demonstrated for some spruce and beech stands in Switzerland and shown to be statistically representative. This relationship is independent of the site index. It can be interpreted as a change in mortality in young stages mainly due to competition and in older stages more to ageing. * A more accurate estimation of the maximal stand density needs to take into account the important variation around the mean course, known as the yield level. A simple method to assess the yield level of any stand regardless of whether it is thinned or not is presented, based on estimating the effect of a stand opening on the basal area.; La loi de Reineke reliant le nombre de tiges au diamètre quadratique moyen est généralement utilisée comme référence pour la modélisation de la densité maximale de peuplements.* On remet en question la linéarité d'une telle relation dans l'espace logarithmique, dans le cas des peuplements non traités aussi bien que pour ceux traités par des interventions conventionnelles. La curvilinéarité de cette relation est démontrée pour quelques peuplements purs d'épicéa et de hêtre en Suisse et dans sa représentativité statistique. La relation est indépendante de l'indice de fertilité et interprétée comme modification du type de mortalité au cours du développement, due pendant le jeune âge à la seule compétition, puis s'y ajoute celle due au vieillissement.* Une estimation appropriée de la densité maximale des peuplements doit tenir compte des variations importantes autour de la courbe moyenne connue comme niveau de production. Une méthode simple de détermination du niveau de production dans tous les cas de traitement antérieur est présentée, fondée sur une estimation de l'effet de l'ouverture du couvert sur la surface terrière.

Mechanically masticated fuelbeds are distinct from natural or logging slash fuelbeds, with different particle size distributions, bulk density, and particle shapes, leading to challenges in predicting fire behavior and effects. Our study quantified some physical properties of fuel particles (e.g. squared quadratic mean diameter, proportion of non-cylindrical particles) and surface fuel loading with planar intercept and plot-based methods in 10 mechanically masticated sites in northern California and south-western Oregon. Total woody fuel load differed among masticated sites, ranging from 15.3 to 63.4 Mg ha–1, with the majority of the load concentrated in the 10-h (53.7%) and 1-h (29.2%) time-lag classes. Masticated fuels were densely packed, with total depths ranging from 4.6 to 8.0 cm and fuelbed bulk densities ranging from 45.9 to 115.3 kg m–3. To accurately quantify loading in masticated fuelbeds, we recommend using a hybrid methodology, where 1-h and 10-h fuel loadings are estimated using a plot-based method and 100-h and 1000-h fuel loadings are estimated using the standard planar intercept method. Most masticated fuelbeds differed in loading by fuel class and fuelbed depth, when compared with existing natural and slash-based fuelbeds, suggesting new fire behavior fuel models specific to masticated fuelbeds may be warranted.

Producción Científica, Stand Density Management Diagrams are useful tools for designing, displaying and evaluating alternative density management regimes in even-aged stands, with which to achieve a desired future stand condition. The stands studied, of Pinus halepensis and Pinus pinaster, have low productivity, and managers need easy, efficient tools to obtain the best yield. These diagrams help the managers of these stands determine thinning prescriptions. The relationship between stand density, dominant height, quadratic mean diameter and stand volume is represented in just one graph. Two equations were fitted simultaneously: one that relates quadratic mean diameter with stand density and dominant height, and another that relates total stand volume with quadratic mean diameter, stand density and dominant height., Los Diagramas de Manejo de Densidad de Masa son útiles herramientas para el diseño, desarrollo y evaluación de regímenes de densidad alternativos en masas regulares, para alcanzar unas condiciones de masa deseadas. Las masas estudiadas, de Pinus halepensis y Pinus pinaster tienen una baja productividad, y los gestores necesitan herramientas fáciles de usar y eficientes para obtener la mayor rentabilidad. Estos diagramas ayudan a los gestores de estas masas en la toma de decisiones selvícolas. La relación entre la densidad de masa, la altura dominante, el diámetro medio cuadrático y el volumen total se la masa se representa en sólo un gráfico. Se ajustaron dos ecuaciones simultáneamente: una que relaciona el diámetro medio cuadrático con la densidad de la masa y la altura dominante, y otra que relaciona el volumen total de la masa con el diámetro medio cuadrático, densidad de la masa y altura dominante., Ministerio de Educación y Ciencia (Project AGL2007-65795-C02-01), Ministerio de Educación y Ciencia (Project AGL2007-65795-C01-01)

The diameter distributions of 125 permanent plots installed in birch dominated (Betula alba L.) stands in Galicia were modelled with the two-parameter Weibull distribution. Four different fitting methods were used: that based on percentiles of the distribution, non linear regression, maximum likelihood and the method of moments. The most accurate fit was obtained with the non linear regression (NLR) approach, considering the following statistics in the comparison: bias, mean absolute error (MAE), mean square error (MSE) and number of plots rejected by the Kolmogoroff-Smirnoff (KS) test. The scale parameter (b) and the shape parameter (c) obtained with the most accurate method (non linear regression), were first modelled with simple linear models and then related to commonly measured prediction variables (quadratic mean diameter, dominant height and stand density) with the parameter prediction model (PPM). The parameters fitted with the method of moments were recovered with the parameter recovery model (PRM) from the first and the second moments of the distribution (mean diameter and variance, respectively). Results indicated that both methods were successful in predicting the diameter frequency distributions. The PRM was more accurate than the PPM method. Las distribuciones diamétricas de 125 parcelas permanentes instaladas en masas puras de abedul (Betula alba L.) en Galicia fueron modelizadas con la distribución Weibull de dos parámetros. Se emplearon cuatro métodos de ajuste: basados en percentiles de la distribución, regresión no lineal, máxima verosimilitud y el método de los momentos. Los ajustes más precisos fueron obtenidos con regresión no lineal, considerando los siguientes estadísticos en la comparación de los resultados: sesgo, error medio absoluto, error medio cuadrático y número de parcelas rechazadas por el test de Kolmogoroff-Smirnoff. El parámetro de escala (b) y el parámetro de forma (c) obtenidos con el método más preciso (regresión no lineal), fueron relacionados con variables de masa de frecuente medición (diámetro medio cuadrático, altura dominante y densidad) mediante modelos lineales sencillos aplicando la metodología de predicción de parámetros. Los parámetros ajustados con el método de los momentos fueron recuperados con modelos de recuperación de parámetros a partir del primer y del segundo momento de la distribución (diámetro medio y varianza, respectivamente). Los resultados indicaron que ambos métodos fueron satisfactorios para predecir las distribuciones de frecuencias de diámetros. El método de recuperación de parámetros fue más preciso que el método de predicción de parámetros.

A generalized height-diameter equation, along with a crown diameter prediction equation for cork oak forests in Spain were developed based on data from the Second Spanish Forest Inventory. Nine generalised height-diameter equations were selected as candidate functions to model the height-diameter under cork relationship, while for the crown diameter prediction model five linear and non-linear equations were tested. The equations were fitted using the mixedeffects model approach. The Stoffels & Van Soest power equation, constrained to pass through the point of dominant diameter and dominant height, was selected as the generalised height-diameter model. Regarding the crown diameter prediction model, the parable function without the intercept and with quadratic mean diameter incorporated as a fixed effect into the b parameter, proved to be the model with best prediction capabilities. The models were validated by characterising the model error using the PRESS (Prediction Sum of Squares) statistic. Both equations will be submodels of the ALCORNOQUE v1.0, a management oriented growth and yield model for cork oak forests in Spain.

A study of the physical properties of Sierra Nevada conifer fuel particles showed that average diameter, squared quadratic mean diameter, surface-area-to-volume ratio, and specific gravity varied significantly by species for all four timelag fuel diameter size classes. The nonhorizontal angle was not significantly affected by size class, and the developmental stage of the overstory did not affect any of the properties. These values are used to calculate fuel weight and predict fire behavior. Regional variation in physical properties can result in fuel weight estimates for the Sierra Nevada that differ from under 40.8 percent to over 8.3 percent from those calculated from Rocky Mountain values. These differences made small changes in predicted fire behavior.

1. A system of equations was developed to describe the reciprocal effects of stand density and quadratic mean diameter through time, by use of data from a loblolly pine (Pinus taeda) plantation. 2. These equations were based on the self-thinning rule, which regulates an overcrowded population by imposing a maximum mean tree size for a given stand density. 3. The system explained 98% of the variations in surviving tree number and quadratic mean diameter, and should provide reasonable extrapolation.

A diagram is presented that can greatly facilitate density management of lodgepole pine (Pinus contorta) stands. Together with site index tab!es or curves, the diagram can be used to estimate average tree sizes and total yields produced under various density management regimes. Its use is illustrated with three alternative regimes. " West. J. Appl. For. 1:6-11,.Jan. 1986 The control of growing stock to achieve specific management objectives is critical to effective forest management. The actual manipulation of stand density is relatively easy, but arriving at levels of growing stock consistent with particular management objectives and constraints is much more difficult (Davis 1966). In this paper we present a density management diagram for lodgepole pine, then we compare the diagram with a computer growth and yield model, and finally we illustrate use of the diagram with three alternative regimes. Ultimately, the control of growing stock requires a biologically meaningful and easily applied index of stand density. The best measures of stand density are those that incorporate both the number and average size of individuals in a population (Curtis 1970, Curtis 1982, Daniel et al. 1979, West 1982). A familiar and easily applied example is Reineke's (1933) stand density index (SDI), which expresses the relation between the number of trees per acre (TPA) and their quadratic mean diameter (Dq): SD! = TPA (Dq/10) •.6 A major advantage of this and other size-density indexes is its independence of site quality and stand age (Curtis 1982, Daniel et al. 1979, Long 1985). Various graphical aides have been developed for use in density management using indexes based on sizedensity relationships. Wilson's (1979) 1 The help of Hank Cheatham, Bob Cottingham, and Reese Pope is gratefully acknowledged. This is Journal Paper No. 2959 of the Utah Agricultural Experiment Station "Stand Density Sheets" allow stocking to be controlled, using an index of stand density based on TPA and average height. Stocking guides of the type first developed by Gingrich (1967) are commonly based on Crown Competition Factor (CCF), another size-density index; the relationships represented by their various stocking lines are easily understood and reproduced using SDI (Daniel et al. 1979). The utility of these basic graphical aides can be greatly enhanced with inclusion of additional size parameters. Ando (1968) developed what he referred to as "stand density control diagrams" for most of the important commercial timber species in Japan. Similar diagrams have been produced for coastal Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) (Drew and Fiewelling 1979) and loblolly pine (Pinus taeda L.) (Fiewelling 1981). An obstacle in the construction of density management diagrams is the scarcity of appropriate data with which to build them. Previously, diagrams have been built using data from research growth plots, but for many species and locales in the Rocky Mountains such data are limited. We examined the feasibility of constructing a diagram with common timber inventory data for lodgepole pine. CONSTRUCTION OF THE LODGEPOLE PINE DENSITY MANAGEMENT DIAGRAM USDA Forest Service Stage II inventory data were compiled for 519 lodgepole pine stands from the Targhee, Salmon, and Medicine Bow National Forests, located in Idaho, Wyoming, and Colorado (Table 1). The only constraint in selecting stands for inclusion in the data set was that lodgepole pine represent at least 80% of the total basal area of eachostand. The Targhee and Medicine Bow data were used to fit the regression equations used to construct the diagram; the Salmon data were then used to validate these quations. Data from each of the stands •nduded estimates of total stand volume (ftS/ac to 4-in top), density (TPA), basal area (ft2/ac) as well as average he•oht (Ht•), and age of site trees (open grown or dominant). Using these variables we calculated Dq, $DI, and mean tree volume (MVOL). A nonlinear least-squares curve-fitting routine was used to develop regression models relating TPA, Dq, Ht•, and MVOL. The first equation, relating MVOœ and TPA to Dq, has a coefficient of determination (R 2) of 87% and a standard error of 0.7 in. Dq = (54.4 MVOL + 5.14) o.36• (1.0 0.00759 TPA) o.•46 The second equation, relating Ht• and Dq to MVOL, has a coefficient of determination (R 2) of 94% and a standard error of 0.8 ft 3. MVOL = ((0.00396 + 0.000779 Dq 227) (1.27 Ht•l.o9)) o.916 Neither regression model was biased with respect to the independent vanables, site index, or stand age. The lodgepole pine density management diagram (Figure 1) has Dq and TPA on the two major axes. These were chosen because, of the variables included, they are the most commonly used and easiest to estimate in the field. The diameter axis ranges from 1-30 in, while the densities range from 50-5000 TPA. Both axes are plotted on a logarithmic scale. The parallel diagonal lines represent SDL The uppermost line corresponds to an SDI of 700, approximating the maximum SD! represented in the data set Table 1. Description oflodgepole pine data including maximum and minimum values. Number of Volume Basal rea Site height Site tree age stands (ft3/ac) TPA (ft2/ac) (ft) (yr) Medicine Bow N.F. 294

To reduce the cost and increase the efficiency of obtaining individual tree height information required for sample plot volume estimation, two general height–diameter (H/D) regression models were developed using two-stage regression analysis and data from 96 lodgepole pine (Pinuscontorta Dougl. var. latifolia Engelm.) sample plots. The derived models were examined using an independent data set of 28 plots. In addition to diameter at breast height (D), these models also included two easily measurable stand parameters as independent variables: quadratic mean diameter (Dq) and the height of a tree with diameter Dq (Hq). With a practical method to estimate Hq (from up to three heights measured) and using these two new H/D models in conjunction with available regional standard volume equations (V = f (D,H)), the stand volume estimates, on the average, were 0.003% higher (SD 4.1%) for the first model and 1.081% lower (SD 4.6%) for the second model than those obtained using traditional H/D curves for each plot based on 30 or more height measurements. The new models are therefore recommended for use in height estimation of lodgepole pine trees within the range of conditions of the data. This approach may be applied to other species and regions.

Key message Self-thinning lines are species- and climate-specific, and they should be used when assessing the capacity of different forest stands to increase biomass/carbon storage. Context The capacity of forests to store carbon can help to mitigate the effects of atmospheric CO2 rise and climate change. The self-thinning relationship (average size measure ∼ stand density) has been used to identify the potential capacity of biomass storage at a given density and to evaluate the effect of stand management on stored carbon. Here, a study that shows how the self-thinning line varies with species and climate is presented. Aims Our main objective is thus testing whether species identity and climate affect the self-thinning line and therefore the potential amount of carbon stored in living biomass. Methods The Ecological and Forest Inventory of Catalonia was used to calculate the self-thinning lines of four common coniferous species in Catalonia, NE Iberian Peninsula (Pinus halepensis, Pinus nigra, Pinus sylvestris and Pinus uncinata). Quadratic mean diameter at breast height was chosen as the average size measure. The self-thinning lines were used to predict the potential diameter at a given density and study the effect of environmental variability. Results Species-specific self-thinning lines were obtained. The self-thinning exponent was consistent with the predicted values of −3/2 and −4/3 for mass-based scaling for all species except P. sylvestris. Species identity and climatic variability within species affected self-thinning line parameters. Conclusion Self-thinning lines are species-specific and are affected by climatic conditions. These relationships can be used to refine predictions of the capacity of different forest stands to increase biomass/carbon storage.

Balanced diameter distributions are widely used to describe stand structure goals for residual growing stock in uneven-aged forests. The quadratic mean diameter is frequently used as a descriptor of a balanced diameter distribution. In this paper the quadratic mean diameter is shown to be independent of stand basal area for balanced diameter distributions with a common class width, maximum and minimum diameters, and de Liocourt's q ratio. Additionally it is shown that the quadratic mean diameter is relatively insensitive to changes in maximum tree size and q ratios for q ratios 1.5 and larger.

Dynamic landscape simulation of the forest requires an initial regeneration stock specific to the characteristics of each simulated stand. Forest inventories, however, are sparse with regard to regeneration. Moreover, statistical regeneration models are rare. We introduce an inventory-based statistical model type that (1) quantifies regeneration biomass as a fundamental regeneration attribute and (2) uses the overstory’s quadratic mean diameter (Dq) together with several other structure attributes and the Site Index as predictors. We form two such models from plots dominated by European beech (Fagus sylvatica L.), one from national forest inventory data and the other from spatially denser federal state forest inventory data. We evaluate the first one for capturing the predictors specific to the larger scale level and the latter one to infer the degree of landscape discretization above which the model bias becomes critical due to yet unquantified determinants of regeneration. The most relevant predictors were Dq, stand density, and maximum height (significance level p < 0.0001). If plot data sets for evaluation differed by the forest management unit in addition to the average diameter, the bias range among them increased from 0.1-fold of predicted biomass to 0.3-fold.

Appropriate management of stand density is necessary to avoid wasted growing space and overcrowding-induced self-thinning and therefore to optimize profitability. We developed a Gingrich-style stocking chart for Korean red pine (Pinus densiflora), Korean white pine (P. koraiensis), and Japanese larch (Larix kaempferi) in Korea. Datasets for even-aged stands were categorized into two censored datasets via relative density based on species-specific stand density indices to assign adequate plots for tree allometry. Censored plot data for maximum density on full stocking were used to develop A-level stocking based on mean individual tree area. In censored plot data for minimum density on full stocking, individual trees represented open-grown trees, and a crown competition factor of 100 was proposed as B-level stocking. Based on parameters estimated from allometry, stocking diagrams comprising quadratic mean diameter, number of trees, and basal area were correctly expressed. A-level stocking at the same quadratic mean diameter revealed that Korean white pine had the most trees and largest basal area, while Japanese larch had the fewest trees and smallest basal area. In contrast, B-level stocking disclosed that Japanese larch had the most trees and basal area, whereas Korean white pine had the fewest trees and smallest basal area. The stocking diagrams suggest that silvicultural treatments for these species should be species-specific.

A stand management density diagram (SDMD) is presented for balsam fir (Abies balsamea (L.) Mill.) forests in New Brunswick. The SDMD incorporates a maximum size density line, as well as quadratic mean diameter and top height isolines. Several mortality functions are evaluated. The resultant SDMD should be a useful tool for projecting early stand development and determining the timing and intensity of thinnings. Key words: Acadian Forest Region, mortality curves

This study deals with the subject biomass estimation. The objective was to achieve the additivity of tree biomass components, which is defined as the compatibility among the component predictions and total tree biomass, using ratio estimates. The biomass estimation model was applied to black wattle trees in forest stands, which include a sample of 670 trees in an age range of 1 to 10.75 years. The adjusted model, in which the total biomass, or sum of predicted components, is a function of the stem volume multiplied by the Scalar Coefficients Proxy of Density, proved to be of great interest for biomass estimation and consistent when compared to the results obtained by WNSUR estimates (traditional method). The natural additivity of the tree biomass components was fully achieved, when modeling them by means of ratio estimation. Equations developed from the proportional behavior of the biomass components at different ages did not require the use of linear regression models and were obtained from calibration with the experimental data. The estimators resulting from these equations proved to be appropriate to make a generic model for correction of ratios coefficients at different ages.

A measure of kind and level of thinning is developed and its relationship to other stand attributes such as number of trees, basal area, and volume removed in thinning is quantified. This measure or thinning index is based on the ratio of the quadratic mean diameter of thinned trees to the quadratic mean diameter of all trees before thinning. The thinning index is then logically incorporated into a thinning multiplier from which is derived a compatible basal-area growth projection model to generalize the previous concepts for thinning effects in systems for predicting growth and yield. Empirical tests with data from thinned and unthinned natural stands of loblolly pine, from thinned and unthinned slash pine plantations, and from thinned western larch stands show the model to provide estimates with improved properties. Hence, the thinning index and the thinning multiplier are also proposed for other situations involving effects of thinning.