RESUMO Previsões precisas do volume de madeira são críticas em florestas hiperdiversas, pois cada espécie tem características específicas de tamanho e forma. Embora modelos genéricos em nível multiespécie sejam amplamente utilizados em florestas manejadas na Amazônia, eles estão sujeitos a maiores vieses devido à variabilidade interespecífica. Usamos um extenso banco de dados de volume de madeira coletado em florestas manejadas para testar a hipótese de que modelos genéricos violam a suposição de independência, pois as previsões variam de acordo com o tamanho específico da espécie. Nossa hipótese foi comprovada pois os resíduos do modelo genérico foram condicionados à espécie e ao tamanho específico. Os modelos multiníveis foram mais precisos nos procedimentos de ajuste e de validação e contabilizaram a variância derivada de espécies e do tamanho específico, fornecendo previsões mais confiáveis. Descobrimos que os modelos específicos de tamanho têm capacidade preditiva semelhante aos específicos da espécie para novas previsões. Isto implica em estimativas mais práticas em florestas hiperdiversas, onde pode ser complexo o ajuste de modelos específicos por espécies. As conclusões são cruciais para o manejo florestal sustentável, pois permitem estimativas mais confiáveis do volume de madeira, conduzindo a menor incerteza financeira e evitando danos aos estoques florestais devido à sub ou superexploração. hiperdiversas forma Amazônia interespecífica independência sustentável superexploração

ABSTRACT Accurate wood volume predictions are critical in hyperdiverse forests because each species has specific size and shape traits. Although generic models at a multispecies level were widely used in Amazonian managed forests, they are subject to more significant bias due to interspecific variability. We used an extensive database of wood volume collected in managed forests to test the hypothesis that generic models violate the independence assumption due to that predictions vary with species-specific size. Our hypothesis was proved as residuals of the generic model were conditioned to species and specific size. The multilevel models were more accurate both in fitting and validation procedures, and accounted for variance derived from species and specific size, providing a more reliable prediction. However, we found that the size-specific models have a similar predictive ability to species-specific models for new predictions. This implies more practical estimates in hyperdiverse forests where fitting species-specific models can be complex. The findings are crucial for sustainable forest management as they allow for more reliable wood volume estimates, leading to less financial uncertainty and preventing damage to forest stocks through under or over-exploitation. traits variability speciesspecific procedures prediction However sizespecific complex overexploitation. overexploitation over exploitation. exploitation over-exploitation

RESUMO A modelagem da distribuição diamétrica em florestas naturais é uma ferramenta importante para compreender a dinâmica de espécies nativas lenhosas, auxiliando na tomada de decisão para o manejo e a recuperação de áreas degradadas. Dessa forma, o objetivo deste trabalho foi ajustar funções de densidade probabilística para avaliar a estrutura diamétrica de três espécies arbóreas de interesse econômico, como Campomansesia xanthocarpa Marl. Ex. O. Berg, Piptadenia gonoacantha (Mart.) J.F. Macbr. e Zeyheria tuberculosa (Vell.) Bureau ex Verl., em um fragmento de Floresta Estacional Semidecidual no estado de São Paulo, Brasil. Os dados foram provenientes de 83 parcelas temporárias de 10 m x 20 m distribuídas sistematicamente ao longo de 164 ha. As funções Log-normal, Gamma e Weibull foram ajustadas para as três espécies por meio do pacote fitdistrplus no programa R. O teste de aderência de Kolmogorov-Smirnov foi aplicado a 5% de probabilidade para avaliar os ajustes. As funções foram .selecionadas por meio do Critério de Informação Akaike (AIC) e do Critério de Informação Bayesiano de Schwaarz (BIC), além da análise gráfica das funções ajustadas. Os resultados indicaram que a estrutura diamétrica das três espécies é assimétrica positiva, as quais apresentam o padrão exponencial, sugerindo uma regeneração natural contínua. As estatísticas de AIC e BIC indicaram a função Log-normal para descrever a distribuição diamétrica de C. xanthocarpa e Z. tuberculosa, enquanto a função Gamma foi a mais adequada para P. gonoacantha. Para as três espécies, a análise gráfica mostrou que a função Gamma resultou no melhor ajuste, não apresentando tendências nas estimativas da densidade de frequências por classe de diâmetro. lenhosas degradadas forma econômico Marl Ex Berg Mart. Mart (Mart. JF J F J.F Macbr Vell. Vell (Vell. Verl Verl. Paulo Brasil 8 1 2 16 ha Lognormal, Lognormal Log normal, normal R KolmogorovSmirnov Kolmogorov Smirnov 5 ajustes selecionadas (AIC BIC, , (BIC) positiva exponencial contínua C Z P ajuste diâmetro (Mart (Vell (BIC

ABSTRACT Modeling diameter distribution in natural forests is an important tool for understanding the native woody species dynamics, supporting decision-making for degraded lands management and restoration. Therefore, this work aimed to fit probabilistic density functions to evaluate the diameter structure of three tree species with economic interest, such as Campomansesia xanthocarpa Marl. Ex. O. Berg, Piptadenia gonoacantha (Mart.) J.F. Macbr. and Zeyheria tuberculosa (Vell.) Bureau ex Verl., in a Semideciduous Seasonal Forest fragment at São Paulo State, Brazil. The data came from 83 temporary plots of 10 m x 20 m systematically distributed along 164 ha. Log-normal, Gamma, and Weibull functions were fitted to the three species using the fitdistrplus-package in the R program. Kolmogorov-Smirnov's adherence test was used to evaluate the fits at a 5% probability level. The functions were selected employing Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC), in addition to a graphical analysis of the fitted functions. The results indicated that the three species diameter structure is positively asymmetric, representing the exponential pattern, representing continuous natural regeneration. AIC and BIC statistics indicated the Log-normal function to describe the diameter distribution of C. xanthocarpa and Z. tuberculosa, while the Gamma function was the most appropriate for P. gonoacantha. For the three species, the graphical analysis showed the Gamma function results in the best fit without tendency for estimating frequency density per diameter class. dynamics decisionmaking decision making restoration Therefore interest Marl Ex O Berg Mart. Mart (Mart. JF J F J.F Macbr Vell. Vell (Vell. Verl Verl. State Brazil 8 1 2 16 ha Lognormal, Lognormal Log normal, normal fitdistrpluspackage fitdistrplus package program KolmogorovSmirnovs Kolmogorov Smirnov s 5 level Akaikes Akaike (AIC Schwarzs Schwarz BIC, , (BIC) asymmetric pattern regeneration C Z P class (Mart (Vell (BIC

Resumen El conocimiento detallado de la estructura de las plantaciones de teca es necesario para los planes de gestión sostenible. La integración de variables de teledetección con la modelización geoestadística en plantaciones de teca ha sido poco estudiada y, por tanto, el objetivo consistía en modelizar la distribución espacial de las variables del rodal de teca, incorporando covariables. El estudio se realizó en plantaciones de teca de 19 años en Brasil con 213 hectáreas en el espacio inicial de 3 m x 3 m. Se asignaron parcelas georreferenciadas de 900 m² y se obtuvieron las variables forestales después del clareo. Los índices de vegetación se calcularon a partir de operaciones aritméticas ejecutadas entre las bandas de imágenes Landsat. La interpolación de las variables forestales se procedió por el método geoestadístico univariante de kriging ordinario, así como por el método multivariante de kriging con deriva externa, considerando las variables de teledetección como covariables. El análisis estadístico de las variables de teledetección muestra una discreta correlación lineal con las variables de la teca, lo que tiende a hacer inviable su uso como covariables en la modelización geoestadística. Sin embargo, el kriging con deriva externa predice los patrones espaciales de las variables forestales con mayor detalle, lo que da como resultado a posibles errores de suavización menores que los obtenidos por el kriging ordinario, y proporciona recomendaciones más precisas para la gestión localizada en plantaciones de teca. La integración de variables de teledetección en el inventario forestal mediante geoestadística es ventajosa para cartografiar la distribución espacial de las variables de los rodales de teca.

Abstract Detailed knowledge of teak stand structure is necessary for sustainable management plans. The integration of remote sensing variables with geostatistical modeling in teak forest stands has not been sufficiently studied and, therefore, the aim was to model the spatial distribution of teak stand variables, adding covariables. The study was carried out on 19-year-old teak stand in Brazil with 213 hectares in the initial spatial of 3 m x 3 m. Geo-referenced plots of 900 m² were allocated, and forest variables were obtained after thinning. Vegetation indices were calculated from arithmetic operations conducted between the Landsat image bands. The interpolation of forest variables was performed by the geostatistical univariate method of ordinary kriging, as well as by the multivariate method of kriging with external drift, considering the remote sensing variables as covariables. Statistical analysis of remote sensing variables shows a weak linear correlation with teak variables, which tends to make them unviable to use as covariables in geostatistical modeling. However, kriging with external drift predicts spatial patterns of forest variables with greater detail, which results in lower possible smoothing errors than those obtained by ordinary kriging and provides more accurate recommendations for localized management in teak stand. The integration of remote sensing variables in forest inventory through geostatistics is advantageous for mapping the spatial distribution of teak stand variables.

Resumo Comparou-se por meio do teste de identidade de modelos estratégias de agrupamento de dados para o ajuste de modelos hipsométricos e volumétricos com o intuito de otimizá-los. A área de estudo tem 248,22 ha com plantio de Pinus oocarpa e Pinus caribaea var. hondurensis, divididos em talhões com idades entre 10 e 16 anos. A área foi inventariada por amostragem utilizando o método de área fixa com 7 parcelas retangulares de 600 m2 distribuídas de forma sistemática em cada povoamento. Diferentes estratégias de agrupamento de dados foram comparadas, a fim de verificar se uma única equação (modelo reduzido) poderia representar diferentes fontes de variação, como parcelas, espécies e idades, em vez de uma equação para cada fonte de variação (modelo completo). Os modelos selecionados para aplicação nas diferentes estratégias de agrupamentos foram avaliados com base no erro padrão da estimativa (Syx%), coeficiente de determinação ajustado (R2 aj.) e análise gráfica dos resíduos. As equações ajustadas para cada estratégia foram submetidas ao teste de identidade de modelos. Constatou-se que em nível de parcela não deve ser utilizada uma equação hipsométrica única (modelo reduzido) para representar todas as parcelas de um inventário, mesmo considerando a espécie e/ou idade. Em relação à variável volume, foi observado, para as espécies Pinus oocarpa e Pinus caribaea var. hondurensis, que uma única equação pode ser utilizada para estimar o volume total das duas espécies desde que estejam com a mesma idade, enquanto para idades diferentes recomenda-se o ajuste em nível de povoamento.

Abstract It was compared data grouping strategies by different models of identity test to fit height-diameter and volume models in order optimize them. The area under study has 248,22 ha with Pinus oocarpa and Pinus caribaea var. hondurensis stands, divided in plots among 10 and 16 years-old. This area was inventoried by fixed area sampling with 7 rectangular plots of 600 m2 distributed in a systematic in each stand. Different strategies for data grouping were compared, checking if only one equation (general model) could represent different sources of variation such as plots, species, and ages, instead of one equation to each source of variation (complete model). The selected models used in different grouping strategies were evaluated based on standard error of estimate (Syx%), adjusted coefficients of determination (R2 aj.) and graphical residues analysis. The fittied equations to each strategy were submitted to model identity test. It was found that related to plots should not be used a single height-diameter equation (general model) to represent all the plots in an inventory even if it is of the same species and/or age. In relation to volume it was observed for the species Pinus oocarpa and Pinus caribaea var. hondurensis that a single equation can be used to estimate the total volume of two species since at the same age, while for different ages it is recommended the fitting for stand level.

Abstract: This study aimed to evaluate the spatial distribution of the air circulation speed and the final moisture content of pine lumber after kiln drying by using geostatistics. Two kilns acting on boards of 27 mm and 42 mm were evaluated. Air circulation speed and final moisture content were collected in different regions of the kilns. There was no significant difference for air circulation speed and final moisture content between the front and rear regions of the equipment. In the horizontal axis (Y-axis), air circulation speed averages did not differ statistically in both situations, but higher values for this variable were obtained from the spaces between the piles. Final moisture content tended to increase when closer to the door opening. In the vertical axis (Z-axis), the lower part tended to reach higher air circulation speed values. Thus, the spatial behavior influences the air circulation speed and final moisture content during lumber drying. Besides, the variograms presented the same tendency in comparison to the data obtained in a conventional manner, which indicates that geostatistics can be used to represent variables in kilns during the drying process.

ABSTRACT Tree-level growth models are being more used in heterogeneous forests, for they can take underlying processes, such as competition, into account. Although it is common in the forest literature to test several indices in order to define the most suitable for each study, the evaluation of plot sizes or competition radii is poorly addressed in competition studies. The objective of this work was to assess the effect of different plot sizes and competitor selection radii on distance-independent and distance-dependent competition indices, as well as test several modifications in previously created indices. We used data of diameter, canopy stratum and crown quality from two stem mapped measurements carried out in a six-year period. Both distance-dependent and independent indices were calculated for different plot sizes and competitor selection radii. The performance of plot sizes and neighborhood radii was evaluated via Spearman’s rank correlation with the annual growth in diameter, and those with the largest correlation coefficient were included in a stepwise regression to estimate diameter growth. For almost all the indices the correlation increased as the plot size or radius increased. A 50 m x 50 m square plot generated the strongest correlation for distance-independent indices. A 20 m radius resulted the largest correlation for the distancedependent indices. Modifications in some of the indices also improved their performance. The stepwise regression selected BAL and Hegyi indices to describe the diameter growth, which means that using only one competition index might not be enough to fully explain the overall competition.

Abstract To characterize the spatial variation behavior of the tree attributes of tropical species in agroforestry systems is important for its management, and in this sense, geostatistics stands out for using techniques able of characterizing this variation. In this work, geostatistical methods were used to evaluate and map spatial variability of diameter (dbh) at 1.3 m from the ground level, commercial height (hc) and commercial volume (vc) of trees Swietenia macrophylla King, planted in an agroforestry system in the Brazilian Amazon. The field sampling was carried out based on a grid of 50 m × 50 m, which resulted in 36 systematics point. At each point, a circular plot of 500 m2 was installed to measure the variables dbh, hc. The vc of trees in the portions was estimated with the best equation adjusted to the 108 trees cubing data. Next, the spatial distribution standard of these variable were modeled with geostatistics and ordinary kriging was used to generate maps with predictions and uncertainties of the variables. The Schumacher-Hall’s model resulted in the best equation for the estimation of vc, and the systematic grid was efficient to detect the spatial patterns of these variables, because the adjusted semivariograms models demonstrated the strong spatial dependence on the dbh, hc and vc, being possible, make precise interpolations, generating cross-validation results without trend, mainly for vc that presented the best adjusted theoretical model.

Resumen La caracterización del comportamiento de la variación espacial de atributos dendrométricos de especies tropicales en sistemas agroforestales es importante para su manejo y, en ese sentido, la geoestadística se destaca por utilizar técnicas capaces de caracterizar esa variación. Se utilizaron métodos geoestadísticos para evaluar y mapear la variabilidad espacial del diámetro a 1.3 m del nivel del suelo (dap), de la altura comercial (hc) y del volumen comercial (vc) de árboles de Swietenia macrophylla King, plantadas en un sistema agroforestal en la Amazonia brasileña. El muestreo de campo se realizó con base en una cuadrícula de 50 m × 50 m, que resultó en 36 puntos sistemáticos. En cada punto, se instaló una parcela circular de 500 m2 para medir el dap y la hc. El vc fue estimado con la ecuación mejor ajustada a los datos de cubicación de 108 árboles. Luego se modelaron los patrones de distribución espacial de las variables por medio de la geoestadística y se utilizó kriging ordinario para generar mapas con predicciones e incertidumbres de las variables. El modelo de Schumacher-Hall resultó en la mejor ecuación para estimar el vc y la cuadrícula sistemática utilizada mostró ser eficiente para detectar los patrones espaciales de esas variables. Los modelos de semivariogramas ajustados demostraron la fuerte dependencia espacial del dap, de la hc y del vc, lo que permitió hacer interpolaciones precisas, generando resultados de validación cruzada sin tendencia, principalmente para vc que presentó el modelo teórico mejor ajustado.

ABSTRACT To quantify the surviving trees in a forest stand and estimate the probability of an individual tree to survival are a fundamental task in forest management planning. Therefore, the main goal of this paper was to estimate the tree survival probability in loblolly pine (Pinus taeda L.) plantations based on generalized linear models (GLM). The data set was obtained from forest inventories carried out in the Midwest of Santa Catarina State, Brazil. The data analysis combined strategies for selecting covariates and different specifications of link functions in a Bernoulli GLM. We performed strategies for covariate selection at plot-level along with the standard stepwise procedure, where we considered the elastic net approach, as well as its special cases the lasso and ridge penalization. Our analyses showed that the stepwise procedure combined with the complementary log-log link function provide the best fit. The variables that most contributed to assess tree survival were basal area, number of individuals, maximum diameter, diameter of the average cross-sectional area and the diameter coefficient of variation per plots. This model presents 81.5% of accuracy given by ROC curve. Finally, we evaluated the fitted model by means of the half-Normal plots and randomized quantile residuals, whose results showed evidence of a suitable fit. We suggest the stepwise procedure for selecting covariates for a tree survival probability model, besides a complementary log-log link function.

Resumo No presente estudo foram aplicados quatro algoritmos de aprendizado de máquina na tarefa de modelagem da relação hipsométrica de povoamentos de Pinus taeda L. em diferentes idades. Centenas de combinações de parâmetros foram testadas para os algoritmos k-vizinhos mais próximos, florestas aleatórias, máquinas de vetores de suporte e redes neurais artificiais. Para seleção do melhor modelo para cada algoritmo, utilizou-se o método de busca em grade combinada ao método de validação cruzada k-fold. Os modelos selecionados foram utilizados para predição da altura total de indivíduos pertencentes a um conjunto de dados independente, e os resultados foram comparados aos obtidos por modelos de regressão linear. Os modelos de aprendizado de máquina apresentaram indicadores estatísticos similares aos modelos de regressão linear, no entanto, tiveram dispersão de resíduos menos tendenciosa, principalmente na análise estratificada por povoamento. A máquina de vetores de suporte e a rede neural artificial foram os modelos mais satisfatórios em precisão e dispersão dos resíduos.

Abstract In the present study, four machine learning algorithms were applied in the task of modeling the height-diameter relationship of Pinus taeda L. stands at different ages. Hundreds of parameter combinations were tested for the k-nearest neighbors, random forests, support vector machines, and artificial neural networks algorithms. In order to select the best model for each algorithm, the grid search and the k-fold cross validation methods were applied. The selected models were used to predict the total height of individuals in an independent data set, and the results were compared to those obtained by linear regression models. The machine learning models presented similar statistical indicators to the linear regression models. However, they had less biased dispersion of residues, especially in the stratified analysis by age. The support vector machine and the artificial neural network were the most satisfactory models in precision and dispersion of residues.

RESUMO O procedimento de inventário florestal é considerado de alta importância no que concerne estudos de estoque madeireiro, estrutura e diversidade florestal, que fornecem informações relevantes para políticas públicas, planos de manejo e pesquisas ecológicas. O presente trabalho buscou avaliar o desempenho de técnicas de inventário na região Amazônica para estimativa de estoques madeireiros com maior nível de acurácia, mantendo a intensidade amostral fixa. Dois processos de amostragem foram avaliados: amostragem aleatória simples e amostragem em dois estágios. Esses processos foram avaliados através de alocação de unidades amostrais com dimensões distintas, e os estimadores gerados foram analisados em função da densidade de árvores e da área basal. A amostragem aleatória simples produziu os menores erros, alcançando 9% quando todas as espécies foram amostradas conjuntamente, e mostrou-se mais eficiente na detecção de variações em parâmetros fitossociológicos. A amostragem em dois estágios produziu os estimadores menos acurados e apresentou respostas mais lentas às variações em parâmetros fitossociológicos.

ABSTRACT Forest inventory procedures are of utmost importance to studies of wood volume stocks, and forest structure and diversity, which provide relevant information to public policies, management plans and ecological research. The present work focused on the performance of inventory techniques in the Amazon region to evaluate wood volume stocks with higher levels of accuracy while maintaining sampling intensity fixed. Two sampling processes were assessed: simple random sampling and two-stage cluster sampling. The processes were evaluated through the allocation of sampling units with different dimensions, and the effectiveness of the generated estimators was analyzed as a function of stand density and basal area. Simple random sampling resulted in the smallest errors, reaching 9% when all species were sampled together. The method depicted forest phytosociological parameters with greater sensitivity, whereas two-stage cluster sampling produced the least accurate estimators and presented slower responses to variation in phytosociological parameters.

ABSTRACT The aim of this study was to evaluate the effects of age, site, and density factors on the dynamics of eucalyptus diameter distribution. Data were obtained from a continuous forest inventory measured at different occasions, stratified according to the factors evaluated and adjusted by the three-parameter Weibull function using nonthinned clonal plots of eucalyptus stands located in the Central region of the state of Minas Gerais. In order to evaluate the diameter distribution behavior, asymmetry and kurtosis measures and graphical analysis for fitted curves were used. In general, an increase was observed in diameter amplitudes with aging, as well as with improvement of site productivity and higher densities. The number of trees decreased in the lower classes and increased in the upper classes, resulting in diameter distribution curves, being displaced to the right and flattened with aging.

RESUMO Considerando a hipótese de que os volumes de madeira apresentam dependência espacial, cujo conhecimento contribui para o manejo de precisão, o objetivo deste trabalho foi estimar a variabilidade espacial do volume de sortimentos de madeira e identificar seus padrões espaciais em povoamentos de Tectona grandis. Utilizou-se um conjunto de dados de 1.038 árvores para ajustar funções de afilamento e estimar os volumes para fuste total, serraria e lenha em 273 parcelas alocadas em povoamentos de T. grandis ao oitavo ano de idade, o qual representa o segundo desbaste que possibilita volumes comerciais. Modelos de semivariogramas foram aplicados para ajustar a dependência espacial e a krigagem pontual foi utilizada para compor mapas de volume. A modelagem geoestatística permitiu estimar a variabilidade espacial de T. grandis e desenvolver mapas de volume de madeira. Assim, tratamentos silviculturais, como desbaste e poda, bem como planejamento de intervenções espaciais, podem ser recomendados para produtos de madeira almejados.

ABSTRACT Considering the hypothesis that the wood volumes present spatial dependence, whose knowledge contributes for the precision forestry, the aim of this work was to estimate the volume spatial variability for timber assortments and identify their spatial patterns on Tectona grandis stands. A dataset of 1,038 trees was used to fit taper models and estimate the total stem, sawlog, and firewood volumes in 273 plots allocated on T. grandis stands at eight years old, which represents the second thinning that enables commercial volumes. Semivariograms models was applied to fit the spatial dependence, and punctual kriging was used to compose volume maps. Geostatistical modeling allowed us to estimate the T. grandis spatial variability and develop timber volume maps. Thus, silvicultural treatments, such as thinning and pruning, as well as for planning spatial interventions, are possible to be recommended for aimed wood products.

RESUMO O objetivo deste estudo foi comparar o desempenho de técnicas de inteligência artificial com funções de afilamento e avaliar a contribuição da idade nessa estimativa. O conjunto de dados foi composto por 135 observações, abrangendo as idades de 6, 12, 18, 24 e 43 anos de um povoamento de Araucaria angustifolia. As funções de afilamento ajustadas foram Kozak modificado, Schöepfer, Hradetzky e Garay. Os modelos de inteligência artificial utilizados foram: RNA e árvore modelo (M5P). Os vetores de entrada foram as mesmas variáveis utilizadas nas equações de afilamento e também o mesmo arranjo com a adição da idade. Foram utilizados 70% dos dados para ajuste e 30% para validação. A função de afilamento de Hradetzky forneceu o melhor ajuste. Dentre os modelos avaliados, a RNA propiciou as melhores estimativas, com destaque para a RNA com adição da variável idade. O desempenho da M5P foi satisfatório, porém, inferior às demais técnicas utilizadas.

ABSTRACT The aim of this study was to compare the performance of artificial intelligence techniques with taper functions and evaluate the effect of age on this estimate. The data set was comprised of 135 observations covering the ages 6, 12, 18, 24 and 43 years of age of a stand of Araucaria angustifolia. Adjusted taper functions were Kozak Schöepfer, Hradetzky and Garay modified. The artificial intelligence models used were: ANN and tree model. The input vectors are the same variables used in taper equations and also the same arrangement with the addition of age. 70% of the data was used for adjustment and 30% for validation. The taper function Hradetzky provided the best fit. Among the models evaluated, the ANN provided the best estimates, highlighting the ANN by adding the age variable. The performance of M5P was satisfactory, however, less effective than the other techniques.

ABSTRACT The aim of this work was to model the spatial dependence of fuel material deposition on the ground in a pine stand, and to simulate and evaluate sampling procedures for estimating it. Branches with diameters up to 0.7 cm (A) and from 0.71 to 2.5 cm (B) were collected. Subsequently, the structures of systematic sampling and linear clusters were simulated for 50%, 33% and 23% of the total sample size, and the spatial dependence was evaluated through geostatistical modeling. The systematic sampling was suitable, with representative spatial coverage and accurate estimators, whereas linear clusters were inadequate. The reduction of the number of sample units affected the estimators, but their sampling errors did not exceed 10% for the sample sizes of 23% for class A of fuel material and 50% for class B in the systematic structure, resulting in consistent estimates.

RESUMO Nas florestas tropicais, a abundância de espécies arbóreas em diferentes formas e dimensões, bem como a elevada diversidade estrutural, dificulta o emprego de fatores de forma ou de equações para a estimativa de volumes individuais. Contudo, o emprego de equações de povoamento possibilita predizer o estoque volumétrico por unidade de área a partir de atributos da floresta, excluindo a necessidade da avaliação individual do volume das árvores. Com isso, o objetivo deste estudo foi selecionar variáveis, ajustar modelos estatísticos e propor equações de povoamento para a estimativa do volume comercial total e explorável em uma floresta sob regime de concessão na Amazônia. Para isso, medidas comumente mensuradas, como a densidade e a área basal, foram empregadas em modelos tradicionais da literatura; além da aplicação de variáveis que consideraram a diversidade e a estrutura florestal em modelos gerados pelo processo Stepwise. Desse modo, os modelos obtidos por Stepwise propiciaram estimativas mais precisas dos estoques volumétricos, reduzindo os erros de estimativa e reduzindo problemas de heterocedasticidade dos resíduos. Além disso, a inserção de variáveis que expressam a diversidade e a estrutura florestal nas equações, como os índices de Shannon e de variação diamétrica e a razão de indivíduos comerciais, contribuiu para a melhoria das predições, sobretudo para o volume comercial explorável, sendo então recomendadas para a avaliação precisa do potencial madeireiro de áreas sob concessão florestal na Amazônia.

ABSTRACT The abundance of tree species in tropical rainforests with different shapes and dimensions, as well as the great structural diversity, makes difficult the employment of form factors or equations to estimate individual volumes. However, the employment of equations at the population level makes possible to predict the volumetric stock per unit of area from forest attributes, excluding the necessity of individual tree volume evaluation. Thereby, the aim of this study was to select variables, fit statistical models and propose stand equations to estimate total and exploitable commercial volumes in an Amazon forest under concession regime. For this, variables commonly measured, like density and basal area, were inserted on traditional commercial volume models; besides the application of variables that considered the diversity and forest structure on models generated by the Stepwise process. After analysis, it was observed that the models obtained through Stepwise propitiated more precise estimation of the volumetric stock, reducing estimation errors and reducing problems with heteroscedasticity of residuals. The insertion of variables that express diversity and forest structure on the equations, like Shannon’s and diametric variation indices and the commercial trees ratio, contribute to predictions’ improvement, especially for the exploitable commercial volume, being recommended for the precise evaluation of timber potential of areas under Amazon forest concession.