ABSTRACT The fitting of volume models by the traditional method (data obtained by means of scaling several trees), is the most used way to obtain volume equations. This method requires a lot of effort and is quite costly, therefore some alternatives have been developed to decrease the sampling of the number of trees and obtain results of estimates similar to that obtained by the traditional method, highlighting the mixed modeling applied to calibrate equations. In this work, the general objective of the research was to calibrate the Schumacher-Hall volume model by predicting random effects at the stand level and comparing it with the equations obtained using the traditional approach. The database is made up of 670 trees with ages varying from 1 to 10.75 years. The calibrations tested in the mixed model were using: (i) the largest tree of variable d for each stand; (ii) the two largest trees of variable d for each stand; (iii) the three largest trees in d for each stand; (iv) the four largest trees in d for each stand; (v) the five largest trees in d for each stand; (vi) the median tree for variable d in each stand; vii) one random tree in each stand; viii) three trees, being the smallest tree, the mean tree and the largest tree for the variable d for each stand; ix) three trees, being the mean tree, the mean tree minus two standard deviations and the mean tree plus two standard deviations for the variable d in each stand. The statistics for evaluating the equations were the coefficient of determination, the standard error of the estimate, the analysis of residuals, and the graphical analysis of the observed and estimated values. The results show that the volume equations can be calibrated at the stand level by sampling three trees: the average tree, the average tree plus two standard deviations, and the average tree minus two standard deviations. Considering that in the traditional method, 50 trees on average are measured in the forest inventory, the reduction of sampling in a new stand would be 94%.

RESUMO O ajuste dos modelos de volume pelo método tradicional (dados obtidos por meio de cubagem de várias árvores) é a maneira mais utilizada para obter equações de volume. Este método demanda muito esforço e é bastante oneroso, portanto algumas alternativas têm sido desenvolvidas para diminuir a amostragem do número de árvores e obter resultados de estimativas semelhantes ao obtido pelo método tradicional, destacando-se a modelagem mista aplicada para calibrar equações. Neste trabalho, o objetivo da pesquisa foi calibrar o modelo de volume de Schumacher-Hall por meio da predição de efeitos aleatórios em nível de povoamento e compará-lo com as equações obtidas pela abordagem tradicional. A base de dados é composta de 670 árvores com idades variando de 1 a 10,75 anos. As calibrações testadas no modelo misto foram: i) a maior árvore da variável d para cada povoamento; ii) as duas maiores árvores da variável d para cada povoamento; iii) as três maiores árvores em d para cada povoamento; iv) as quatro maiores árvores em d para cada povoamento; v) as cinco maiores árvores em d para cada povoamento; vi) a árvore mediana para a variável d em cada povoamento; vii) uma árvore aleatória em cada povoamento; viii) três árvores, sendo a menor árvore, a árvore média e a maior da variável d para cada povoamento; ix) três árvores, sendo a árvore média, a árvore média menos dois desvios padrões e a árvore média mais dois desvios padrões para a variável d em cada povoamento. As estatísticas para avaliação das equações foram o coeficiente de determinação, o erro padrão da estimativa, a análise de resíduos e a análise gráfica dos valores observados e estimados. Os resultados evidenciam que as equações de volume podem ser calibradas em nível de povoamento por meio da amostragem de três árvores sendo elas, a árvore média, a árvore média mais dois desvios padrões e a árvore média menos dois desvios padrões, considerando que no método tradicional são cubadas 50 árvores em média no inventário florestal, a redução da amostragem em um novo povoamento seria de 94%.

Abstract We investigated the spatial distribution of population data and diameter classes and modeled the diameter structure of Vouacapoua americana Aubl. (Acapu) trees in a community forest management area. A forest census of trees with diameters ≥ 33 cm was carried out in the 2015 Annual Production Unit (APU-2015). Ripley’s univariate K function and the global Moran’s index were used to describe spatial autocorrelation. Three harvest intensities (50, 70, and 80%) were simulated for the potential trees. The Weibull (3P) function provided the best performance to describe the diameter distribution of the original tree population, as well as in the harvested 50 and 70% intensities. In general, the spatial pattern of V. americana was aggregated. However, other natural factors, as population size, dynamics, geographic distribution, should be used as indicators for forest management and conservation of the specie.

ABSTRACT Tree volumes can alternatively be obtained by ratio estimates, instead of applying linear regression modeling. An interesting question was considered by the authors when comparing the precision of tree volumes obtained by these two statistical approaches, that allowed us to formulate a new hypothesis to conduct this study: “Is it possible to obtain better volume estimates if the form factor is associated only to the exponent of the independent variable that presents higher correlation with the stem volume?”. The research was conducted in commercial stands of black wattle (Acacia mearnsii De Wild) in the municipalities of Cristal, Encruzilhada do Sul and Piratini to answer this question. Forest stands were sampled in a sequence of ages after planting, varying from 1 to 14 years. In each forest stand, trees were felled, and the following characteristics were evaluated: diameter at breast height, total height, and stem scaling. The three age groups were specified according to the behavior of the form factor values. It was proposed three models to be solved by ratio estimates. A comparison of the proposed models with the Schumacher-Hall model, fitted by regression analysis, was done. The model in which the form factor was associated to the exponent of the diameter variable produced the best results, owing to a powerful correlation resulted of this confounding with volume as a dependent variable. Ratio estimates resulted in more accurate tree volumes predominantly, when compared with those obtained by the traditional Schumacher-Hall model fitted through regression analysis. Therefore, we recommend the application of model 2 fitted by ratio estimate.

RESUMO Os objetivos desse trabalho foram propor equações aditivas de biomassa dos componentes (fuste e copa) com a biomassa total para a espécie acácia negra (Acacia mearnsii De Wild.) e demonstrar a inconsistência de equações de biomassa ajustadas independentemente. Dois procedimentos foram utilizados para ajustar equações não lineares de biomassa: i) independente e ii) sistemas de equações. O segundo procedimento, definido pela aplicação do modelo de regressão aparentemente não relacionada, apresenta melhores propriedades biológicas e estatísticas para estimar equações alométricas de biomassa dos componentes e biomassa total, quando comparado com a estimação independente. Uma propriedade efetiva desse procedimento é a aditividade, isto é, as estimativas de biomassa dos componentes são compatíveis com as de biomassa total. As equações ajustadas independentes não consideram a dependência entre os componentes de biomassa, assim, além das estimativas não serem aditivas, propriedade indesejável, resultarão em estimativas com maior variância.

ABSTRACT The objectives of this work were to propose additive equations for biomass components (stem and crown) and total biomass for black wattle (Acacia mearnsii De Wild.) and show the inconsistency of independently adjusted biomass equations. Two procedures were used to fit nonlinear equations of biomass: i) independent and ii) systems of equations. The second procedure, defined by the application of the seemingly unrelated regression model, has better biological and statistical properties to estimate allometric equations of biomass components and total biomass when compared with the independent estimation. An effective property of this procedure is the additivity, i.e., the estimates of component biomass are compatible with those of total biomass. Independent fitted adjusted equations do not consider the dependence between the biomass components, thus, besides the estimates being non-additive, which is an undesirable property, they will result in estimates with larger variance.

Abstract: 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.

Abstract Woody debris, defined as standing and downed deadwood, consists in an essential component of the forest carbon stock. However, few studies have been carried out to get an efficient and accurate sampling procedure for estimating it. This work proposes two methodologies to estimate the woody debris volume in a Brazilian mixed tropical forest: 1) two-stage systematic sampling, using a mixed methodology, in which the Strand’s method is applied to standing dead trees and stumps, and line intercept sampling is used to fallen trees and branches; and 2) ratio estimate of the sum of cross-sectional areas of deadwood pieces and forest basal area, aiming to obtain the total woody debris volume indirectly in the natural forest. Conversions for biomass and carbon stocks were made applying the mean basic density on the estimates of deadwood volumes. Both methodologies are accurate for woody debris volume estimates, with a sampling error equal to 16.1% (methodology 1) and 5.7% (methodology 2), at a 95% probability level. Thus, the methodology 2 has potential to be used in strategic forest inventories of woody debris, such as in National Forest Inventories, due to increasing importance of its quantification in all forest ecosystems.

RESUMO A melhor tomada de decisão é uma tarefa difícil no manejo florestal, pois envolve um grande número de variáveis de mercado e de produção. Simulou-se o crescimento e produção de Pinus taeda L. em sítios altamente produtivos, com objetivo de indicar regimes de desbaste e densidades de plantio que maximizam a produção de toras grossas (diâmetro da ponta fina >35 cm), bem como avaliá-los economicamente. O software OpTimber-LP para otimização de problemas florestais foi usado. As simulações envolveram quatro densidades de plantio (1.111; 1.600; 2.000; e 2.500 plantas/ha); três desbastes com diferentes pesos, frequências e idades de aplicação; e corte raso aos 25 anos. Essas combinações totalizaram em 2.916 regimes de manejo. VPLA foi calculado com variação de taxas de interesse e considerando custos de produção e retornos provenientes de desbastes e do corte raso. Os resultados indicaram maior produção de toras grossas em regimes com menores densidades de plantio. A intensidade de desbaste de 60% destacou-se por ter sido ideal para quase todos os processos, principalmente nas densidades de 2.000 e 2.500 plantas/ha. Essa intensidade também foi ideal para o primeiro desbaste, independentemente da densidade de plantas. A produção nos melhores regimes variou de 480 e 260 m3/ha, para as densidades de 1.111 e 2.500 plantas/ha, respectivamente. VPLA variou de ~1.300 a ~2.100 R$/ha. Como conclusão, regimes de manejo menos densos propiciaram maior produção de toras grossas, porém, menor em volume total; como consequência, o VPLA foi maior para os regimes mais densos, uma vez que a receita obtida pela produção de toras de alto valor não compensou a receita de toras mais finas (que também são mais baratas). Regimes com alta densidade podem fracassar com um único primeiro desbaste errado, enquanto regimes com menor densidade podem ter produção realmente prejudicada quando são sujeitos a consecutivos desbastes errados.

ABSTRACT The best decision-making is a difficult task in forest management because it involves a large number of market and production variables. We simulated the growth and yield of loblolly pine in high-quality sites, aiming to indicate thinning regimes and planting densities that maximize the production of large diameter logs (minor diameter >35 cm), as well as economically evaluating such regimes. We used the software OpTimber-LP for forest optimization problems. Simulations involved four planting densities (1,111; 1,600; 2,000; and 2,500 plants/ha); three thinnings with different weights, frequencies and ages of application; and clear cut at 25 years. Such combinations totalized in 2,916 simulated regimes. We computed ANPV assuming variations in interest rates, besides costs of production and returns resulting from thinnings and from clear cut. The findings indicated great productions of large diameter logs in regimes with low planting densities. Heavy thinnings (60% removal of trees) highlighted by being ideal to almost all regimes, mainly those ones with densities of 2,000 and 2,500 plants/ha. Heavy intensity also was ideal to the first thinning, regardless the planting density. The most productive regimes presented large diameter log volumes ranging from 480 to 260 m3/ha, for regimes with 1,111 and 2,500 plants/ha, respectively. ANPV ranged from ~1.300 to ~2.100 R$/ha. As conclusion, less dense regimes provide largest productions in large diameter log, but the lowest productions in total volume; as consequence, ANPV was larger in denser regimes, once the revenue obtained from high-value logs did not overcome that one obtained from finer (and consequently cheaper) logs. High-density regimes may produce less timber volume due to only one improper thinning, whereas low-density stands may have production really affected when are subjected to consecutive improper thinnings.

ABSTRACT It is presented the theme additivity of biomass of tree components. To evaluate and discuss this context, experimental information collected in forests of Acacia mearnsii De Wild. was used. Equations for components (stem and crown) and total biomass were fitted by means of two procedures: 1) generalized nonlinear least squares and 2) weighted-nonlinear seemingly unrelated regressions. Analyzing the performance of the estimators, it can be concluded that the two tested procedures are equivalent. On the other hand, this conclusion differs when evaluated the consistency and efficiency of the estimators. Fitting equations for the components and for the total biomass by an independent way is not realistic, because from a biological point of view the estimates of biomass are inconsistent, i.e., are not additive. The biomass estimates of the components and of the total, resulting from equations adjusted by means of systems of equations, provided narrower confidence intervals in relation to the equations adjusted independently, and is therefore more efficient. The second procedure presents better biological properties and statistics to estimate allometric equations for biomass of the components and for the total when compared with the independent estimation, thus it should be the method to be used.

ABSTRACT The objective of the study was to present mathematical models and strategies for fitting equations to estimate dry biomass for tree species in forest restoration areas. The presence of outliers was analyzed in each fitted equation using values of the matrix H, leverage points, means of standard and studentized residuals, and of influential points through DFFITS, DFBETAS and COOK distance values. Furthermore, the normality, homoscedasticity and independence of residuals were checked. The accuracy of the fitted equations was evaluated by means of the R2adj., Syx, analysis of residuals, and AIC and BIC criteria. The results showed that the model for estimating dry biomass as a function of the variables Dc2, DBH2, Hc2 and DBH provides the more accurate solution, with Syx = 40.91% and R2adj. = 0.92. We concluded that the performance of this equation improves when adjusted to data stratified by classes of height-diameter ratio, which reduces the value of the estimated error.

ABSTRACT We reviewed key studies published so far regarding Eremanthus erythropappus (DC.) MacLeish (Candeia), in order to approach the sustainable management of this species. The objective of this study was to discuss what is already known by the scientific community, presenting the current scenario and outlining the main challenges that still need to be addressed. Candeia is a tree species found in some Brazilian states, being used in the production of fence posts, and essential oils. It aids in the preservation and restoration of natural areas when properly managed, promoting social development through the creation of jobs and economic growth, due to the current high demand and market value for its products. Due to the high value of its timber, there is a strong anthropic pressure on this species, and it has consequently been exploited in an unsustainable manner. However, already published research suggests that well-managed stands of Eremanthus erythropappus can be economically feasible.

ABSTRACT The aim of the present study was to propose a prediction system to estimate the diameter distribution and wood production in unthinned eucalyptus clone plantations. Data was obtained from permanent sample units, with ages from 28 to 78 months. The Weibull distribution was used to estimate the frequency of the number of trees per diameter class. Models were used to relate the Weibull distribution coefficients with forest stand attributes. The forest stand variables most correlated with the Weibull distribution parameters were the minimum, medium, maximum and quadratic diameters and the dominant height. The projected frequency of tree numbers and the production by diameter class obtained by the system of equations did not differ statistically from the observed values evaluated by the t-test at 95% probability.

RESUMO Este trabalho teve como objetivo avaliar o desempenho das funções densidade de probabilidade (fdp) com diferentes procedimentos de ajustes e estatísticas de avaliação, a fim de expressar a distribuição diamétrica de um fragmento de Floresta Ombrófila Mista. A área de estudo faz parte da Floresta Nacional de Irati (FLONA), estado do Paraná. Os dados utilizados são provenientes de 25 parcelas permanentes de 1 ha (100 m x 100 m), que foram instaladas e medidas em 2002 e remedidas em 2005 e 2008. Os ajustes foram feitos considerando todas as espécies amostradas na remedição de 2008. Foram testadas as funções Beta, Weibull 2 e 3 Parâmetros e Exponencial de Meyer (tipos I e II), empregando-se os métodos de ajustes dos Momentos e da Máxima Verossimilhança para a função Beta e Percentis e Máxima Verossimilhança para a função Weibull 2 e 3 Parâmetros. A Programação Não Linear foi utilizada como tentativa de melhorar os ajustes realizados das funções, exceto para Meyer. Para avaliação dos ajustes, foram aplicados os testes de aderência de Kolmogorov-Smirnov (K-S) e Hollander-Proschan (H-P), além do Erro Padrão de Estimativa (%), índice de Reynolds (IR) e análise de resíduos. Os resultados indicaram que a função Weibull 3P ajustada pelo método da Máxima Verossimilhança foi a melhor para descrever a distribuição diamétrica da floresta como um todo, no entanto, o método dos Percentis apresentou resultados similares. A função Beta apresentou resultados satisfatórios, podendo também ser empregada para avaliar a distribuição diamétrica da área de estudo. Quanto às estatísticas utilizadas, o índice de Reynolds mostrou ser uma ferramenta estatística com boa performance para selecionar funções densidade de probabilidade. Para o intervalo de classe utilizado, o teste Kolmogorov-Smirnov apresentou um maior número de aderências quando comparado ao teste Hollander-Proschan, porém, o teste K-S é sensível quando a frequência é alta, levando a uma não aderência.

ABSTRACT The aim of this work was to evaluate the performance of the probability density functions with different fitting procedures and statistical evaluation to describe the diameter distribution of a Mixed Ombrophyllous Forest fragment. The study area is part of the Irati National Forest (FLONA), in Parana State. Data used were derived from 25 permanent 1-ha plots (100 m x 100m) established and measured in 2002 and re-measured in 2005 and 2008. The fittings were done considering all the species sampled on the re-measurement in 2008. Beta, Weibull 2 and 3 Parameters and Exponential Meyer I and II functions were tested, employing Moments and Maximum Likelihood methods for Beta and Percentiles and Maximum Likelihood for Weibull 2 and 3 Parameters. The Nonlinear Programming was used as an attempt to improve the fittings, except for Meyer model. To evaluate the fittings, the goodness-of-fit tests Kolmogorov-Smirnov (K-S) and Hollander-Proschan (H-P) were used, as well as, the Standard Error (%), Reynolds Index (IR) and Residual Dispersion. The results showed that Weibull 3P function was the best to describe the diameter distribution for the forest as a whole, however the Beta function showed satisfactory results, and it can also be used to evaluate the diameter distribution for the studied area. About the statistics used, it was observed that Reynolds Index presented good results to evaluate the performance to probability density functions and, for the interval class used, the Kolmogorov-Smirnov test presented a higher number of good fitness values when compared with Hollander-Proschan test, nevertheless the K-S is sensible when the frequency is high, causing a non-adherence.

A utilização do laser terrestre para levantamentos em povoamentos florestais tem como objetivo prover dados à modelagem tridimensional das árvores, no entanto, para que seja possível aplicar tal modelo, é necessário realizar a detecção dos pontos que fazem parte de árvores na varredura. O presente estudo propõe um método para a detecção de árvores a partir da nuvem de pontos 3D de plantios florestais. Inicialmente, procura-se reconstituir a distribuição espacial das árvores a partir da aplicação de um algoritmo de segmentação em uma seção transversal (1 metro) da nuvem de pontos. Em seguida, é apresentado um algoritmo para detectar a posição das árvores com base no padrão de alinhamento do povoamento. Por fim, os resultados obtidos são apresentados para validação pelo usuário da nuvem de pontos. O método apresentado foi testado em parcelas circulares instaladas em povoamentos de Eucalyptus spp. levantados por varreduras simples e múltiplas. Os resultados apontaram a necessidade de utilização de múltiplas estações de TLS para redução do efeito de sombreamento no levantamento das parcelas circulares. A aplicação do método de detecção de árvores em conjunto com a análise visual resultou na identificação de 100% das árvores a partir das nuvens de pontos das parcelas

Terrestrial LIDAR measurements in forest stands is often used to gather data for 3D tree models. However, such models require the detection of points representing trees in the scanning field. The present study offers a method for tree detection from a 3D point cloud of forest plantations. Initially the spatial distribution of trees is reconstructed by applying a segmentation algorithm in a transverse slice (1 meter) through the point cloud. This is followed by an algorithm for detecting tree position based on plantation stand row alignment. Finally, the results are presented for validation by the point cloud user. The methods were evaluated over young Eucalyptus spp. stands (i.e. 2, 4 and 5 years) exploring single and multiple positioning of the TLS device inside the circular plots. Results suggest that several TLS stations should be used to reduce shading effects in mapping circular plots. Employing the tree detection method with the visual analysis of point clouds of each plot were identified 100 % of the trees.

RESUMO O objetivo deste texto foi avaliar estatisticamente o efeito de desbastes e da qualidade de sítio na área basal (G) e no volume total do fuste (v) e do sortimento de Pinus taeda. Os desbastes ocorreram entre 8 e 9 anos de idade, cortando uma em cinco linhas de plantio mais 66%, 54%, 42%, 30% e 19% de árvores do dossel inferior. Entre 3 e 4 anos pós-desbaste, foram mensurados diâmetros e cubadas as árvores, possibilitando calcular a G e os volumes. Estruturou-se um delineamento em blocos casualizados, adotando-se blocos e tratamentos como sítios e regimes de desbaste, respectivamente. O v foi modelado por parcela, possibilitando estimar o volume por sortimentos pelo software SISPINUS. Concluiu-se que a relação volumétrica entre tratamentos varia para árvores mais grossas. Entre blocos, reduz sua inclinação ao piorar a qualidade do sítio. A capacidade produtiva exerce mais efeito nas variáveis analisadas do que os desbastes variando em peso.

ABSTRACT An experiment in Pinus taeda stands was conducted aiming to evaluate the effect of thinnings and forest site quality on basal area (G), total volume, stem volume (v) and assortment of Pinus taeda. Thinnings occurred between 8 and 9 years old, where the fifth row plus 66%, 54%, 42%, 30% e 19% of the existing trees was cut. Thinnings were followed by measurement of diameters and along the stem to calculate its volume. An analysis of variance in randomized blocks was made adopting the sites as blocks and the mixed thinnings as treatments. Volumetric relation was modeled for the plots and from this, log assortments could be estimated using a software named SISPINUS. In conclusion, thinning affect the volumetric relation especially to larger trees, while its inclination curve reduces from richest sites to poorest sites. Sites exert greater effect than thinnings when considering basal area, total volume, boles volume and volume per assortment.

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.