Selection criteria for linear regression models to estimate individual tree biomasses in the Atlantic Rain Forest, Brazil.

BACKGROUND: Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed. RESULTS: The adjusted coefficient of determination ([Formula: see text]) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection. CONCLUSIONS: It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.

A model based on environmental factors for diameter distribution in black wattle in Brazil.

This article discusses the dynamics of a diameter distribution in stands of black wattle throughout its growth cycle using the Weibull probability density function. Moreover, the parameters of this distribution were related to environmental variables from meteorological data and surface soil horizon with the aim of finding a model for diameter distribution which their coefficients were related to the environmental variables. We found that the diameter distribution of the stand changes only slightly over time and that the estimators of the Weibull function are correlated with various environmental variables, with accumulated rainfall foremost among them. Thus, a model was obtained in which the estimators of the Weibull function are dependent on rainfall. Such a function can have important applications, such as in simulating growth potential in regions where historical growth data is lacking, as well as the behavior of the stand under different environmental conditions. The model can also be used to project growth in diameter, based on the rainfall affecting the forest over a certain time period.

On the use of data mining for estimating carbon storage in the trees.

Forests contribute to climate change mitigation by storing carbon in tree biomass. The amount of carbon stored in this carbon pool is estimated by using either allometric equations or biomass expansion factors. Both of the methods provide estimate of the carbon stock based on the biometric parameters of a model tree. This study calls attention to the potential advantages of the data mining technique known as instance-based classification, which is not used currently for this purpose. The analysis of the data on the carbon storage in 30 trees of Brazilian pine (Araucaria angustifolia) shows that the instance-based classification provides as relevant estimates as the conventional methods do. The coefficient of correlation between the estimated and measured values of carbon storage in tree biomass does not vary significantly with the choice of the method. The use of some other measures of method performance leads to the same result. In contrast to the convention methods the instance-based classification does not presume any specific form of the function relating carbon storage to the biometric parameters of the tree. Since the best form of such function is difficult to find, the instance-based classification could outperform the conventional methods in some cases, or simply get rid of the questions about the choice of the allometric equations.

Acuracidade da distribuição diamétrica entre métodos de projeção em Floresta Ombrófila Mista / Accuracy of the diameter distribution of projection methods in Araucaria's Forest

O estudo tem como objetivo avaliar a acuracidade das projeções diamétricas em uma Floresta Ombrófila Mista, empregando os modelos da Matriz de Transição e Razão de Movimentação, aplicados em três amplitudes temporais (2, 3 e 4 anos), sendo utilizados duas amplitudes de classes diamétricas (5 e 10cm). Os dados utilizados no estudo são oriundos de parcelas permanentes instaladas na Floresta Nacional de São Francisco de Paula - RS. A eficiência das projeções foi verificada com base nos valores observados, adotando-se os testes de Kolmogorov Smirnov e a análise de variância. Embora tenham sido influenciadas pelas Propriedades Markovianas, as projeções realizadas mostraram eficiência para descrever a estrutura futura da floresta, sendo o modelo da Razão de Movimentação o que gerou as projeções mais eficientes se comparada às projeções da Matriz de Transição. A amplitude temporal de 4 anos, associada à amplitude de classe diamétrica de 5cm, apresentou o resultado mais acurado do estudo, superestimando em 1,7% o número total de indivíduos da floresta.

This study aims to evaluate accuracy of projections in diametric Araucaria Forest, using models of the transition matrix and movement ratio, applied in three temporal amplitude (2, 3 and 4 years), and two employees amplitudes diameter classes (5 and 10cm). The information used in the study are from permanent plots established in the National Forest of São Francisco de Paula - RS. The efficiency of the projections was verified based on observed values, using Kolmogorov Smirnov test and analysis of variance. Although they have been influenced by the Markovian properties, projections carried out showed efficiency to describe the future structure of the forest, but the model the movement ratio projections generated more efficient compared to those described by the transition matrix. The time span of 4 years applied the range of 5cm diameter class had the most accurate results of the study overestimated by 1.7% the total number of individuals in the forest.