Evaluation of direct and indirect methods for modelling the joint distribution of tree diameter and height data with the bivariate Johnson’s SBB function to forest stands

Aim of study: In this study, both the direct and indirect methods by conditional maximum likelihood (CML) and moments for fitting Johnson’s SBB were evaluated. To date, Johnson’s SBB has been fitted by either indirect (two-stage) method using well-known procedures for the marginal diameter and heights, or direct methods, where all parameters are estimated at once. Application of bivariate Johnson’s SBB for predicting height and improving volume estimation requires a suitable fitting method.Area of study: E. globulus, P. pinaster and P. radiata stands in northwest Spain.Material and methods: The data set comprised of 308, 184 and 96 permanent sample plots (PSPs) from the aforementioned species. The suitability of the method was evaluated based on height and volume prediction. Indices including coefficient of determination (R2), root mean square Error (RMSE), model efficiency (MEF), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC) were used to assess the model predictions. Significant difference between observed and predicted tree height and volumes were tested using paired sample t-test at 5% level for each plot by species.Main results: The indirect method by CML was the most suitable method for height and volume prediction in the three species. The R2 and RMSE for height prediction ranged from 0.994 – 0.820 and 1.454 – 1.676, respectively. The percentage of plot in which the observed and predicted heights were significant was 0.32%. The direct method was the least performed method especially for height prediction in E. globulus.Research highlights: The indirect (two-stage) method, especially by conditional maximum likelihood, was the most suitable method for the bivariate Johnson’s SBB distribution.Keywords: conditional maximum likelihood; moments; two-stage method; direct method; tree volume

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the SBB Johnson’s distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait. stands, 97 research plots in Pinus radiata D. Don stands, and 128 research plots in Eucalyptus globulus Labill. Most of the eucalyptus stands were measured three times giving a total of 304 measurements. All plots are located in northwestern Spain. The Bias, Mean Absolute Error (MAE) and Mean Square Error (MSE) of the mean relative frequency of trees were used to evaluate the goodness-of-fit of the different functions, as well as the Kolmogorov-Smirnov statistic Dn. The Gumbel and the Weibull cumulative distribution functions (CDFs) proved suitable for describing extreme values of height distributions of the above-mentioned tree species in northwestern Spain. The Fréchet distribution was only used to model maximum values and yielded the poorest results in all casesGobierno del Principado de Asturias (Spain), project “Estudio del crecimiento y producción de Pinus pinaster Ait. en Asturias” (CN-07-094). Ministerio de Ciencia e Innovación (Spain), project “Influencia de los tratamientos selvícolas de claras en la producción, estabilidad mecánica y riesgo de incendios forestales en masas de Pinus radiata D. Don y Pinus pinaster Ait. en el Noroeste de España” (AGL2008-02259). Ministerio de Ciencia e Innovación (Spain) and ERDF programme (EU) for the period 2011-2013, project “Growth and yield modelling of clonal and seedling plantations of Eucalyptus globulus Labill. of NW Spain” (AGL2010-22308-C02-01). The Sustainable Forest Management Unit (UXFS) is funded by the Xunta de Galicia, Spain (“Consolidation and Structuring Program of Competitive Research Units 2011”) and by the ERDF programme (EU)S

La ordenación de las poblaciones de fauna cinegética para la práctica de la caza. El caso del TECOR Oleiros-Rioaveso (Villalba, Lugo)

En este artículo se argumenta sobre la necesidad de los proyectos de ordenación de los recursos cinegéticos y se pone como ejemplo el caso del TECOR Oleiros-Rioaveso (Villalba, Lugo), en el que se hace una descripción del medio natural, del estado de las poblaciones de fauna con interés cinegético y se propone un plan de caza para las principales especies que pueblan o van a poblar el coto: corzo, jabalí, zorro, perdiz roja, faisán y aves migratorias. También se mencionan las principales actuaciones de mejora (en infraestructuras, sobre el medio y sobre las especies cinegéticas). Finalmente se expone el balance económico resultado de la ordenación

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiata and Pinus sylvestris stands in northwest Spain

The purpose of this study was to compare the accuracy of the Weibull, Johnson’s SB and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson’s SB function by Conditional Maximum Likelihood and by Knoebel and Burkhart’s method, and those of the beta function with the method based on the moments of the distribution. The beta and the Johnson’s SB functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson’s SB and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson’s SB functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters methodEl objetivo de este estudio fue comparar la precisión de las distribuciones Weibull, SB de Johnson y beta, ajustadas por alguno de los métodos más habituales y fijando diferentes valores para los parámetros de localización, para describir distribuciones diamétricas en masas regulares de Pinus pinaster, Pinus radiata y Pinus sylvestris en el noroeste de España. Se midieron un total de 155 parcelas permanentes en masas de Pinus sylvestris en Galicia, 183 parcelas de Pinus pinaster en Galicia y en Asturias y 325 parcelas de Pinus radiata en ambas regiones para describir sus distribuciones diamétricas. Los parámetros de la función Weibull fueron estimados por las aproximaciones de los Momentos y Máxima Verosimilitud, los de la función SB de Johnson por los estimadores condicionados de Máxima Verosimilitud y por el método de Knoebel y Burkhart, y los de la función beta por el método basado en los Momentos de la distribución. Las funciones beta y SB de Johnson fueron ligeramente superiores a la función Weibull en las masas de Pinus pinaster; las funciones SB de Johnson y beta fueron más precisas en los mejores ajustes en las masas de Pinus radiata, y los mejores resultados de las funciones Weibull y SB de Johnson fueron ligeramente superiores a los de la función beta en las masas de Pinus sylvestris. No obstante, las tres funciones son apropiadas para estas masas siempre que se elija un valor de localización y método de estimación de los parámetros apropiadoThe present study was financially supported by the Gobierno del Principado de Asturias with the projects: “Estudio del crecimiento y producción en pinares regulares de Pinus radiata D. Don. en Asturias (PC04- 57)” and “Estudio del crecimiento y producción de Pinus pinaster Ait. en Asturias (CN-07-094)”; and by the Comisión Interministerial de Ciencia y Tecnología (CICYT) and the Comisión Europea with the projects: “Repoblación y gestión selvícola de Pino radiata y Pino de Oregón en Galicia (1FD97-0585-C03-03)” and “Crecimiento y evolución de masas de pinar en Galicia (AGL2001-3871-C02-01)”S

Crecimiento y distribución de biomasa aérea en clones de castaño híbrido a edad temprana

Se presentan los resultados de la medición en 228 ejemplares de castaños híbridos de 20 clones distintos en vivero, de edades comprendidas entre 4 y 7 años. Se realizaron muestreos destructivos para caracterizar las principales potencialidades de los clones en lo que se refiere a crecimiento y distribución de la biomasa aérea (fuste y ramas). Así, se elaboró una tarifa de biomasa total (peso seco), conjunta para todos los clones, en cuyo ajuste las mejores variables fueron el diámetro en la base y el diámetro normal, con R2 = 0,87 y REMC = 0,61 kg árbol-1. Además, se establecieron unos rankings de clones según su capacidad para obtener: — Una mayor capacidad de ramificación (medida mediante la biomasa de ramas), por su influencia en la aptitud para producción de fruto. — Una mayor producción de biomasa del fuste y del crecimiento en diámetro y altura, por su influencia en la aptitud para uso forestal maderableBOIBEL FORESTAL S.L.(proyectos “SOUTONOVO: cooperación para o desenvolvemento dun novo proceso integrado de talladía do castiñeiro”, “INTEGRACASTANEA: Proxecto de integración vertical do castiñeiro: da mellora xenética ás producións finais”

A comparison of estimation methods for fitting Weibull and Johnson’s SB functions to pedunculate oak (Quercus robur) and birch (Betula pubescens) stands in northwest Spain

<p><em>Aim of study:</em> In this study we compared the accuracy of the Weibull and the Johnson’s S_B functions for describing diameter distributions in pedunculate oak (<em>Quercus robur</em> L.) and birch (<em>Betula pubescens </em>Ehrh.) stands.</p><p><em>Area of study: </em>Galicia (Northwest Spain).</p><p><em>Material and Methods: </em>A total of 172 diameter distributions in pedunculate oak and 202 in birch stands were finally evaluated. We compared the accuracy of three commonly used estimation methods of the Weibull and four estimation methods of the Johnson’s S_B functions for describing these diameter distributions.</p><p><em>Main results. </em>For <em>Quercus robur </em>L. stands, the most suitable methods were the Percentiles followed by Maximum Likelihood for the Weibull PDF and the method of Moments for the Johnson’s S_B PDF. For <em>Betula pubescens </em>Ehrh. stands, the best fits obtained with the Percentiles and Maximum Likelihood methods were also superior to the method of Moments, whereas the Conditional Maximum Likelihood and method of Moments provided the best results for the Johnson’s S_B PDF, depending on the statistic and the value of the location parameter considered.</p><p><em>Research highlights:</em> Both distributions were suitable. The results were better for pedunculate oak than for birch stands.</p><p><strong>Keywords:</strong> Knoebel and Burkhart; location parameter; percentiles; maximum likelihood; moments; mode.</p