The Richit-Richards family of distributions and its use in forestry

Johnson's SB and the logit-logistic are four-parameter distribution models that may be obtained from the standard normal and logistic distributions by a four-parameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logit-logistic with a one-parameter “standard Richards” distribution and transforming by a five-parameter Richards function, we obtain a new six-parameter distribution model, the “Richit-Richards”. The Richit-Richards includes the “logit-Richards”, the “Richit-logistic”, and the logit-logistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the Richit-Richards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the four-parameter logit-logistic for large data sets

Modélisation de la qualité des stations et de la croissance individuelle des arbres dans des peuplements purs et mélangés de Pinus brutia dans le nord-est de la Grèce

International audienc

Crescimento de eucalipto sob efeito de desfolhamento artificial

O objetivo deste trabalho foi avaliar os efeitos do desfolhamento total, realizado após o plantio e ao longo do primeiro ano de cultivo, sobre o crescimento de Eucalyptus grandis, desde a implantação até ao corte do povoamento. Foram avaliados cinco tratamentos: sem desfolhamento; um desfolhamento aos 56 dias após o plantio (DAP); dois desfolhamentos, aos 56 e 143 DAP; dois desfolhamentos, aos 56 e 267 DAP; e três desfolhamentos, aos 56, 143 e 278 DAP. Foram mensurados os diâmetros do tronco a 1,3 m e a altura total de 60 árvores por tratamento, em oito avaliações, do 21º ao 92º mês de cultivo. O crescimento médio em cada tratamento foi descrito por modelos de regressão não lineares e comparados por testes de identidade para comparar as tendências entre a testemunha e os demais tratamentos. O desfolhamento causou reduções significativas nas taxas de crescimento em diâmetro e altura das plantas, e diminuição expressiva no faturamento ao final da rotação, mesmo quando realizado uma única vez, no início do plantio. Maiores danos, no entanto, foram verificados após consecutivos desfolhamentos ao longo do primeiro ano de cultivo. A manutenção de áreas que tenham sofrido desfolhamento total na fase inicial de plantio pode tornar-se uma medida economicamente inviável.The objective of this work was to evaluate the effects of total defoliation at planting initial stages, and along the first year of cultivation, on Eucalyptus grandis growth, from planting to plantation cut. Five treatments were tested: without defoliation; one defoliation, at 56th day after planting (DAP); two defoliations, at 56th and 143th DAP; two defoliations, at 56th and 267th DAP; and three defoliations, at 56th, 143th and 278th DAP. Trunk diameter at 1.30-m height and the total height of 60 trees were measured from the 21st to the 92th cultivation months. The average growth of each treatment was described by nonlinear models and compared by identity tests in order to estimate the tendencies between control and the other treatments in each variable. Defoliation significantly reduces diameter of the trunk and height growth rates, and expressively decreases the income at the plantation cut. However, greater losses were verified after consecutive defoliation, along the first cultivation year. Maintaining areas that suffered severe defoliations at initial planting stages can become economically unfeasible

Individual tree growth models for eucalyptus in northern Brazil

The diameter and height growth model is one of three submodels used for simulating individual tree growth. In Brazil, there are few studies on the dimensional growth of individual trees be they native or exotic species, despite their potential. This study aimed to evaluate diameter and height growth models for individual trees for eucalyptus stands and to validate the best fitting model. Tree diameter and height data were obtained from 48 permanent plots of unthinned stands of Eucalyptus grandis × Eucalyptus urophylla hybrid located in northern Brazil. The evaluation of the diameter and height growth models was based on adjusted coefficient of determination, standard error of estimate as a percentage, trend, root mean square error and Akaike Information Criterion. Analysis also included distribution of residual percentage, statistical significance and signs of the coefficients. The Lundqvist-Korf model provided the most accurate estimates for diameter and height growth, in comparison with the other models, providing better statistical values, greater proximity to observed values and better distribution of residual percentages. The use of this type of model is feasible and can result in significant improvements in the accuracy of yield estimates