& Context Families of the Gumbel (type I), Fréchet (type II) and Weibull (type III) distributions can be combined in the generalized extreme value (GEV) family of distributions. Maximum and minimum values of diameters in forest stands can be used in forest modelling, mainly to define parameters of the functions used in diameter class models as well as in some practical cases, such as modelling maximum diameters for sawing and processing purposes. & Aims The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the distribution of the minimum and the maximum values of representative sets of tree diameter samples. Both of these functions were applied to the lower and upper values of the diameter distributions of the main forest species in northwest Spain: Quercus robur L., Betula pubescens Ehrh., Pinus radiata D. Don, Pinus pinaster Ait. and Pinus sylvestris L. & Methods Parameters of the Gumbel function were estimated using the mode and the moments of the distributions, and parameters of the Weibull function were estimated using the moments method.& Results In general, the Weibull distribution was the most suitable model for describing the maximum diameters. The mode method of the Gumbel yielded the best results for minimum diameters of birch and Monterrey pine. The Gumbel distribution, fitted by either the mode-or momentsbased methods, proved more suitable than the Weibull distribution for describing the minimum diameters in maritime pine and Scots pine stands. & Conclusion In some cases, better results were obtained with the Gumbel than the Weibull distribution for describing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first example of the application of the Gumbel distribution in forest modelling.
Site index curves were created for natural Aleppo pine (Pinus halepensis Mill.) stands in the Ebro Valley (northeastern Spain). Data were obtained from 54 felled dominant trees. The Generalized Algebraic Difference Approach (GADA) was used to fit 11 equations with a longitudinal data structure that included all possible growth intervals. Three statistical criteria were used for model comparison: root mean square error (RMSE), adjusted coefficient of determination (R2adj) and Akaike’s information criterion (AIC). Graphical evaluation of the data (plots of observed against predicted values and of residuals against predicted values) was also conducted. In addition, the root mean square error (RMSE) was plotted against age. Finally, fitted site index curves for different site qualities were superimposed on the profile plots of the stems analysed. The best reference age (60 years) was calculated from the relative error in the dominant height prediction. The Hossfeld IV model proved the most suitable for representing site index in the study area. Furthermore, only three site index curves (6, 10 and 14 m at 60 years) were suitable for classifying the entire study area because of the low productivity of the stands. These were compared with other site index curves developed for Spain and other countries, for the natural range of distribution of the species. Specific site index curves must be created for the study area, because the existing qualities and growth patterns are not well-represented in other models.
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