Modelling diameter distribution of Tetraclinis articulata in Tunisia using normal and Weibull distributions with parameters depending on stand variables

doi:10.3832/ifor1688-008

Modelling diameter distribution of Tetraclinis articulata in Tunisia using normal and Weibull distributions with parameters depending on stand variables

Tahar Sghaier⁽¹⁾ , Isabel Cañellas⁽²⁾, Rafael Calama⁽²⁾, Mariola Sánchez-González⁽²⁾

iForest - Biogeosciences and Forestry, Volume 9, Issue 5, Pages 702-709 (2016)
doi: https://doi.org/10.3832/ifor1688-008
Published: May 17, 2016 - Copyright © 2016 SISEF

Research Articles

PDF Version

Full Text

Citation

The objective of this study was to evaluate the effectiveness of both Normal and two-parameter Weibull distributions in describing diameter distribution of Tetraclinis articulata stands in north-east Tunisia. The parameters of the Weibull function were estimated using the moments method and maximum likelihood approaches. The data used in this study came from temporary plots. The three diameter distribution models were compared firstly by estimating the parameters of the distribution directly from individual tree measurements taken in each plot (parameter estimation method), and secondly by predicting the same parameters from stand variables (parameter prediction method). The comparison was based on bias, mean absolute error, mean square error and the Reynolds’ index error (as a percentage). On the basis of the parameter estimation method, the Normal distribution gave slightly better results, whereas the Weibull distribution with the maximum likelihood approach gave the best results for the parameter prediction method. Hence, in the latter case, the Weibull distribution with the maximum likelihood approach appears to be the most suitable to estimate the parameters for reducing the different comparison criteria for the distribution of trees by diameter class in Tetraclinis articulata forests in Tunisia.

Keywords

Diameter Class Model, Normal Distribution, Weibull Distribution, Maximum Likelihood Approach, Moments Method, Tetraclinis articulata

Authors’ address

(1)

Institut National de Recherches en Génie Rural, Eaux et Forêts (INRGREF), B.P. 10, Avenue Hédi Karray 2080, Ariana (Tunisia)

(2)

INIA-CIFOR, Ctra A Coruña. km 7.5, 28040 Madrid (Spain)

Corresponding author

Tahar Sghaier
sghaier.tahar@iresa.agrinet.tn

Citation

Sghaier T, Cañellas I, Calama R, Sánchez-González M (2016). Modelling diameter distribution of Tetraclinis articulata in Tunisia using normal and Weibull distributions with parameters depending on stand variables. iForest 9: 702-709. - doi: 10.3832/ifor1688-008

Academic Editor

Chris Eastaugh

Paper history

Received: Apr 25, 2015
Accepted: Dec 21, 2015

First online: May 17, 2016
Publication Date: Oct 13, 2016
Publication Time: 4.93 months

Open Access

This article is distributed under the terms of the Creative Commons Attribution-Non Commercial 4.0 International (https://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Breakdown by View Type

(Waiting for server response...)

Article Usage

Total Article Views: 46425
(from publication date up to now)

Breakdown by View Type
HTML Page Views: 39388
Abstract Page Views: 1910
PDF Downloads: 3935
Citation/Reference Downloads: 40
XML Downloads: 1152

Web Metrics
Days since publication: 3110
Overall contacts: 46425
Avg. contacts per week: 104.49

Article Citations

Article citations are based on data periodically collected from the Clarivate Web of Science web site
(last update: Feb 2023)

Total number of cites (since 2016): 9
Average cites per year: 1.13

(no Plumx Metrics available for this paper)

Publication Metrics

by Dimensions ^©

Articles citing this article

List of the papers citing this article based on CrossRef Cited-by.

(1)

Alvarez González JG (1997)
Estudio de distribuciones diamétricas en masas regulares de Pinus pinaster Ait. en Galicia. [Diameter distribution studies of Pinus pinaster Ait. in Galicia]. PhD thesis, Universidad Politécnica de Madrid, ETS de Ingenieros de Montes, Madrid, Spain, pp. 270.
Gscholar

(2)

Bailey RL, Dell TR (1973)
Quantifying diameter distributions with the Weibull function. Forest Science 19: 97-104.
Gscholar

(3)

Ben Mansoura A, Garchi S (2001)
Caractérisation de la croissance et de la régénération du Thuya par une technique modifiée de mesure de distances. [Characterization of the growth and the regeneration of the Thuya by a modified technique of distances measurement]. Les Annales de l’INRGREF, Numéro spécial 2001: 54-76.
Gscholar

(4)

Binoti DHB, Binoti MLMS, Leite HG, Fardin L, Oliveira JC (2012)
Probability density functions for description of diameter distribution in thinned stands of Tectona grandis. Cerne, Lavras 18 (2): 185-196.
CrossRef | Gscholar

(5)

Bliss CI, Reinker KA (1964)
A log normal approach to diameter distributions in even-aged stands. Forest Science 10: 350-360.
Gscholar

(6)

Burk TE, Newberry JD (1984)
A simple algorithm for moment-based recovery of Weibull distribution parameters. Forest Science 30 (2): 329-332.
Online | Gscholar

(7)

Borders BE, Souter RA, Bailey RI, Ware KD (1987)
Percentile-based distributions characterize forest stands tables. Forest Science 33 (2): 570-576.
Online | Gscholar

(8)

Calama R, Sánchez-González M, Garchi S, Ammari Y, Cañellas I, Sghaier T (2012)
Towards the sustainable management of thuya (Tetraclinis articulata (Vahl.) Mast.) forests in Tunisia: models for main tree attributes. Forest Systems 21 (2): 210-217.
CrossRef | Gscholar

(9)

Campos JCC, Leite HG (2009)
Mensuração florestal: perguntas e respostas. [Forest measurements: questions and answers] (3rd edn). Universidad Federal de Viçosa, Viçosa, MG, Brazil, pp. 548.
Gscholar

(10)

Cao QV (2004)
Predicting parameters of a Weibull function for modelling diameter distributions. Forest Science 50: 682-685.
Online | Gscholar

(11)

Cao QV, McCarty SM (2006)
News methods for estimating parameters of Weibull functions to characterize future diameter distributions in forest stands. In: Proceedings of the “13th Biennial Southern Silvicultural Research Conference”. General Technical Report SRS-92, Southern Research Station, USDA Forest Service, Asheville, NC, USA, pp. 338-340.
Gscholar

(12)

Charco J (1999)
El bosque mediterráneo en el norte de África: biodiversidad y lucha contra la desertificación. [The Mediterranean forest in North Africa: biodiversity and fight against the desertification]. Ed. Mundo Árabe e Islam - AECI, Madrid, Spain, pp. 370.
Gscholar

(13)

Clutter JL, Bennett FA (1965)
Diameter distribution in old-field slash pine plantations. Report no. 13, Georgia Forest Research Council, Macon, GA, USA, pp. 9.
Gscholar

(14)

Condés S (1997)
Simulación de parcelas arboladas con datos del II Inventario Forestal Nacional [Simulation of plots hoisted with data of the II National Forest Inventory]. PhD thesis, Universidad Politécnica de Madrid, ETS de Ingenieros de Montes, Madrid, Spain, pp. 616.
Gscholar

(15)

Dagnelie P (1998)
Statistique théorique et appliquée. Tome 1: Statistique descriptive et base de l’inférence statistique. [Descriptive statistics and basis of the statistical inference]. De Boeck, Bruxelles, Belgium, pp. 508.
Gscholar

(16)

DGF (1995)
Résultats du premier inventaire forestier national en Tunisie [Results of the first national forest inventory in Tunisia]. Direction Générale des Forêts, Tunisie, pp. 88.
Gscholar

(17)

DREF (2002)
Thuya: importance écologique et économique. [Thuya: Ecological and economic importance]. Terre et Vie 52: 4.
Gscholar

(18)

El-Mouridi M, Laurent T, Famiri A, Kabouchi B, Alméras T, Calchéra G, El Abid A, Ziani M, Gril J, Hakam A (2011)
Caractérisation physique du bois de la loupe de Thuya (Tetraclinis articulata (Vahl) Masters). [Physical characterization of the magnifying glass wood of the Thuya (Tetraclinis articulata (Vahl) Masters)]. Physical Chemical News 59: 57-64.
Online | Gscholar

(19)

Esteve-Selma J, Martinez-Fernandez J, Hernández I, Montávez JP, Lopez JJ, Calvo JF, Robledano F (2010)
Effects of climatic change on the distribution and conservation of Mediterranean forests: the case of Tetraclinis articulata in the Iberian Peninsula. Biodiversity and Conservation 19: 3809-3825.
CrossRef | Gscholar

(20)

Eerikäinen K, Maltamo M (2003)
A percentile based basal area diameter distribution model for predicting the stand development of Pinus kesiya plantations in Zambia and Zimbabwe. Forest Ecology and Management 172: 109-124.
CrossRef | Gscholar

(21)

Fonseca T, Marques C, Parresol BR (2009)
Describing maritime pine diameter distributions with Johnson’s SB distribution using a new all-parameter recovery approach. Forest Science 55 (4): 367-373.
Online | Gscholar

(22)

Frazier JR (1981)
Compatible whole-stand and diameter distribution models for loblolly pine. PhD thesis, School of Forestry and Wildlife, Virginia Polytechnic Institute and State University, Blackburg, VA, USA, pp. 125.
Gscholar

(23)

Gorgoso JJ (2003)
Caracterización de las distributions diametricas de Betula alba L. en Galicia. [Characterization of diameter distribution of Betula alba L. in Galicia]. PhD thesis, Universidad Santiago de Compostela, Chile, pp. 176.
Gscholar

(24)

Gorgoso JJ, Alvarez González JG, Rojo A, Grandas-Arias JA (2007)
Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Investigation Agraria Sistemas Recursos Forestales 16 (2): 113-123.
CrossRef | Gscholar

(25)

Gorgoso JJ, Rojo A, Camara-Obregon A, Dieguez-Aranda U (2012)
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. Forest Systems 21 (3): 446-459.
CrossRef | Gscholar

(26)

García-Guëmes C, Cañadas N, Montero G (2002)
Modelización de la distribución diamétrica de las masas de Pinus pinea L. de Valladolid (España) mediante la función de Weibull. [Modelling diameter distribution of Pinus pinea L. stands in Valladolid (Spain) by using Weibull function]. Investigation Agraria Sistemas Recursos Forestales 11: 264-282.
Gscholar

(27)

Hafley WL, Schreuder HT (1977)
Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research 4: 481-487.
CrossRef | Gscholar

(28)

Jonhson NL, Kotz S (1970)
Distribution in statistics: continuous univariate distributions. Houghton Mifflin Co, Boston, MA, USA, vol 2, pp. 306.
Gscholar

(29)

Lejeune P (1994)
Construction d’un modèle de répartition des arbres par classes de grosseur pour les plantations d’épicéa commun (Picea abies L Karst) en Ardenne belge. [Construction of a distribution model of trees by diameter classes for the common spruce (Picea abies L Karst) plantations in Belgian Ardenne]. Annals of Forest Science 51: 53-65.
CrossRef | Gscholar

(30)

Lei Y (2008)
Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis). Journal of Forest Science 54 (12): 566-571.
Online | Gscholar

(31)

Leite HG, Binoti DHB, Guimarães DP, Silva MLM, Garcia SLR (2010)
Avaliação do ajuste das funções Weibull e hiperbólica a dados de povoamentos de eucalipto submetidos a desbaste. [Evaluation of Weibull and hyperbolic functions for fitting data from eucalyptus stands under thinning]. Revista Árvore, Viçosa 34 (2): 305-311.
CrossRef | Gscholar

(32)

Mabvurira D, Maltamo M, Kangas A (2002)
Predicting and calibrating diameter distributions of Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe. New Forests 23: 207-223.
CrossRef | Gscholar

(33)

Mateus A, Tomé M (2011)
Modelling the diameter distribution of eucalyptus plantations with Johnson’s SB probability density function: parameters recovery from a compatible system of equations to predict stand variables. Annals of Forest Science 68: 325-335.
CrossRef | Gscholar

(34)

Maltamo M, Puumalainen J, Päivinen R (1995)
Comparison of Beta and Weibull functions for modelling basal area diameter distributions in stands of Pinus sylvestris and Picea abies. Scandinavian Journal of Forest Research 10: 284-295.
CrossRef | Gscholar

(35)

Merganic J, Sterba H (2006)
Characterization of diameter distribution using the Weibull function: method of moments. European Journal of Forest Research 125: 427-439.
CrossRef | Gscholar

(36)

Nabil MA (1989)
Essai de synthèse sur la végétation et la phyto-écologie tunisiennes. I - Elément de botanique et de phyto-écologie. [Synthesis assay on the Tunisian vegetation and phytoecology. I - Botany and phytoecology element] (vol. 4-6). Faculté des Sciences, Tunis, Tunisia, pp. 247.
Gscholar

(37)

Nanang DM (1998)
Suitability of the normal, log-normal and Weibull distributions for fitting diameter distributions of neem plantations in Northern Ghana. Forest Ecology and Management 103: 1-7.
CrossRef | Gscholar

(38)

Nanos N, Montero G (2002)
Spatial prediction of diameter distributions models. Forest Ecology and Management 161: 147-158.
CrossRef | Gscholar

(39)

Nelson TC (1964)
Diameter distribution and growth of loblolly pine. Forest Science 10: 105-115.
Online | Gscholar

(40)

Nogueira GS, Leite HG, Campos JCC, Carvalho AF, Souza AL (2005)
Modelo de distribuição diamétrica para povoamentos de Eucalyptus sp. submetidos a desbaste [Diametric distribution model for thinned Eucalyptus sp. stands]. Revista Árvore, Viçosa 29 (4): 579-589.
CrossRef | Gscholar

(41)

Palahi M, Pukkala T, Trasobares A (2006)
Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function. Forestry 79 (5): 553-562.
CrossRef | Gscholar

(42)

Palahi M, Pukkala T, Blasco E, Trasobares A (2007)
A comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modelling diameter distribution of forest stands in Catalonia (north-east of Spain). European Journal of Forest Research 126 (4): 563-571.
CrossRef | Gscholar

(43)

Reynolds MR, Burk TE, Huang WC (1988)
Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Science 34: 373-399.
Online | Gscholar

(44)

Sevillano Marco E, Fernández-Manso A, Castedo-Dorado F (2009)
Development and application of a growth model for Pinus radiata D. Don plantations El Bierzo (Spain). Investigation Agraria Sistemas Recursos Forestales 18 (1): 64-80.
Gscholar

(45)

Sghaier T, Palm R (2002)
Répartition des arbres et des volumes par classes de grosseurs dans les peuplements de pin d’Alep (Pinus halepensis Mill.) en Tunisie. [Distribution of trees and volumes by diameter classes of the Aleppo pine (Pinus halepensis Mill.) stands in Tunisia]. Annals of Forest Science 59: 293-300.
CrossRef | Gscholar

(46)

Sghaier T, Tomé M, Tomé J, Sánchez-González M, Cañellas I, Calama R (2013)
Distance-independent individual tree diameter-increment model for Thuya (Tetraclinis articulata (VAHL.) MAST.) stands in Tunisia. Forest Systems 22 (3): 433-441.
CrossRef | Gscholar

(47)

Sghaier T, Sánchez-González M, Garchi S, Ammari Y, Cañellas I, Calama R (2015)
Developing a stand based growth and yield model for thuya (Tetraclinis articulata (Vahl) Mast) in Tunisia. iForest - Biogeosciences and Forestry 9 (1): 79-88.
CrossRef | Gscholar

(48)

Tenbergen B, Günster A, Schreiber KF (1995)
Harvesting runoff: the minicatchment technique - An alternative to irrigated tree plantations in semiarid regions. Ambio 24 (2): 72-76.
Gscholar

(49)

Zhang L, Packard KC, Liu C (2003)
A comparison of estimation methods for fitting Weibull and Johnson’s SB distributions to mixed spruce-fir stands in northeastern North America. Canadian Journal of Forest Research 33: 1340-1347.
CrossRef | Gscholar

iForest - Biogeosciences and Forestry

Contents

Search

Journal Info

Journal Subjects and Fields

For Authors

For Reviewers

For Readers

SISEF Publishing

Search iForest Contents