journal of forest science

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JOURNAL OF FOREST SCIENCE (continuation of the journal LESNICTVÍ-FORESTRY) An international journal published under the authorization by the Ministry of Agriculture and under the direction of the Czech Academy Agricultural Sciences Managing Editorial Board-Redakní rada Chairman - Pedseda Prof. Ing. VLADIMÍR CHALUPA, DrSc., Praha Members - lenové Prof. Ing. JIÍ BARTUNK, DrSc., Brno Ing. JOSEF BLE, CSc., Praha Prof. Ing. JOSEF GROSS, CSc., Praha Prof. Ing. JAROSLAV KOBLÍŽEK, CSc., Brno Prof. Ing. JAN KOUBA, CSc., Praha I g. VLADIMÍR KREMER, CSc., Praha . Ing. VÁCLAV LOCHMAN, CSc., Praha Ing. FRANTIŠEK ŠACH, CSc., Opono RNDr. STANISLAV VACEK, CSc., Opono Advisory Editorial Board - Mezinárodní poradní sbor Prof. Dr. DON J. DURZAN, Davis, California, U.S.A. Prof. Dr. LARS H. FRIVOLD, Aas, Norway Prof. Ing. MILAN HLADÍK, CSc., Zvolen, Slovak Republic Prof. Dr. ANDRZEJ JAWORSKI, Krakow, Poland Dr. KEITH W. MOSER, Tallahassee, U.S.A. Prof. Dr. HANS PRETZSCH, Freising, Germany Prof. Dr. FRANZ SCHMITHÜSEN, Zurich, Switzerland Prof. Dr. Dr. h. c. BRANISLAV SLOBODA, Göttingen, Germany Dr. JACK R. SUTHERLAND, Victoria, B.C., Canada Prof. Dr. SARA VON ARNOLD, Uppsala, Sweden Prof. Dr. NIKOLAJ A. VORONKOV, Moskva, Russia Executtive Editor-Vedoucí redaktorka Mgr. RADKA CHLEBEKOVÁ, Praha, Czech Rcpublic Aim and scope: The journal publishes original results of basic and applied research from all fields of forestry related to European forest ecosystems. Abstracts from the journal are comprised in the databases: Agris, LAB Abstracts, Czcch Agricultural Bibliography, Toxline Plus. Periodicity: The journal is published monthly (12 issues per year), Volume 47 appcaring in 2001. Acceptance of manuscripts: Two copies of manuscript should be addrcssed to: Mgr. Radka Chlebeková, executive editor, Institute of Agricultural and Food Information, Slezská 7, 120 56 Praha 2, tcl.: + 420 2 27 O1 03 55, fax: + 420 2 27 01 0l l6, e-mail: forcst@uzpi.cz. The day the manuscript reaches the editor for the first time is given upon publication as the date of receipt. Subscription information: Subscription orders can be entered only by calendar year (January-Deccmber) and should be sent to: Institute of Agricultural and Food Information, Slezská 7, 120 56 Praha 2. Subscription price for 2001 is 195 USD (Europe), 214 USD (overseas). Up-to-date information are available at address http://www.u zpi.cz © Institute of Agricultural and Food Information, Prague 2001 Mezinárodní vdecký asopis vydávaný z povení Ministerstva zemdlství eské republiky a pod gescí eské akademie zemdlských vd Odborná nápl: asopis publikuje pvodní výsledky základního a aplikovaného výzkumu ze všech obor lesnictví, mající vztah k evropským lesním ekosystémm. Abstrakty z asopisu jsou zahrnuty v tchto dat abázích: Agris, CAB Abstracts, Czech Agricultural Bibliography, Toxline Plus. Periodicita: asopis vychází msín (12x ron), roník 97 vychází v roce 2001. Pijímání rukopis: Rukopisy ve dvou vyhotoveních je teba zaslat na adresu redakce: Mgr. Radka Chlebeková, vedoucí redaktorka, Ústav zemdlských a potravináských informací, Slezská 7, l20 56 Praha 2, tel.: + 420 27 O1 03 55, fax: + 420 2 27 01 01 16, c-mail: forest@uzpi.cz. Den doruení rukopisu do redakce je publikován jako datum pijetí k publikaci. Informace o pedplatném: Objednávky na pedplatné jsou pijímány pouze na celý rok (leden-prosinec) a mly by být zaslány na adresu: Ústav zem dlských a potravináských informací, Slezská 7, 120 56 Praha 2. Cena pedplatného pro rok 2001 je 1 128 K. Aktuální informace najdete na URL adrese http://www.uzpi.cz F 132
JOURNAL O OREST SCIENCE, 47, 2001 (7): 285–293 Simultaneous modelling of stand volume yield, dominant height and basal area growth models L.YUANCAI 1 , C. P. MARQUES 2 , J. M. BENTO 2 1 Research Institute of Forest Resource Information Technique, Chinese Academy of Forestry, Beijing, China 2 Department of Forestry, Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal ABSTRACT: Forest growth and yield models are often composed of a system of compatible, interdependent and analytically related equations rather than of a single equation. Most forest researchers have recognized that the forest stand dynamics system should be described by a system of simultaneous and interdependent equations. The two- and three-stage least squares (2SLS and 3SLS) and seemingly unrelated regression (SUR) techniques from econometrics have been widely used to estimate the coefficients of forest growth and yield model system. This study analyzes a system of three interdependent equations for predicting the future stand volume yield, the future stand dominant height and the future stand basal area for eucalyptus plantations as an integrated system given by initial stand conditions. The coefficients of the system are estimated from Eucalyptus globulus Labill. stands in the Central inland of Portugal by using 3SLS, SUR and OLS, respectively. The three methods are evaluated and compared on some statistic indicators. The results indicate that there is a small difference between the three approaches in the particular case, but the system estimation methods perform better for a system of simultaneously interdependent equations in theory. Therefore, the appropriate system estimation approaches are recommended for estimating coefficients in simultaneously interdependent systems of forestry equations. Keywords: comparison; growth and yield model; simultaneous equation Modelling methodology of growth models at present is becoming increasingly sophisticated as forest biometricians put forward new biological rationale, advanced statistical techniques, and powerful computing technology to solve growth and yield prediction problems. An extensive variety of growth and yield models have been developed. However, growth and yield models, which describe forest stand dynamics by using data from permanent sample plots or inventory sample plots with real growth series, are often composed of a system of compatible, interdependent and analytically related equations (CLUTTER 1963; SULLIVAN, CLUTTER 1972; BOR- DERS, BAILEY 1986; BURKHART 1986; REED 1986; DANIELS, BURKHART 1988). Most forest researchers have recognized that there is a strong correlation and feedback mechanism between variables that are used to describe growth and yield relationships. Therefore, forest stand dynamics should be described by a simultaneous and interdependent system of equations rather than by separate and isolated individual equations. Financial support for this work was partially provided by the NSFC program (30070620). In forest biometrics, there are two categories of methods for estimating simultaneous and interdependent systems of equations. One method of estimating parameters in a system of equations is to fit one (or more) of the equations using Ordinary Least Squares (OLS) techniques and to solve for the coefficients in the other(s) by invoking the specified algebraic relationships between parameters (SULLI- VAN, CLUTTER 1972). This solution has obvious shortcomings. As the parameter estimates are stochastic, the final result will depend on the arbitrary choice which equation(s) is(are) fitted and which is(are) derived. Thus, BURKHART and SPRINZ (1984), REED and GREEN (1984), BYRNE and REED (1986), KNOEBEL et al. (1986) and REED (1986) simultaneously estimated the structural parameters by minimizing the squared error loss function, which brought about a substantial improvement for the total system. However, BORDERS and BAILEY (1986) and LEMAY (1990) indicated that estimates obtained by minimizing squared error loss functions may not be con- J. FOR. SCI., 47, 2001 (7): 285–293 285
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JOURNAL OF FOREST SCIENCE Volume 47
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