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Merchantable volume system for pedunculate oak in northwestern Spain

Un modèle pour l’estimation du volume commercialisable de chêne pédonculé dans le Nord-Ouest de l’Espagne

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Abstract

A model is required for accurate estimation of the merchantable volume of pedunculate oak (Quercus robur L.) trees in Galicia, northwestern Spain. Accordingly, the purpose of the present study was to obtain equations for predicting merchantable volumes and stem profiles of individual trees. For this reason, two compatible and four non-compatible volume systems were initially evaluated and fitted to data from 251 destructively sampled trees which were collected in stands located throughout the area of distribution of the species in Galicia. The outliers were removed to provide a data set of measurements from 3 090 sections, which was then available for fitting. A second-order continuous autoregressive error structure was used to account for autocorrelation. Comparison of the models was carried out using overall goodness-of-fit statistics and box plots of residuals against relative height or diameter class. The compatible volume system of Fang et al. [22] provided the best compromise in describing the stem profile and estimating merchantable height, merchantable volume and total volume and is therefore recommended for pedunculate oak stands in Galicia.

Résumé

Un modèle d’estimation précise du volume marchand du chêne pédonculé (Quercus robur L.) à l’échelle des individus en Galice au Nord-Ouest de l’Espagne était indispensable. En conséquence, cette étude a été réalisée pour obtenir des équations de prédiction du volume marchand et du profil de tronc d’arbres individuels. Pour cela, deux modèles compatibles et quatre modèles non compatibles de volume ont été analysés et comparés à un échantillon de 251 arbres récoltés dans des peuplements de la zone de distribution de l’espèce en Galice. Les données extrêmes ont été éliminées pour fournir un ensemble de 3 090 sections disponibles pour l’étude. Une structure d’erreur auto-régressive continue a été utilisée pour prendre en compte l’autocorrélation. La comparaison des modèles a été réalisée en utilisant les statistiques de meilleur ajustement et les nuages de points des résidus comparés aux classes de hauteur relative ou de diamètre. Le système de volume compatible de Fang et al. [22] a fourni le meilleur compromis pour la description du profil de tronc et l’estimation de la hauteur marchande, du volume marchand et du volume total et son usage est donc recommandé pour les peuplements de chêne pédonculé en Galice.

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References

  1. Avery T.E., Burkhart H.E., Forest measurements, 5th ed., McGraw-Hill, New York, 2002.

    Google Scholar 

  2. Balboa-Murias M.A., Rojo A., Álvarez J.G., Merino A., Carbon and nutrient stocks in mature Quercus robur L. stands in NW Spain, Ann. For. Sci. 63 (2006) 557–565.

    Article  CAS  Google Scholar 

  3. Barrio M., Álvarez Gonzalez J.G., Díaz-Maroto I.J., Elaboración de una tarifa con clasificación de productos para Quercus robur L. en Galicia basada en un modelo de volumen porcentual, Invest. Agrar.: Sist. Recur. For. 13 (2004) 506–517.

    Google Scholar 

  4. Barrio M., Diéguez-Aranda U., Site quality of pedunculate oak (Quercus robur L.) stands in Galicia (northwest Spain), Eur. J. For. Res. 124 (2005) 19–28.

    Google Scholar 

  5. Behre C.E., Preliminary notes on studies of tree form, J. For. 21 (1923) 507–511.

    Google Scholar 

  6. Belsey D.A., Conditioning diagnostics, collinearity and weak data in regression, John Wiley & Sons, Inc., New York, 1991.

    Google Scholar 

  7. Bi H., Trigonometric variable-form taper equations for Australian eucalyptus, For. Sci. 46 (2000) 397–409.

    Google Scholar 

  8. Brink C., Gadow K.v., On the use of growth and decay functions for modelling stem profiles, EDV in Medizin und Biologie 17 (1985) 20–27.

    Google Scholar 

  9. Bruce D., Wensel L.C., Modelling forest growth: approaches, definitions and problems, in: Ek A.R., Shifley S.R., Burke T.E. (Eds.), Forest Growth Modelling and Prediction Conference, USDA For. Ser. Gen. Tech. Rep. NC-120, 1988, p. 1–8.

  10. Bullock B.P., Burkhart H.E., Equations for predicting green weight of loblolly pine trees in the south, South. J. Appl. For. 27 (2003) 153–159.

    Google Scholar 

  11. Burkhart H.E., Cubic-foot volume of loblolly pine to any merchantable top limit, South. J. Appl. For. 1 (1977) 7–9.

    Google Scholar 

  12. Cailliez F., Estimación del volumen forestal y predicción del rendimiento, FAO, Roma, 1980.

    Google Scholar 

  13. Cao Q.V., Burkhart H.E., Max T.A., Evaluations of two methods for cubicfoot volume prediction of loblolly pine to any merchantable limit, For. Sci. 26 (1980) 71–80.

    Google Scholar 

  14. Castedo F., Modelo dinámico de crecimiento para las masas de Pinus radiata D. Don en Galicia. Simulation de alternativas selví-colas con inclusión del riesgo de incendio, Doctoral Thesis, Escola Politécnica Superior, University of Santiago de Compostela, 2004.

  15. Clark A., Thomas C.E., Weight equations for southern tree species. When are and what is needed, in: Daniels R.F., Dunhan P.H. (Eds.), Proceedings of the 1983 southern forest biomass workshop, USDA Forest Service, Southern Forest Experimental Station, 1984, pp. 100–106.

  16. Clutter J.L., Development of taper functions from variable-top merchantable volume equations, For. Sci. 26 (1980) 117–120.

    Google Scholar 

  17. Corral-Rivas J., Diéguez-Aranda U., Castedo F., Corral S., A merchantable volume system for major pine species in El Salto, Durango (Mexico). For. Ecol. Manage. 238 (2007) 118–129.

    Article  Google Scholar 

  18. Demaerschalk J., Converting volume equations to compatible taper equations, For. Sci. 18 (1972) 241–245.

    Google Scholar 

  19. Díaz-Fernández P.M., Jiménez P., Martín S., De Tuero Y., Reyna M., Gil L., Regiones de procedencia de Quercus robur L., Quercus petraea (Matt.) Liebl, y Quercus humillis (Miller), MAPA, Madrid, 1995.

    Google Scholar 

  20. Díaz-Maroto I.J., Vila-Lameiro P., Silva-Pando F.J., Autoécologie des chaînes de Quercus robur L. en Galicie (Espagne), Ann. For. Sci. 62 (2005) 737–749.

    Article  Google Scholar 

  21. Diéguez-Aranda U., Castedo-Dorado F., Álvarez-González J.G., Rojo A., Compatible taper function for Scots pine (Pinus sylvestris L.) plantations in north-western Spain, Can. J. For. Res. 36 (2006) 1190–1205.

    Article  Google Scholar 

  22. Fang Z., Borders B.E., Bailey R.L., Compatible volume-taper models for loblolly and slash pine based on a system with segmentedstem form factors, For. Sci. 46 (2000) 1–12.

    Google Scholar 

  23. Furnival G.M., An index for comparing equations used in constructing volume tables, For. Sci. 7 (1961) 337–341.

    Google Scholar 

  24. Goulding C.J., Murray J., Polynomial taper equations that are compatible with tree volume equations, N. Z. J. For. Sci. 5 (1976) 313–322

    Google Scholar 

  25. Gregoire T.G., Schabenberger O., Barrett J.P., Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements, Can. J. For. Res. 25 (1995) 137–156.

    Article  Google Scholar 

  26. Gregoire T.G., Schabenberger O., A non-linear mixed-effects model to predict cumulative bole volume of standing trees, J. Appl. Stat. 23 (1996) 257–271.

    Article  Google Scholar 

  27. Harvey A.C., Estimating regression models with multiplicative heteroscedasticity, Econometrica 44 (1976) 461–465.

    Article  Google Scholar 

  28. Hirsch R.P., Validation samples, Biometrics, 47 (1991) 1193–1194.

    PubMed  CAS  Google Scholar 

  29. Huang S., Yang Y., Wang Y., A critical look at procedures for validating growth and yield models, in: Amaro A., Reed D., Soares P. (Eds.), Modelling forest systems, CAB International, Wallingford, Oxfordshire, UK, 2003, 271–293.

    Google Scholar 

  30. Judge G.G., Carter R., Griffiths W.E., Lutkepohl H., Lee T.C., Introduction to the theory and practice of econometrics, John Wiley & Sons, New York, 1988.

    Google Scholar 

  31. Kozak A., A variable-exponent taper equation, Can. J. For. Res. 18 (1988) 1363–1368.

    Article  Google Scholar 

  32. Kozak A., Effects of multicollinearity and autocorrelation on the variableexponent taper functions, Can. J. For. Res. 27 (1997) 619–629.

    Article  Google Scholar 

  33. Kozak A., My last words on taper equations, For. Chron. 80 (2004) 507–515.

    Google Scholar 

  34. Kozak A., Kozak R.A., Does cross validation provide additional information in the evaluation of regression models? Can. J. For. Res. 33 (2003) 976–987.

    Article  Google Scholar 

  35. McTague J.P., Bailey R.L., Simultaneous total and merchantable volume equations and a compatible taper function for loblolly pine, Can. J. For. Res. 17 (1987) 87–92.

    Article  Google Scholar 

  36. Muhairwe C.K., Taper equations for Eucalyptus pilularis and Eucalyptus grandis for the north coast in New South Wales, Australia, For. Ecol. Manage. 113 (1999) 251–269.

    Article  Google Scholar 

  37. Myers R.H., Classical and modern regression with applications, 2nd ed., Duxbury Press, Belmont, California, 1990.

    Google Scholar 

  38. Neter J., Kutner M.H., Nachtsheim C.J., Wasserman W., Applied linear statistical models, 4th ed., McGraw-Hill, New York, 1996.

    Google Scholar 

  39. Newnham R., Variable-form taper functions for four Alberta tree species, Can. J. For. Res. 22 (1992) 210–223.

    Article  Google Scholar 

  40. Parresol B.R., Additivity of nonlinear biomass equations, Can. J. For. Res. 31 (2001) 865–878.

    Article  Google Scholar 

  41. Pretzsch H., Biber P., Durský J., Gadow K.v., Hasenauer H., Kändler G., Kenk G., Kublin E., Nagel J., Pukkala T., Skovsgaard J.P., Sodtke R., Sterba H., Recommendations for standardized documentation and further development of forest growth simulators, Forstw. Cbl. 121 (2002) 138–151.

    Article  Google Scholar 

  42. Rawlings J.O., Sastry G.P., Dickey D.A., Applied Regression Analysis: A research tool, Springer-Verlag, New York, 1998

    Book  Google Scholar 

  43. Reed D., Green E., Compatible stem taper and volume ratio equations, For. Sci. 30 (1984) 977–990.

    Google Scholar 

  44. Riemer T., Gadow K.v., Sloboda B., Ein Modell zur Beschreibung von Baumschäften, Allg. Forst-Jagdztg. 166 (1995) 144–147.

    Google Scholar 

  45. Rose C.E., Lynch T.B., Estimating parameters for tree basal area growth with a system of equations and seemingly unrelated regressions, For. Ecol. Manage. 148 (2001) 51–61.

    Article  Google Scholar 

  46. Ryan T.P., Modern regression methods, John Wiley & Sons, New York, 1997.

    Google Scholar 

  47. SAS Institute Inc., SAS/STAT® 9.1.2, User’s Guide, Cary, NC: SAS Institute Inc, 2004.

    Google Scholar 

  48. SAS Institute Inc., SAS/ETS® 9.1.2. User’s Guide, Cary, NC: SAS Institute Inc., 2004.

    Google Scholar 

  49. SAS Institute Inc., SAS OnlineDoc® 9.1.2, Cary, NC: SAS Institute Inc., 2004.

  50. Spurr S.H., Forest Inventory, The Ronald Press Co., New York, 1952.

    Google Scholar 

  51. Tarp-Johansen M.J., Skovsgaard J.P., Madsen S.F., Johannsen V.K., Skovgaard I., Compatible stem taper and stem volume functions for oak (Quercus robur L. and Quercus petraea (Matt.) liebl.) in Denmark, Ann. Sci. For. 54 (1997) 577–595.

    Article  Google Scholar 

  52. Tasissa G., Burkhart H.E., Amateis R.L., Volume and taper equations for thinned and unthinned loblolly pine trees in Cutover, site-prepared plantations, South. J. Appl. For. 21 (1997) 146–152.

    Google Scholar 

  53. Teshome T., A ratio method for predicting stem merchantable volume and associated taper equations for Cupressus lusitanica, Ethiopia, For. Ecol. Manage. 204 (2005) 171–179.

    Article  Google Scholar 

  54. Tomé M., Ribeiro F., Soares P., O modelo Globulus 2.1, Universidade Técnica de Lisboa-ISA, GIMREF, 2001.

  55. Trincado G., Gadow K.v., Zur Sortimentschätzung stehender Laubbäume, Cent.bl. Gesamte Forstwes. 113 (1996) 27–38.

    Google Scholar 

  56. Trincado G., Gadow K.v., Tewari V.P., Comparison of three stem profile equations for Quercus robur L. South Afr. For. J. 177 (1996) 23–29.

    Google Scholar 

  57. Valdez J.R., Lynch T.B., Ecuaciones para estimar volumen comercial y total en rodales aclareados de pino patula en Puebla, México, Agrociencia 34 (2000) 747–758.

    Google Scholar 

  58. Van Deusen P.C., Sullivan A.D., Matney T.G., A prediction system for cubic foot volume of loblolly pine applicable through much of its range, South. J. Appl. For. 5 (1981) 186–189.

    Google Scholar 

  59. Van Deusen P.C., Matney T.G., Sulivan A.D., A compatible system for predicting the volume and diameter of sweetgum tree to any height, South. J. Appl. For. 6 (1982) 159–163.

    Google Scholar 

  60. Vanclay J.K., Skovsgaard J.P., Evaluating forest growth models, Ecol. Modell. 98 (1997) 1–12.

    Article  Google Scholar 

  61. West P.W., Ratkowsky D.A., Davis A.W., Problems of hypothesis testing of regressions with multiple measurements from individual sampling units, For. Ecol. Manage. 7 (1984) 207–224.

    Article  Google Scholar 

  62. Xunta de Galicia, O monte Galego en cifras, Dirección Xeral de Montes e Medio Ambiente Natural, Santiago de Compostela, 2001.

  63. Zellner A., An efficient method of estimating seemingly unrelated regressions and test for aggregation bias, J. Am. Stat. Assoc. 57 (1962) 348–368.

    Article  Google Scholar 

  64. Zimmerman D.L., Núñez-Antón V., Parametric modelling of growth curve data: An overview (with discussion), Test 10 (2001) 1–73.

    Article  Google Scholar 

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Authors and Affiliations

  1. Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela. Escuela Politécnica Superior, Campus universitario, 27002, Lugo, Spain

    Marcos Barrio Anta, Ulises Diéguez-Aranda & Juan Gabriel Álvarez González

  2. Departamento de Ingeniería Agraria, Universidad de León. Escuela Superior y Técnica de Ingeniería Agraria, Avenida de Astorga, 24400, Ponferrada, Spain

    Fernando Castedo-Dorado

  3. Institut für Waldinventur und Waldwachstum, Georg-August-Universität Göttingen, Büsgenweg 5, 37077, Göttingen, Germany

    Klaus von Gadow

  4. Departamento de Sistemas y Recursos Forestales, CIFOR-INIA, Carretera de la Coruña km. 7, 28080, Madrid, Spain

    Marcos Barrio Anta

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  1. Marcos Barrio Anta
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  2. Ulises Diéguez-Aranda
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  3. Fernando Castedo-Dorado
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  5. Klaus von Gadow
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Correspondence to Marcos Barrio Anta.

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Barrio Anta, M., Diéguez-Aranda, U., Castedo-Dorado, F. et al. Merchantable volume system for pedunculate oak in northwestern Spain. Ann. For. Sci. 64, 511–520 (2007). https://doi.org/10.1051/forest:2007028

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