##article.highlights##
- The data analyzed correspond to Pinus arizonica and P. durangensis from mixed-species stands.
- The height-diameter at breast height relationship was expanded to the height-diameter-age relationship.
- The relationships were studied as a prediction and projection equation systems.
- The relationships showed significant accuracy in the evaluated fitting statistics.
- The equations can be used as input variables in growth and yield models.
Abstract
Introduction: Total height (H) and diameter at breast height (DBH) are important variables in forest inventory and they are the basis for growth and yield systems.
Objective: To generate three prediction and projection equation systems for Pinus arizonica Engelmann (Pa) and Pinus durangensis Martinez (Pd) in mixed stands in Durango, Mexico.
Materials and methods: The outside-bark DBH equations as functions of the inside-bark DBH were developed and the H-DBH relationship was extended to three relationships with the use of age (A): H-DBH, H-A and DBH-A. The equation systems of H-DBH-A were developed from a database of 46 and 66 stem analysis trees with 601 and 760 longitudinal measurements of Pa and Pd, respectively. The equations were fitted with apparently unrelated regression and Dummy variables approach with common and specific parameters.
Results and discussion: The relationships showed significant accuracy in the assessed fitting statistics (adjusted coefficient of determination, root mean square error, Akaike's information criterion, standard error of the estimate and bias). The inverse equations of the three relationships formed a global system of prediction and projection equations.
Conclusions: The equations are useful for predicting and projecting H and DBH and they can be used as input variables in growth and yield models.
References
Adame, P., del Río, M., & Cañellas, I. (2008). A mixed nonlinear height-diameter model for pyrenean oak (Quercus pyrenaica Willd.). Forest Ecology and Management, 256(1), 88‒98. doi: https://doi.org/10.1016/j.foreco.2008.04.006
Bailey, R. L., & Clutter, J. L. (1974). Base-age invariant polymorphic site curves. Forest Science, 20(2), 155‒159. doi: https://doi.org/10.1093/forestscience/20.2.155
Bi, H., Fox, J. C., Li, Y., Lei, Y., & Pang, Y. (2012). Evaluation of nonlinear equations for predicting diameter from tree height. Canadian Journal of Forest Research, 42(4), 789‒806. doi: https://doi.org/10.1139/x2012-019
Calama, R., & Montero, G. (2004). Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, 34(1), 150‒163. doi: https://doi.org/10.1139/x03-199
Carmean, W. H. (1972). Site index curves for upland oaks in the central states. Forest Science, 18(2), 109‒120. doi: https://doi.org/10.1093/forestscience/18.2.109
Cieszewski, C. J., & Bailey, R. L. (2000). Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes. Forest Science, 46(1), 116‒126. doi: https://doi.org/10.1093/forestscience/46.1.116
Cieszewski, C. J., Harrison, M., & Martin, S. W. (2000). Practical methods for estimating non-biased parameters in self-referencing growth and yield models. Retrieved from https://www.researchgate.net/profile/Stacey_Martin/publication/237633129_Practical_methods_for_estimating_non-biased_parameters_in_self-referencing_growth_and_yield_models/links/0046352cdb6b9c21df000000.pdf
Corral-Rivas, S., Álvarez-González, J. G., Crecente-Campo, F., & Corral-Rivas, J. J. (2014). Local and generalized height-diameter models with random parameters for mixed, uneven-aged forests in northwestern Durango, Mexico. Forest Ecosystems, 1(1), 2‒9. doi: https://doi.org/10.1186/2197-5620-1-6
Crecente-Campo, F., Corral-Rivas, J. J., Vargas-Larreta, B., & Wehenkel, C. (2014). Can random components explain differences in the height-diameter relationship in mixed uneven-aged stands? Annal of Forest Science, 71(1), 51‒70. doi: https://doi.org/10.1007/s13595-013-0332-6
Crecente-Campo, F., Tomé, M., Soares, P., & Diéguez-Aranda, U. (2010). A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management, 259(5), 943‒952. doi: https://doi.org/10.1016/j.foreco.2009.11.036
Diéguez-Aranda, U., Burkhart, H. E., & Amateis, R. L. (2006). Dynamic site model for loblolly pine (Pinus taeda L.) plantations in the United States. Forest Science, 52(3), 262‒272. doi: https://doi.org/10.1093/forestscience/52.3.262
Duan, G., Gao, Z., Wang, Q., & Fu, L. (2018). Comparison of different height-diameter modelling techniques for prediction of site productivity in natural uneven-aged pure stands. Forests, 9(2), 1‒18. doi: https://doi.org/10.3390/f9020063
Dyer, M. E., & Bailey, R. L. (1987). A test of six methods for estimating true heights from stem analysis data. Forest Science, 33(1), 3‒13. doi: https://doi.org/10.1093/forestscience/33.1.3
Fang, Z., & Bailey, R. L. (1998). Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110(1), 315‒327. doi: https://doi.org/10.1016/S0378-1127(98)00297-7
Fu, L., Lei, X., Sharma, R. P., Li, H., Zhu, G., Hong, L., . . . Tang, S. (2018). Comparing height-age and height-diameter modelling approaches for estimating site productivity of natural uneven-aged forests. Forestry: An International Journal of Forest Research, 91(4), 419‒433. doi: https://doi.org/10.1093/forestry/cpx049
García-Espinoza, G. G., Aguirre-Calderón, O. A., Quiñonez-Barraza, G., Alanís-Rodríguez, E., González-Tagle, M. A., & García-Magaña, J. J. (2019). Local-global and fixed-random parameters to model dominant height growth of Pinus pseudostrobus Lindley. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 25(1), 141‒156. doi: https://doi.org/10.5154/r.rchscfa.2018.06.047
García, E. (2004). Modificaciones al sistema de clasificación climática de Kóppen (5.a ed.). México: Universidad Autónoma Nacional de México, Instituto de Geografía.
Gómez-García, E., Diéguez-Aranda, U., Castedo-Dorado, F., & Crecente-Campo, F. (2014). A comparison of model forms for the development of height-diameter relationships in even-aged stands. Forest Science, 60(3), 560‒568. doi: https://doi.org/10.5849/forsci.12-099
Gonzalez-Benecke, C., Zhao, D., Samuelson, L., Martin, T., Leduc, D., & Jack, S. (2018). Local and general above-ground biomass functions for Pinus palustris trees. Forests, 9(6), 2‒17. doi: https://doi.org/doi.org/10.3390/f9060310
Gonzalez-Benecke, C. A., Gezan, S. A., Martin, T. A., Cropper, J. W. P., Samuelson, L. J., & Leduc, D. J. (2014). Individual tree diameter, height, and volume functions for Longleaf pine. Forest Science, 60(1), 43‒56. doi: https://doi.org/10.5849/forsci.12-074
Kearsley, E., Moonen, P. C., Hufkens, K., Doetterl, S., Lisingo, J., Boyemba, B. F., . . . Verbeeck, H. (2017). Model performance of tree height-diameter relationships in the central Congo Basin. Annals of Forest Science, 74(1), 2‒13. doi: https://doi.org/10.1007/s13595-016-0611-0
Lu, J., & Zhang, L. (2012). Geographically local linear mixed models for tree height-diameter relationship. Forest Science, 58(1), 75‒84. doi: https://doi.org/10.5849/forsci.09-123
MacPhee, C., Kershaw, J. A., Weiskittel, A. R., Golding, J., & Lavigne, M. B. (2018). Comparison of approaches for estimating individual tree height-diameter relationships in the Acadian forest region. Forestry: An International Journal of Forest Research, 91(1), 132‒146. doi: https://doi.org/10.1093/forestry/cpx039
Mehtätalo, L., de-Miguel, S., & Gregoire, T. G. (2015). Modeling height-diameter curves for prediction. Canadian Journal of Forest Research, 45(7), 826‒837. doi: https://doi.org/10.1139/cjfr-2015-0054
Misik, T., Antal, K., Kárász, I., & Tóthmérész, B. (2016). Nonlinear height-diameter models for three woody, understory species in a temperate oak forest in Hungary. Canadian Journal of Forest Research, 46(11), 1337‒1342. doi:https://doi.org/10.1139/cjfr-2015-0511
Ni, C., & Zhang, L. (2007). An analysis and comparison of estimation methods for self-referencing equations. Canadian Journal of Forest Research, 37(8), 1472‒1484. doi: https://doi.org/10.1139/X06-285
Paulo, J. A., Tomé, J., & Tomé, M. (2011). Nonlinear fixed and random generalized height-diameter models for Portuguese cork oak stands. Annals of Forest Science, 68(2), 295‒309. doi: https://doi.org/10.1007/s13595-011-0041-y
Pukkala, T., & Gadow, K. (2011). Managing forest ecosystems: Continuous cover forestry (2nd ed.). New York, USA: Springer Science & Business Media.
Quiñonez-Barraza, G., De los Santos-Posadas, H., M, Cruz-Cobos, F., Velázquez-Martínez, A., Ángeles-Pérez, G., & Ramírez-Valverde, G. (2015). Site index with complex polymorphism of forest stands in Durango, Mexico. Agrociencia, 49(4), 439‒454. Retrieved from https://www.colpos.mx/agrocien/Bimestral/2015/may-jun/art-7.pdf
Quiñonez-Barraza, G., Tamarit-Urias, J. C., Martínez-Salvador, M., García-Cuevas, X., Héctor, M., & Santiago-García, W. (2018). Maximum density and density management diagram for mixed-species forests in Durango, Mexico. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 24(1), 73‒90. doi: https://doi.org/10.5154/r.rchscfa.2017.09.05
Quiñonez-Barraza, G., Zhao, D., de los Santos-Posadas, H. M., Santiago-García, W., Tamarit-Urias, J. C., & Nájera-Luna, J. A. (2019). Compatible taper, volume, green weight, biomass and carbon concentrationsystem for Quercus sideroxyla Bonpl. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 25(1), 49‒69. doi: https://doi.org/10.5154/r.rchscfa.2018.06.050
Quiñonez-Barraza, G., Zhao, D., De los Santos Posadas, H. M., & Corral-Rivas, J. J. (2018). Considering neighborhood effects improves individual DBH growth models for natural mixed-species forests in Mexico. Annals of Forest Science, 75(3), 1‒11. doi: https://doi.org/10.1007/s13595-018-0762-2
Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany, 10(2), 290‒301. doi: https://doi.org/10.1093/jxb/10.2.290
Rijal, B., Weiskittel, A. R., & Kershaw, J. A. (2012). Development of regional height to diameter equations for 15 tree species in the North American Acadian Region. Forestry: An International Journal of Forest Research, 85(3), 379‒390. doi: https://doi.org/10.1093/forestry/cps036
Santos, F. M., Terra, G., Chaer, G. M., & Monte, M. A. (2018). Modeling the height-diameter relationship and volume of young African mahoganies established in successional agroforestry systems in northeastern Brazil. New Forests, 50, 389‒407. doi: https://doi.org/10.1007/s11056-018-9665-1
SAS Institute Inc. (2015). Base SAS 9.4® Procedures Guide: Statistical Procedure (3rd. ed.). Cary, NC, USA: Author.
Saunders, M. R., & Wagner, R. G. (2008). Height-diameter models with random coefficients and site variables for tree species of Central Maine. Annals of Forest Science, 65(2), 203. doi: https://doi.org/10.1051/forest:2007086
Sharma, M. (2016). Comparing height-diameter relationships of boreal tree species grown in plantations and natural stands. Forest Science, 62(1), 70‒77. doi: https://doi.org/10.5849/forsci.14-232
Vargas-Larreta, B., Castedo-Dorado, F., Álvarez-González, J. G., Barrio-Anta, M., & Cruz-Cobos, F. (2009). A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico). Forestry: An International Journal of Forest Research, 82(4), 445‒462. doi: https://doi.org/10.1093/forestry/cpp016
Wang, G. G. (1998). Is height of dominant trees at a reference diameter an adequate measure of site quality? Forest Ecology and Management, 112(1), 49‒54. doi: https://doi.org/10.1016/S0378-1127(98)00315-6
Wang, M., Borders, B. E., & Zhao, D. (2008). An empirical comparison of two subject-specific approaches to dominant heights modeling: The dummy variable method and the mixed model method. Forest Ecology and Management, 255(7), 2659‒2669. doi: https://doi.org/10.1016/j.foreco.2008.01.030
Wang, M., Kane, M. B., & Zhao, D. (2017). Correlation-regression analysis for understanding dominant height projection accuracy. Forest Science, 63(6), 549‒558. doi: https://doi.org/10.5849/FS-2016-092
Wang, X., Yu, D., Wang, S., Lewis, B. J., Zhou, W., Zhou, L., . . . Li, M.-H. (2017). Tree height-diameter relationships in the alpine treeline ecotone compared with those in closed forests on Changbai Mountain, northeastern China. Forests, 8(4), 1‒13. doi: https://doi.org/10.3390/f8040132
Zang, H., Lei, X., & Zeng, W. (2016). Height-diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models. Forestry: An International Journal of Forest Research, 89(4), 434‒445. doi: https://doi.org/10.1093/forestry/cpw022
Zellner, A. (1962). An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association, 57(298), 348‒368. doi: https://doi.org/10.1080/01621459.1962.10480664
Zimmerman, D. L., Núñez-Antón, V., Gregoire, T. G., Schabenberger, O., Hart, J. D., Kenward, M. G., . . . Vieu, P. (2001). Parametric modelling of growth curve data: an overview. Test, 10(1), 1‒73. doi: https://doi.org/10.1007/BF02595823

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