Keywords
growth space
Stand Density Index
stochastic frontier regression
Reineke
How to Cite
##article.highlights##
- Density was analyzed for mixed-species stands at UMAFOR 1005 “Santiago Papasquiaro y Anexos” in Durango, Mexico.
- Reineke’s model adjust to the density of mixed-species stands
- The stochastic frontier regression with normal-truncated approach models best the maximum density line.
- The density management diagram helps to prescribe thinning in mixed-species stands.
- Thinning can be applied with cutting intensities greater than 30 %.
Abstract
Introduction: Stand density affects productivity and the structure and functions of forests.
Objectives: To compare maximum density lines for mixed-species forests adjusted with Ordinary least Squares (OLS) and Stochastic Frontier Regression (SFR); and generate a density management diagram (DMD) to prescribe thinning.
Materials and methods: The data was obtained in mixed-species stands from the Forest Management Unit 1005 “Santiago Papasquiaro y Anexos” in Durango, Mexico. The density-size relationship was established using the Reineke’s model. The maximum density line was adjusted with OLS and SFR, the latter with the half-normal (H-N), normal-exponential (N-E) and normal-truncated (N-T) approaches. The DMD was constructed with the SFR equation with the normal-truncated distribution approach.
Results and discussion: The maximum density line, modeled through SFR with N-T approach showed better fit to the upper limit of the maximum density of the mixed-species stand data. DMD suggests that thinning for these stands can be applied with high cutting intensities, contrary to conventional practices, where rarely more than 30 % of the basal area or volume is cut.
Conclusion: The maximum density line for mixed-species forests in Durango, Mexico, was generated with stochastic frontier regression, as a normal-truncated model.
References
Aigner, D., Lovell, C. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21–37. doi: https://doi.org/10.1016/0304-4076(77)90052-5
Bi, H., Wan, G., & Turvey, N. D. (2000). Estimating the self-thinning boundary line as a density-dependent stochastic biomass frontier. Ecology, 81(6), 1477–1483. doi: https://doi.org/10.1890/0012-9658(2000)081[1477:etstbl]2.0.co;2
Burkhart, H. E. (2013). Comparison of maximum size–density relationships based on alternate stand attributes for predicting tree numbers and stand growth. Forest Ecology and Management, 289, 404–408. doi: https://doi.org/10.1016/j.foreco.2012.10.041
Cao, Q. V., & Dean, T. J. (2008). Using segmented regression to model the density–size relationship in direct-seeded slash pine stands. Forest Ecology and Management, 255(3-4), 948–952. doi: https://doi.org/10.1016/j.foreco.2007.10.004
Cao, Q. V., Dean, T. J., & Baldwin, V. C. (2000). Modeling the size-density relationship in direct-seeded slash pine stands. Forest Science, 46(3), 317–321. Retrieved from https://pdfs.semanticscholar.org/879c/bf449903b84b34cce8898c4b171beb562d94.pdf
Chen, K., Kang, H. M., Bai, J., Fang, X. W., & Wang, G. (2008). Relationship between the virtual dynamic thinning line and the self‐thinning boundary line in simulated plant populations. Journal of Integrative Plant Biology, 50(3), 280–290. doi: https://doi.org/10.1111/j.1744-7909.2007.00618.x
Chisman, H., & Schumacher, F. (1940). On the tree-area ratio and certain of its applications. Journal of Forestry, 38(4), 311–317.
Coelli, T. J., Rao, D. S. P., O'Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. New York, USA: Springer Science & Business Media.
Comeau, P. G., White, M., Kerr, G., & Hale, S. E. (2010). Maximum density-size relationships for Sitka spruce and coastal Douglas-fir in Britain and Canada. Forestry, 83(5), 461–468. doi: https://doi.org/10.1093/forestry/cpq028
Curtis, R. O. (1970). Stand density measures: An interpretation. Forest Science, 16(4), 403–414.
Daniel, T. W., Helms, J. A., & Baker, F. S. (1979). Principles of silviculture. New York, NY, USA: McGraw-Hill Book Company.
del Río, M., Pretzsch, H., Alberdi, I., Bielak, K., Bravo, F., Brunner, A., …Bravo-Oviedo, A. (2015). Characterization of the structure, dynamics, and productivity of mixed-species stands: review and perspectives. European Journal of Forest Research, 135(1), 23–49. doi: https://doi.org/10.1007/s10342-015-0927-6
Drew, T. J., & Flewelling, J. W. (1979). Stand density management: an alternative approach and its application to Douglas-fir plantations. Forest Science, 25(3), 518–532.
García, E. M. (1981). Modificaciones al sistema de clasificación climática de Kóppen. México: UNAM.
García, O. (2012). Self-thinning limits in two and three dimensions. Mathematical and Computational Forestry & Natural-Resource Sciences (MCFNS), 4(2), 66–72. Retrieved from http://mcfns.net/index.php/Journal/article/view/144/MCNFS-4.2_66
Gilmore, D. W., O'Brien, T. C., & Hoganson, H. M. (2005). Thinning red pine plantations and the Langsaeter hypothesis: a northern Minnesota case study. Northern Journal of Applied Forestry, 22(1), 19–26. Retrieved from https://www.researchgate.net/publication/233515610_Thinning_Red_Pine_Plantations_and_the_Langsaeter_Hypothesis_A_Northern_Minnesota_Case_Study
Hibbs, D. E. (1987). The self-thinning rule and red alder management. Forest Ecology and Management, 18(4), 273–281. doi: https://doi.org/10.1016/0378-1127(87)90131-9
Jondrow, J., Lovell, C. A. K., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics, 19(2-3), 233–238. doi: https://doi.org/10.1016/0304-4076(82)90004-5
Krajicek, J. E., Brinkman, K. A., & Gingrich, S. F. (1961). Crown competition. A measure of density. Forest Science, 7(1), 35–42. Retrieved from http://cmapspublic3.ihmc.us/rid=1N4TSFQX6-GWW4BN-14PZ/Crown%20competition%20-%20A%20measure%20of%20density.pdf
Kumbhakar, S. C., & Lovell, C. K. (2003). Stochastic frontier analysis. New York, USA: Cambridge University Press.
Langsaeter, A. (1941). Om tynning i enaldret gran-og furuskog. Meddelelser fra Det norske Skogforsøksvesen, 8, 131–216. Retrieved from http://www.skogoglandskap.no/filearchive/medd_dns_8_om_tynning_i_enaldret_gran_og_furuskog.pdf
Long, J. N., & Shaw, J. D. (2005). A density management diagram for even-aged ponderosa pine stands. Western Journal of Applied Forestry, 20(4), 205–215.
Long, J. N., & Shaw, J. D. (2012). A density management diagram for even-aged Sierra Nevada mixed-conifer stands. Western Journal of Applied Forestry, 27(4), 187–195. doi: https://doi.org/10.5849/wjaf.11-036
Long, J. N., & Vacchiano, G. (2013). A comprehensive framework of forest stand property–density relationships: perspectives for plant population ecology and forest management. Annals of Forest Science, 71(3), 325–335. doi: https://doi.org/10.1007/s13595-013-0351-3
McCarthy, J. W., & Weetman, G. (2007). Self-thinning dynamics in a balsam fir (Abies balsamea (L.) Mill.) insect-mediated boreal forest chronosequence. Forest Ecology and Management, 241(1-3), 295–309. doi:10.1016/j.foreco.2007.01.001
Newton, P. F. (1997). Stand density management diagrams: Review of their development and utility in stand-level management planning. Forest Ecology and Management, 98(3), 251–265. doi: https://doi.org/10.1016/s0378-1127(97)00086-8
Pretzsch, H. (2009). Forest dynamics, growth and yield. Berlin, Germany: Springer.
Pretzsch, H., & Biber, P. (2005). A re-evaluation of Reineke's rule and stand density index. Forest Science, 51(4), 304–320.
Quiñonez-Barraza, G., de los Santos-Posadas, H. M., Cruz-Cobos, F., Velázquez-Martínez, A., Ángeles-Pérez, G., & Ramírez-Valverde, G. (2015). Índice de sitio con polimorfismo complejo para masas forestales de Durango, México. Agrociencia, 49(4), 439–454. Retrieved from http://www.scielo.org.mx/pdf/agro/v49n4/v49n4a7.pdf
Reineke, L. H. (1933). Perfecting a stand-density index for even-aged forests. Journal of Agricultural Research, 46(7), 627–638. Retrieved from https://naldc.nal.usda.gov/download/IND43968212/PDF
Reyes-Hernandez, V., Comeau, P. G., & Bokalo, M. (2013). Static and dynamic maximum size–density relationships for mixed trembling aspen and white spruce stands in western Canada. Forest Ecology and Management, 289, 300–311. doi: https://doi.org/10.1016/j.foreco.2012.09.042
Santiago-García, W., de los Santos-Posadas, H. M., Ángeles-Pérez, G., Valdez-Lazalde, J. R., del Valle-Paniagua, D. H., & Corral-Rivas, J. J. (2013). Auto-aclareo y guías de densidad para Pinus patula mediante el enfoque de regresión de frontera estocástica. Agrociencia, 47, 75–89. Retrieved from http://www.scielo.org.mx/pdf/agro/v47n1/v47n1a7.pdf
Smith, D. M., Larson, B. C., Kelty, M. J., & Ashton, P. M. S. (1997). The practice of silviculture: applied forest ecology. USA: John Wiley and Sons, Inc.
Statistical Analysis System (SAS Institute Inc.). (2011). SAS/ETS® 9.3 User's Guide. Cary, NC, USA: Author.
Sterba, H., & Monserud, R. A. (1993). The maximum density concept applied to uneven-aged mixed-species stands. Forest Science, 39(3), 432–452. Retrieved from https://www.researchgate.net/publication/233494358_The_Maximum_Density_Concept_Applied_to_Uneven-Aged_Mixed-Species_Stands
Torres-Rojo, J. M., & Velázquez-Martínez , A. (2000). Indice de densidad relativa para rodales coetáneos mezclados. Agrociencia, 34(4), 497–507. Retrieved from https://www.researchgate.net/publication/308142004_RELATIVE_STAND_DENSITY_INDEX_FOR_MIXED_EVEN-AGED_STANDS
Wilson, F. (1946). Numerical expression of stocking in terms of height. Journal of Forestry, 44(10), 758–761.
Yoda, K., Tatuo, K., Husato, O., & Kazuo, H. (1963). Self-thinning in overcrowded pure stands under cultivated and natural conditions. Journal of Biology, 14, 107–129.
Zeide, B. (1985). Tolerance and self-tolerance of trees. Forest Ecology and Management, 13(3-4), 149–166. doi: https://doi.org/10.1016/0378-1127(85)90031-3
Zeide, B. (2004). Optimal stand density: a solution. Canadian Journal of Forest Research, 34(4), 846–854. doi:10.1139/x03-258
Zeide, B. (2005). How to measure stand density. Trees, 19(1), 1–14. doi: https://doi.org/10.1007/s00468-004-0343-x
Zhang, L., Bi, H., Gove, J. H., & Heath, L. S. (2005). A comparison of alternative methods for estimating the self-thinning boundary line. Canadian Journal of Forest Research, 35(6), 1507–1514. doi: https://doi.org/10.1139/x05-070
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) 2018 Revista Chapingo Serie Ciencias Forestales y del Ambiente