##article.highlights##
- Maximum size-density relationship (MSDR) without species ratio is linear and exponential.
- Maximum MSDR is also dependent on the species ratio in mixed forests.
- Size-density allometric coefficients relate species tolerance and self-tolerance.
- Shade tolerant species showed a negative estimated slope.
Abstract
Introduction: The maximum size-density relationship (MSDR) describes the dynamics of species-mixed stands, and it is essential in the implementation of silvicultural treatments for density control.
Objective: To analyze the influence of species composition on MSDR in mixed temperate forests of Nuevo San Juan Parangaricutiro, Michoacán, Mexico.
Materials and methods: MSDR was analyzed with a potential and an exponential model under two approaches with observations of mixed species stands. The first (E1) described the MSDR trajectory without taking into account the proportion of species and the second (E2) included the proportion of species in four groups: Pinus, Quercus, other conifers and broadleaves. Both approaches were analyzed with stochastic frontier regression (SFR) and quantile regression (QR).
Results and discussion: E1 results were favorable with the use of RC, as it showed a higher trajectory of the data to define MSDR in a linear and concave manner. In E2, the allometric coefficients of the size-density relationship for the four species groups were different and RC estimated the MSDR with species proportion adequately. In shade tolerant species (other conifers and broadleaves), the estimated slope was more negative compared to intolerant species (Pinus and Quercus).
Conclusions: For mixed forests, MSDR is adequately explained when it is dependent on species composition, because it influences the behavior of the maximum density line, useful for planning density management strategies in mixed forests.
References
Aguirre, A., del Río, M., & Condés, S. (2018). Intra-and inter-specific variation of the maximum size-density relationship along an aridity gradient in Iberian pinewoods. Forest Ecology and Management, 411, 90‒100. https://doi.org/10.1016/j.foreco.2018.01.017
Aigner, D., Lovell, C. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21‒37. https://doi.org/10.1016/0304-4076(77)90052-5
Andrews, C., Weiskittel, A., D'Amato, A. W., & Simons-Legaard, E. (2018). Variation in the maximum stand density index and its linkage to climate in mixed species forests of the North American Acadian Region. Forest Ecology and Management, 417, 90‒102. https://doi.org/10.1016/j.foreco.2018.02.038
Battese, G. E., & Corra, G. S. (1977). Estimation of a production frontier model: with application to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics, 21(3), 169‒179. https://doi.org/10.1111/j.1467-8489.1977.tb00204.x
Bi, H. (2004). Stochastic frontier analysis of a classic self‐thinning experiment. Austral Ecology, 29(4), 408‒417. https://doi.org/10.1111/j.1442-9993.2004.01379.x
Cao, Q. V., Dean, T. J., & Baldwin Jr, V. C. (2000). Modeling the size–density relationship in direct-seeded slash pine stands. Forest Science, 46(3), 317‒321. https://doi.org/10.1093/forestscience/46.3.317
Condés, S., Vallet, P., Bielak, K., Bravo-Oviedo, A., Coll, L., Ducey, M. J., Pach, M., Pretzsch, H., Sterba, H., Vayreda, J., & del Río, M. (2017). Climate influences on the maximum size-density relationship in Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) stands. Forest Ecology and Management, 385, 295‒307. https://doi.org/10.1016/j.foreco.2016.10.059
Dirección Técnica Forestal. (2017). Modificación al programa de manejo forestal, nivel avanzado para el aprovechamiento de recursos forestales maderables por incorporación de superficie. Comunidad Índigena de Nuevo San Juan Parangaricutiro, Michoacán, México.
de Prado, R. D., San Martín, R., Bravo, F., & de Aza, H. C. (2020). Potential climatic influence on maximum stand carrying capacity for 15 mediterranean coniferous and broadleaf species. Forest Ecology and Management, 460, 117824. https://doi.org/10.1016/j.foreco.2019.117824
del Río, M., Bravo-Oviedo, A., Ruiz-Peinado, R., & Condés, S. (2019). Tree allometry variation in response to intra-and inter-specific competitions. Trees, 33(1), 121‒138. https://doi.org/10.1007/s00468-018-1763-3
del Río, M., Pretzsch, H., Alberdi, I., Bielak, K., Bravo, F., Brunner, A., Condés, S., Ducey, M. J., Fonseca, T., Lüpke, N., Pach, M., Peric, S., Perot, T., Souidi, Z., Spathelf, P., Sterba, H., Tijardovic, M., Tomé, M., Vallet, P., & Bravo-Oviedo, A. (2016). Characterization of the structure, dynamics, and productivity of mixed-species stands: review and perspectives. European Journal of Forest Research, 135(1), 23‒49. https://doi.org/10.1007/s10342-015-0927-6
Ducey, M. J., & Knapp, R. A. (2010). A stand density index for complex mixed species forests in the northeastern United States. Forest Ecology and Management, 260(9), 1613‒1622. https://doi.org/10.1016/j.foreco.2010.08.014
Ducey, M. J., Woodall, C. W., & Bravo-Oviedo, A. (2017). Climate and species functional traits influence maximum live tree stocking in the Lake States, USA. Forest Ecology and Management, 386, 51‒61. https://doi.org/10.1016/j.foreco.2016.12.007
Kimsey, M. J., Shaw, T. M., & Coleman, M. D. (2019). Site sensitive maximum stand density index models for mixed conifer stands across the Inland Northwest, USA. Forest Ecology and Management, 433, 396‒404. https://doi.org/10.1016/j.foreco.2018.11.013
Koenker, R. (2019). Quantile regression in R: a vignette. https://cran.r-project.org/web/packages/quantreg/vignettes/rq.pdf
Koenker, R., & Bassett Jr., G. (1978). Regression quantiles. Society Econometrica: Journal of the Econometric, 46(1), 33‒50. https://doi.org/10.2307/1913643
Long, J. N., & Daniel, T. W. (1990). Assessment of growing stock in uneven-aged stands. Western Journal of Applied Forestry, 5(3), 93‒96. https://doi.org/10.1093/wjaf/5.3.93
Meeusen, W., & van den Broeck, J. (1977). Technical efficiency and dimension of the firm: some results on the use of frontier production functions. Empirical Economics, 2(2), 109‒122. https://doi.org/10.1007/BF01767476
Ningre, F., Ottorini, J.-M., & Le Goff, N. (2016). Modeling size-density trajectories for even-aged beech (Fagus silvatica L.) stands in France. Annals of forest science, 73(3), 765‒776. https://doi.org/10.1007/s13595-016-0567-0
Pretzsch, H., & Biber, P. (2005). A re-evaluation of Reineke's rule and stand density index. Forest Science, 51(4), 304‒320. https://doi.org/10.1093/forestscience/51.4.304
Pretzsch, H., & Biber, P. (2016). Tree species mixing can increase maximum stand density. Canadian Journal of Forest Research, 46(10), 1179‒1193. https://doi.org/10.1139/cjfr-2015-0413
Quiñonez-Barraza, G., & Ramírez-Maldonado, H. (2019). Can an exponential function be applied to the asymptotic density–size relationship? Two wew stand-density indices in mixed-species forests. Forests, 10(1), 9. https://doi.org/10.3390/f10010009
Quiñonez-Barraza, G., Tamarit-Urias, J. C., Martínez-Salvador, M., García-Cuevas, X., Santos-Posadas, H. 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. https://doi.org/10.5154/r.rchscfa.2017.09.056
R Core Team. (2020). R: A language and environment for statistical computing [software]. R Foundation for Statistical Computing. https://www.R-project.org/
Reineke, L. H. (1933). Perfection a stand-density index for even-aged forest. Journal of Agricultural Research, 46, 627‒638.
Reyes-Hernández, 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. https://doi.org/10.1016/j.foreco.2012.09.042
Rivoire, M., & Moguedec, L. G. (2012). A generalized self-thinning relationship for multi-species and mixed-size forests. Annals of Forest Science, 69(2), 207‒219. https://doi.org/10.1007/s13595-011-0158-z
Salas‐Eljatib, C., & Weiskittel, A. R. (2018). Evaluation of modeling strategies for assessing self‐thinning behavior and carrying capacity. Ecology and Evolution, 8(22), 10768-10779. https://doi.org/10.1002/ece3.4525
Schütz, J.-P., & Zingg, A. (2010). Improving estimations of maximal stand density by combining Reineke’s size-density rule and the yield level, using the example of spruce (Picea abies (L.) Karst.) and European Beech (Fagus sylvatica L.). Annals of Forest Science, 67(5), 507. https://doi.org/10.1051/forest/2010009
Solomon, D. S., & Zhang, L. (2002). Maximum size–density relationships for mixed softwoods in the northeastern USA. Forest Ecology and Management, 155(1), 163‒170. https://doi.org/10.1016/S0378-1127(01)00556-4
Sterba, H., & Monserud, R. A. (1993). The maximum density concept applied to uneven-aged mixed-species stands. Forest Science, 39(3), 432‒452. https://doi.org/10.1093/forestscience/39.3.432
Tang, X., Pérez-Cruzado, C., Vor, T., Fehrmann, L., Álvarez-González, J. G., & Kleinn, C. (2016). Development of stand density management diagrams for Chinese fir plantations. Forestry: An International Journal of Forest Research, 89(1), 36‒45. https://doi.org/10.1093/forestry/cpv024
Tian, D., Bi, H., Jin, X., & Li, F. (2021). Stochastic frontiers or regression quantiles for estimating the self-thinning surface in higher dimensions? Journal of Forestry Research, 32(4), 1515‒1533. https://doi.org/10.1007/s11676-020-01196-6
Torres-Rojo, J. M., & Velázquez-Martínez, A. (2000). Indice de densidad relativa para rodales coetáneos mezclados. Agrociencias, 34(4), 497‒507. https://agrociencia-colpos.mx/index.php/agrociencia/article/view/54
VanderSchaaf, C. L. (2010). Estimating individual stand size–density trajectories and a maximum size–density relationship species boundary line slope. Forest Science, 56(4), 327‒335. https://doi.org/10.1093/forestscience/56.4.327
VanderSchaaf, C. L., & Burkhart, H. E. (2007). Comparison of methods to estimate Reineke's maximum size-density relationship species boundary line slope. Forest Science, 53(3), 435‒442. https://doi.org/10.1093/forestscience/53.3.435
VanderSchaaf, C. L., & Burkhart, H. E. (2008). Using segmented regression to estimate stages and phases of stand development. Forest Science, 54(2), 167‒175. https://doi.org/10.1093/forestscience/54.2.167
VanderSchaaf, C. L., & Burkhart, H. E. (2012). Development of planting density–specific density management diagrams for loblolly pine. Southern Journal of Applied Forestry, 36(3), 126‒129. https://doi.org/10.5849/sjaf.10-043
Weiskittel, A., Gould, P., & Temesgen, H. (2009). Sources of variation in the self-thinning boundary line for three species with varying levels of shade tolerance. Forest Science, 55(1), 84‒93. https://doi.org/10.1093/forestscience/55.1.84
Woodall, C. W., Miles, P. D., & Vissage, J. S. (2005). Determining maximum stand density index in mixed species stands for strategic-scale stocking assessments. Forest Ecology and Management, 216(1), 367‒377. https://doi.org/10.1016/j.foreco.2005.05.050
Zeide, B. (1985). Tolerance and self-tolerance of trees. Forest Ecology and Management, 13(3-4), 149‒166. https://doi.org/10.1016/0378-1127(85)90031-3
Zeide, B. (1995). A relationship between size of trees and their number. Forest Ecology and Management, 72(2-3), 265‒272. https://doi.org/10.1016/0378-1127(94)03453-4
Zeide, B. (2005). How to measure stand density. Trees, 19(1), 1‒14. https://doi.org/10.1007/s00468-004-0343-x
Zeide, B. (2010). Comparison of self-thinning models: an exercise in reasoning. Trees, 24(6), 1117‒1126. https://doi.org/10.1007/s00468-010-0484-z
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. https://doi.org/10.1139/x05-070

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