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Research Article | Open Access

Analysis of the inflection points of height-diameter models

Tzeng Yih Lama( ), Mark J. Duceyb
Department of Forest Resources Management, Faculty of Forestry, The University of British Columbia, 2045-2424 Main Mall, Vancouver, BC, V6T 1Z4 Canada
Department of Natural Resources and the Environment, University of New Hampshire, 114 James Hall, Durham, NH 03824, USA
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Abstract

The inflection point is an important feature of sigmoidal height-diameter (H-D) models. It is often cited as one of the properties favoring sigmoidal model forms. However, there are very few studies analyzing the inflection points of H-D models. The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset. The six models were the Wykoff (WYK), Schumacher (SCH), Curtis (CUR), Hossfeld Ⅳ (HOS), von Bertalanffy-Richards (VBR), and Gompertz (GPZ) models. The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution. The distributions of the estimated inflection points were similar between the two-parameter models WYK, SCH, and CUR, but were different between the three-parameter models HOS, VBR, and GPZ. GPZ produced some of the largest inflection points. HOS and VBR produced concave H-D curves without inflection points for 12.7% and 39.7% of the tree species. Evergreen species or decreasing shade tolerance resulted in larger inflection points. The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape. Furthermore, HOS could produce concave H-D curves for portions of the landscape. Based on the studied behaviors, the choice between two-parameter models may not matter. We recommend comparing several three-parameter model forms for consistency in estimated inflection points before deciding on one. Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one. Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

Keywords

ConcavityForest inventory and analysisGeneralized height-diameter modelsGrowth functionsHeight-diameter functionsMixed-effects modelingPoints of inflectionSpecies-specific models

References

 

Adame, P., del Río, M., Cañellas, I., 2008. A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.). For. Ecol. Manag. 256, 88–98. https://doi.org/10.1016/j.foreco.2008.04.006.
Crossref Google Scholar
 

Aishan, T., Halik, Ü., Betz, F., Gärtner, P., Cyffka, B., 2016. Modeling height–diameter relationship for Populus euphratica in the Tarim riparian forest ecosystem, Northwest China. J. For. Res. 27, 889–900. https://doi.org/10.1007/s11676-016-0222-5.
Crossref Google Scholar
 
Bechtold, W.A., Patterson, P.L., 2005. The Enhanced Forest Inventory and Analysis Program - National Sampling Design and Estimation Procedures. U.S. Department of Agriculture, Forest Service, Southern Research Station, Asheville, NC, USA.
 
Bell, J.F., Alexander, L.B., 1957. Application of the Variable Plot Method of Sampling Forest Stands. Oregon State Board of Forestry, Salem, OR, USA.
 

Bi, H., Fox, J.C., Li, Y., Lei, Y., Pang, Y., 2012. Evaluation of nonlinear equations for predicting diameter from tree height. Can. J. For. Res. 42, 789–806. https://doi.org/10.1139/x2012-019.
Crossref Google Scholar
 

Bronisz, K., Mehtätalo, L., 2020. Mixed-effects generalized height–diameter model for young silver birch stands on post-agricultural lands. For. Ecol. Manag. 460, 117901. https://doi.org/10.1016/j.foreco.2020.117901.
Crossref Google Scholar
 
Burnham, K.P., Anderson, D.R., 2002. Model Selection and Multimodel Inference, second ed. Springer-Verlag, New York, NY, USA.
 

Castedo-Dorado, F., Crecente-Campo, F., Álvarez-Álvarez, P., Barrio-Anta, M., 2009. Development of a stand density management diagram for radiata pine stands including assessment of stand stability. Forestry 82, 1–16. https://doi.org/10.1093/forestry/cpm032.
Crossref Google Scholar
 

Ciceu, A., Chakraborty, D., Ledermann, T., 2023. Examining the transferability of height–diameter model calibration strategies across studies. Forestry. https://doi.org/10.1093/forestry/cpad063.
Crossref Google Scholar
 
Coulston, J.W., Reams, G.A., 2004. The effect of blurred plot coordinates on interpolating forest biomass: a case study. In: Proceedings of the Joint Meeting of the 15th Annual Conference of the International Environmetrics Society and the 6th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences. The International Environmetrics Society, Portland, ME, USA.
 

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? Ann. For. Sci. 71, 51–70. https://doi.org/10.1007/s13595-013-0332-6.
Crossref Google Scholar
 

Curtis, R.O., 1967. Height-diameter and height-diameter-age equations for second-growth Douglas-Fir. For. Sci. 13, 365–375. https://doi.org/10.1093/forestscience/13.4.365.
Crossref Google Scholar
 

Ducey, M.J., 2012. Evergreenness and wood density predict height–diameter scaling in trees of the northeastern United States. For. Ecol. Manag. 279, 21–26. https://doi.org/10.1016/j.foreco.2012.04.034.
Crossref Google Scholar
 

Fang, Z., Bailey, R.L., 1998. Height–diameter models for tropical forests on Hainan Island in southern China. For. Ecol. Manag. 110, 315–327. https://doi.org/10.1016/S0378-1127(98)00297-7.
Crossref Google Scholar
 
Faraway, J.J., 2006. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, first ed. Chapman and Hall/CRC, Boca Raton, FL, USA.
 

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

Gao, H., Cui, K., von Gadow, K., Wang, X., 2023. Using functional traits to improve estimates of height–diameter allometry in a temperate mixed forest. Forests 14, 1604. https://doi.org/10.3390/f14081604.
Crossref Google Scholar
 

Gompertz, B., 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil. Trans. Roy. Soc. Lond. 115, 513–583.
Crossref Google Scholar
 

Greenhill, A.G., 1881. Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and the greatest height to which a tree of given proportions can grow. Proc. Camb. Phil. Soc. 4, 65–73.
Google Scholar
 

Han, Y., Lei, Z., Ciceu, A., Zhou, Y., Zhou, F., Yu, D., 2021. Determining an accurate and cost-effective individual height-diameter model for Mongolian pine on sandy land. Forests 12, 1144. https://doi.org/10.3390/f12091144.
Crossref Google Scholar
 

Huang, S., Price, D., Titus, S.J., 2000. Development of ecoregion-based height–diameter models for white spruce in boreal forests. For. Ecol. Manag. 129, 125–141. https://doi.org/10.1016/S0378-1127(99)00151-6.
Crossref Google Scholar
 

Huang, S., Titus, S.J., Wiens, D.P., 1992. Comparison of nonlinear height–diameter functions for major Alberta tree species. Can. J. For. Res. 22, 1297–1304. https://doi.org/10.1139/x92-172.
Crossref Google Scholar
 
Kershaw, J.A. Jr., Ducey, M.J., Beers, T.W., Husch, B., 2016. Forest Mensuration, fifth ed. John Wiley & Sons Ltd, West Sussex, UK.
Crossref
 

Kruchelski, S., Trautenmüller, J.W., Orso, G.A., Roncatto, E., Triches, G.P., Behling, A., de Moraes, A., 2022. Modeling of the height-diameter relationship in eucalyptus in integrated crop-livestock systems. Pesqui. Agropecu. Bras. 57, e02785. https://doi.org/10.1590/S1678-3921.pab2022.v57.02785.
Crossref Google Scholar
 

Lam, T.Y., Kershaw, J.A. Jr., Nur Hajar, Z.S., Abd Rahman, K., Weiskittel, A.R., Potts, M.D., 2017. Evaluating and modelling genus and species variation in height-todiameter relationships for Tropical Hill Forests in Peninsular Malaysia. Forestry 90, 268–278. https://doi.org/10.1093/forestry/cpw051.
Crossref Google Scholar
 
Lei, Y., Parresol, B.R., 2001. Remarks on Height-Diameter Modeling. U.S. Department of Agriculture, Forest Service, Southern Research Station, Asheville, NC, USA.
 

Lei, Y.C., Zhang, S.Y., 2004. Features and partial derivatives of Bertalanffy-Richards growth model in forestry. Nonlinear Anal. Model. Control 9, 65–73.
Crossref Google Scholar
 

Liu, S., Liu, Y., Li, G., Mou, C., 2023. Disentangling interspecific and intraspecific variability in height–diameter allometry of dominant tree species in the Rocky Mountains across broad spatial scales. Forestry 97, 363–375. https://doi.org/10.1093/forestry/cpad048.
Crossref Google Scholar
 

Long, S., Zeng, S., Liu, F., Wang, G., 2020. Influence of slope, aspect and competition index on the height-diameter relationship of Cyclobalanopsis glauca trees for improving prediction of height in mixed forests. Silva Fenn. 54, 10242. https://doi.org/10.14214/sf.10242.
Crossref Google Scholar
 

Lujan-Soto, J.E., Corral-Rivas, J.J., Aguirre-Calderón, O.A., Gadow, K. v., 2015. Grouping forest tree species on the Sierra Madre Occidental, Mexico. Allg. Forst-u J-Ztg. 186, 63–71.
Google Scholar
 

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 91, 132–146. https://doi.org/10.1093/forestry/cpx039.
Crossref Google Scholar
 

Marziliano, P.A., Tognetti, R., Lombardi, F., 2019. Is tree age or tree size reducing height increment in Abies alba Mill. at its southernmost distribution limit? Ann. For. Sci. 76, 1–12. https://doi.org/10.1007/s13595-019-0803-5.
Crossref Google Scholar
 

McMahon, T.A., 1973. Size and shape in biology. Science 179, 1201–1204. https://doi.org/10.1126/science.179.4079.1201.
Crossref Google Scholar
 

Mehtätalo, L., de-Miguel, S., Gregoire, T.G., 2015. Modeling height-diameter curves for prediction. Can. J. For. Res. 45, 826–837. https://doi.org/10.1139/cjfr-2015-0054.
Crossref Google Scholar
 
Miles, P.D., Smith, W.B., 2009. Specific Gravity and Other Properties of Wood and Bark for 156 Tree Species Found in North America. U.S. Department of Agriculture, Forest Service, Northern Research Station, Newtown Square, PA, USA.
Crossref
 

Nigul, K., Padari, A., Kiviste, A., Noe, S.M., Korjus, H., Laarmann, D., Frelich, L.E., Jõgiste, K., Stanturf, J.A., Paluots, T., Põldveer, E., Kängsepp, V., Jürgenson, H., Metslaid, M., Kangur, A., 2021. The possibility of using the Chapman–Richards and Näslund functions to model height–diameter relationships in hemiboreal old-growth forest in Estonia. Forests 12, 184. https://doi.org/10.3390/f12020184.
Crossref Google Scholar
 

Niinemets, Ü., Valladares, F., 2006. Tolerance to shade, drought, and waterlogging of temperate northern hemisphere trees and shrubs. Ecol. Monogr. 76, 521–547. https://doi.org/10.1890/0012-9615(2006)076[0521:TTSDAW]2.0.CO;2.
Crossref Google Scholar
 

O'Brien, S.T., Hubbell, S.P., Spiro, P., Condit, R., Foster, R.B., 1995. Diameters, height, crown, and age relationships in eight neotropical tree species. Ecology 76, 1926–1939. https://doi.org/10.2307/1940724.
Crossref Google Scholar
 

Özçelik, R., Yavuz, H., Karatepe, Y., Gürlevik, N., Kiriş, R., 2014. Development of ecoregion-based height-diameter models for 3 economically important tree species of southern Turkey. Turk. J. Agric. For. 38, 399–412. https://doi.org/10.3906/tar-1304-115.
Crossref Google Scholar
 

Paulo, J.A., Tomé, J., Tomé, M., 2011. Nonlinear fixed and random generalized height–diameter models for Portuguese cork oak stands. Ann. For. Sci. 68, 295–309. https://doi.org/10.1007/s13595-011-0041-y.
Crossref Google Scholar
 

Peschel, W., 1938. Mathematical methods for growth studies of trees and forest stands and the results of their application. Tharandter. Forstl. Jahrb. 89, 169–247.
Google Scholar
 

Pilli, R., Anfodillo, T., Carrer, M., 2006. Towards a functional and simplified allometry for estimating forest biomass. For. Ecol. Manag. 237, 583–593. https://doi.org/10.1016/j.foreco.2006.10.004.
Crossref Google Scholar
 
Pinheiro, J.C., Bates, D.M., 2000. Mixed-Effects Models in S and S-PLUS, first ed. Springer-Verlag, New York, USA.
Crossref
 
R Core Team, 2024. R: A Language and Environment for Statistical Computing. R. Foundation for Statistical Computing, Vienna, Austria.
 

Raptis, D.I., Kazana, V., Kazaklis, A., Stamatiou, C., 2021. Mixed-effects height–diameter models for black pine (Pinus nigra Arn.) forest management. Trees (Berl.) 35, 1167–1183. https://doi.org/10.1007/s00468-021-02106-x.
Crossref Google Scholar
 

Richards, F.J., 1959. A flexible growth function for empirical use. J. Exp. Bot. 10, 290–301. https://doi.org/10.1093/jxb/10.2.290.
Crossref Google Scholar
 

Schumacher, F.X., 1939. A new growth curve and its application to timber yield studies. J. Fr. 37, 819–820.
Google Scholar
 

Shen, J., Hu, Z., Sharma, R.P., Wang, G., Meng, X., Wang, M., Wang, Q., Fu, L., 2020. Modeling height–diameter relationship for poplar plantations using combinedoptimization multiple hidden layer back propagation neural network. Forests 11, 442. https://doi.org/10.3390/f11040442.
Crossref Google Scholar
 

Somers, G.L., Farrar Jr., R.M., 1991. Biomathematical growth equations for natural longleaf pine stands. For. Sci. 37, 227–244. https://doi.org/10.1093/forestscience/37.1.227.r.
Crossref Google Scholar
 

Temesgen, H., Hann, D.W., Monleon, V.J., 2007. Regional height–diameter equations for major tree species of Southwest Oregon. West. J. Appl. For. 22, 213–219. https://doi.org/10.1093/wjaf/22.3.213.
Crossref Google Scholar
 

Thomas, S.C., 1996. Relative size at onset of maturity in rain forest trees: a comparative analysis of 37 Malaysian species. Oikos 76, 145–154. https://doi.org/10.2307/3545756.
Crossref Google Scholar
 

Tjørve, K.M.C., Tjørve, E., 2017. The use of Gompertz models in growth analyses, and new Gompertz-model approach: an addition to the Unified-Richards family. PLoS One 12, e0178691. https://doi.org/10.1371/journal.pone.0178691.
Crossref Google Scholar
 

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 82, 445–462. https://doi.org/10.1093/forestry/cpp016.
Crossref Google Scholar
 
Weiskittel, A.R., Hann, D.W., Kershaw, J.A. Jr., Vanclay, J.K., 2011. Forest Growth and Yield Modeling, first ed. John Wiley & Sons Ltd, Chichester, UK.
Crossref
 

West, G.B., Brown, J.H., Enquist, B.J., 2001. A general model for ontogenetic growth. Nature 413, 628–631. https://doi.org/10.1038/35098076.
Crossref Google Scholar
 
Woudenberg, S.W., Conkling, B.L., O'Connell, B.M., LaPoint, E.B., Turner, J.A., Waddell, K.L., 2010. The Forest Inventory and Analysis Database: Database Description and Users Manual Version 4.0 for Phase 2. U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO, USA.
Crossref
 
Wykoff, W.R., Crookston, N.L., Stage, A.R., 1982. User's Guide to the Stand Prognosis Model. U.S. Department of Agriculture, Forest Service, Intermountain Forest & Range Experiment Station, Ogden, UT, USA.
Crossref
 

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 89, 434–445. https://doi.org/10.1093/forestry/cpw022.
Crossref Google Scholar
 

Zhang, X., Chhin, S., Fu, L., Lu, L., Duan, A., Zhang, J., 2019. Climate-sensitive tree height–diameter allometry for Chinese fir in southern China. Forestry 92, 167–176. https://doi.org/10.1093/forestry/cpy043.
Crossref Google Scholar
 

Zucchini, W., Schmidt, M., Gadow, K.v., 2001. A model for the diameter-height distribution in an uneven-aged beech forest and a method to assess the fit of such models. Silva Fenn. 35, 594. https://doi.org/10.14214/sf.594.
Crossref Google Scholar
Forest Ecosystems
Volume 11 Issue 4,
August 2024
Article number: 100202
DOI: 10.1016/j.fecs.2024.100202
Cite this article:
Lam TY, Ducey MJ. Analysis of the inflection points of height-diameter models. Forest Ecosystems, 2024, 11(4): 100202. https://doi.org/10.1016/j.fecs.2024.100202

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Received: 14 March 2024
Revised: 30 April 2024
Accepted: 03 May 2024
Published: 11 May 2024
© 2024 The Authors.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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