A comparison of artificial neural networks and regression modeling techniques for predicting dominant heights of Oriental spruce in a mixed stand

Keywords: dominant height, mixed-effects, dummy variable, machine learning, growth curve, biological interpretation


Aim of study: This paper introduces comparative evaluations of artificial neural network models and regression modeling techniques based on some fitting statistics and desirable characteristics for predicting dominant height.

Area of study: The data of this study were obtained from Oriental spruce (Picea orientalis L.) felled trees in even-aged and mixed Oriental spruce and Scotch pine (Pinus sylvestris L.) stands in the northeast of Türkiye.

Material and methods: A total of 873 height-age pairs were obtained from Oriental spruce trees in a mixed forest stand. Nonlinear mixed-effects models (NLMEs), autoregressive models (ARM), dummy variable method (DVM), and artificial neural networks (ANNs) were compared to predict dominant height growth.

Main results: The best predictive model was NLME with a single random parameter (root mean square error, RMSE: 0.68 m). The results showed that NLMEs outperformed ARM (RMSE: 1.09 m), DVM in conjunction with ARM (RMSE: 1.09 m), and ANNs (RMSE: from 1.11 to 2.40 m) in the majority of the cases. Whereas considering variations among observations by random parameter(s) significantly improved predictions of dominant height, considering correlated error terms by autoregressive correlation parameter(s) enhanced slightly the predictions. ANNs generally underperformed compared to NLMEs, ARM, and DVM with ARM.

Research highlights: All regression techniques fulfilled the desirable characteristics such as sigmoidal pattern, polymorphism, multiple asymptotes, base-age invariance, and inflection point. However, ANNs could not replicate most of these features, excluding the sigmoidal pattern. Accordingly, ANNs seem insufficient to assure biological growth assumptions regarding dominant height growth.


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Aertsen W, Kint V, Van Orshoven J, Özkan K, Muys B, 2010. Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests. Ecol Modell 221: 1119-1130. https://doi.org/10.1016/j.ecolmodel.2010.01.007

Bailey RL, Clutter JL, 1974. Base-age invariant polymorphic site curves. For Sci 20: 155-159.

Brosofske KD, Froese RE, Falkowski MJ, Banskota A, 2014. A review of methods for mapping and prediction of inventory attributes for operational forest management. For Sci 60: 733-756. https://doi.org/10.5849/forsci.12-134

Calama R, Montero G, 2004. Interregional nonlinear height diameter model with random coefficients for stone pine in Spain. Can J For Res 34: 150-163. https://doi.org/10.1139/x03-199

Calegario N, Daniels RF, Maestri R, Neiva R, 2005. Modeling dominant height growth based on nonlinear mixed-effects model: a clonal eucalyptus plantation case study. For Ecol Manag 204: 11-21. https://doi.org/10.1016/j.foreco.2004.07.051

Carmean WH, 1972. Site index curves for upland oaks in the Central States. For Sci 18: 109-120.

Castaño-Santamaría J, Crecente-Campo F, Fernández-Martínez JL, Barrio-Anta M, Obeso JR, 2013. Tree height prediction approaches for uneven-aged beech forests in northwestern Spain. For Ecol Manag 307: 63-73. https://doi.org/10.1016/j.foreco.2013.07.014

Chapman DG, 1961. Statistical problems in population dynamics. Proc 4th Symp on Mathematical Statistics and Probability, Univ of California Press, Berkeley, pp. 153-168.

Cieszewski CJ, 2002. Comparing fixed-and variable-base-age site equations having single versus multiple asymptotes. For Sci 48: 7-23.

Cieszewski CJ, Bailey R, 2000. Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes. For Sci 46: 116-126.

Cieszewski CJ, Harrison M, Martin SW, 2000. Practical methods for estimating non-biased parameters in self-referencing growth and yield models. University of Georgia PMRC-TR 7.

Clutter JL, 1961. Development of compatible analytic models for growth and yield of loblolly pine. Ph.D. dissertation, Duke University, Durham, NC, USA.

Corral-Rivas JJ, Álvarez González JG, Ruíz González AD, von Gadow K, 2004. Compatible height and site index models for five pine species in El Salto, Durango (Mexico). For Ecol Manage 201(2-3): 145-160. https://doi.org/10.1016/j.foreco.2004.05.060

Curtis RO, Clendenan GW, Demars DJ, 1981. A new stand simulator for coast douglas-fir: DFSIM users guide. U.S. Forest Service General Technical Report PNW-128.

Diéguez-Aranda U, Burkhart HE, Amateis RL, 2006. Dynamic site model for loblolly pine (Pinus taeda L.) plantations in the United States. For Sci 52 (3): 262-272.

Ercanlı İ, 2010. Trabzon ve Giresun Orman Bölge Müdürlükleri sınırları içerisinde yer alan Doğu Ladini (Picea orientalis (L.) Link)-Sarıçam (Pinus sylvestris L.) karışık meşcerelerine ilişkin büyüme modelleri. PhD, Graduate School of Natural and Applied Sciences, Karadeniz Technical University, Trabzon, Türkiye.

Fabbio G, Frattegiani M, Manetti MC, 1994. Height estimation in stem analysis using second differences. For Sci 40: 329-340.

Fortin M, Daigle, G, Ung C-H, Bégin J, Archambault L, 2007. A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling. Eur J For Res 126: 573-585. https://doi.org/10.1007/s10342-007-0179-1

García O, 2005. Comparing and combining stem analysis and permanent sample plot data in site index models. For Sci 51: 277-283.

Goelz J, Burk T, 1992. Development of a well-behaved site index equation: jack pine in north central Ontario. Can J For Res 22: 776-784. https://doi.org/10.1139/x92-106

Grégoire TG, Schabenberger O, Barrett JP, 1995. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can J For Res 25: 137-156. https://doi.org/10.1139/x95-017

Gregorie TG, 1987. Generalized error structure for forestry yield models. For Sci 33: 423-444.

Guan BT, Gertner G, 1991. Modeling red pine tree survival with an artificial neural network. For Sci 37: 1429-1440.

Jevšenak J, Levanič T, 2016. Should artificial neural networks replace linear models in tree ring based climate reconstructions? Dendrochronologia 40: 102-109. https://doi.org/10.1016/j.dendro.2016.08.002

Lappi J, Bailey RL, 1988. A height prediction model with random stand and tree parameters: an alternative to traditional site index methods. For Sci 34: 907-927.

Martín-Benito D, Gea-Izquierdo G, Del Río M, Canellas I, 2008. Long-term trends in dominant-height growth of black pine using dynamic models. For Ecol Manag 256: 1230-1238. https://doi.org/10.1016/j.foreco.2008.06.024

MathWorks Inc., 2015. MATLAB User's guide, vers 2015a. The MathWorks, Inc., Natick, MA, USA. Matlab user manual.

Nothdurft A, Kublin E, Lappi J, 2006. A non-linear hierarchical mixed model to describe tree height growth. Eur J For Res 125: 281-289. https://doi.org/10.1007/s10342-006-0118-6

Özçelik R, Diamantopoulou MJ, Crecente-Campo F, Eler U, 2013. Estimating Crimean juniper tree height using nonlinear regression and artificial neural network models. For Ecol Manag 306: 52-60. https://doi.org/10.1016/j.foreco.2013.06.009

Pinheiro J, Bates D, 2006. Mixed-effects models in S and S-PLUS. Springer-Verlag, New York.

Poudel KP, Cao QV, 2013. Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. For Sci 59: 243-252. https://doi.org/10.5849/forsci.12-001

Richards FJ, 1959. A flexible growth function for empirical use. J Exp Bot 10 (29): 290-300. https://doi.org/10.1093/jxb/10.2.290

SAS Inst., 2004. SAS/ETS 9.1 User's Guide. SAS Institute, Cary, NC, USA.

Sharma M, Subedi N, Ter-Mikaelian M, Parton J, 2014. Modeling climatic effects on stand height/site index of plantation-grown jack pine and black spruce trees. For Sci 61: 25-34. https://doi.org/10.5849/forsci.13-190

Skovsgaard JP, Vanclay JK, 2008. Forest site productivity: a review of the evolution of dendrometric concepts for even-aged stands. Forestry 81: 13-31. https://doi.org/10.1093/forestry/cpm041

Wang Y, LeMay VM, Baker TG, 2007. Modelling and prediction of dominant height and site index of Eucalyptus globulus plantations using a nonlinear mixed-effects model approach. Can J For Res 37: 1390-1403. https://doi.org/10.1139/X06-282

Wang M, Borders BE, Zhao D, 2008. An empirical comparison of two subject-specific approaches to dominant heights modeling: The dummy variable method and the mixed model method. For Ecol Manag 255: 2659-2669. https://doi.org/10.1016/j.foreco.2008.01.030

Wang M, Bhatti J, Wang Y, Varem-Sanders T, 2011. Examining the gain in model prediction accuracy using serial autocorrelation for dominant height prediction. For Sci 57: 241-251.

Wang M, Kane MB, Borders BE, Zhao D, 2013. Direct variance-covariance modeling as an alternative to the traditional guide curve approach for prediction of dominant heights. For Sci 60: 652-662. https://doi.org/10.5849/forsci.13-019

Weiskittel AR, Hann DW, Hibbs DE, Lam TY, Bluhm AA, 2009. Modeling top height growth of red alder plantations. For Ecol Manag 258: 323-331. https://doi.org/10.1016/j.foreco.2009.04.029

Yee D, Prior M, Florence L, 1993. Development of predictive models of laboratory animal growth using artificial neural networks. Bioinformatics 9: 517-522. https://doi.org/10.1093/bioinformatics/9.5.517

How to Cite
ERCANLII., BOLATF., & YAVUZH. (2023). A comparison of artificial neural networks and regression modeling techniques for predicting dominant heights of Oriental spruce in a mixed stand. Forest Systems, 32(1), e004. https://doi.org/10.5424/fs/2023321-19134
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