Comparison of different non-linear models for prediction of the relationship between diameter and height of velvet maple trees in natural forests (Case study: Asalem Forests, Iran) Navroodi I., Alavi S.J., Ahmadi M.K., Radkarimi M. (2016): Comparison of different non-linear models for prediction of the relationship between diameter and height of velvet maple trees in natural forests (Case study: Asalem Forests, Iran). J. For. Sci., 62: 65-71.
download PDF

Velvet maple (Acer velutinum) is one of the woody species in the Hyrcanian forests. In this study, the relationship between height and diameter of velvet maple was surveyed. A complete list of the selected height-diameter models was used and nineteen candidate models were considered. Various criteria were chosen and applied to evaluate the predictive performance of the models. These criteria include Akaike information criterion (AIC), Bayesian information criterion (BIC), root mean square error (RMSE), mean error (ME), and adjusted coefficient of determination (R2adj). Fitting of nineteen height-diameter models using nonlinear least square regression showed that all of the parameters in models were significant (P < 0.01). The results of goodness of fit for the calibration and k-fold validation and the performance criteria (RMSE, ME, AIC, R2adj and BIC) showed that R2adj ranged from 0.743 (model 8) to 0.8592 (model 11) and RMSE from 2.6983 (model 11) to 10.1897 (model 9). The range of ME among the models is from –7.0787 (model 9) up to 0.063m (model 7). By considering the AICfor each model it is evident that model (11) and model (9) have the lowest and highest values, respectively. Plotting the residuals showed that for all these models the residuals were randomly distributed and the models had heterogeneous residuals. According to the results, models (11), (14), (13), (15) and (12) had a better fitness compared to other models. Among these models, model (11) was the best model for predicting total height of Acer velutinum trees in this region.

Ahmadi K., Alavi S.J., Tabari Kouchaksaraei M., Aertsen W. (2013): Non-linear height-diameter models for oriental beech (Fagus orientalis Lipsky) in the Hyrcanian forests, Iran. Biotechnologie, Agronomie, Société et Environnement, 17: 431–440.
Aertsen Wim, Kint Vincent, van Orshoven Jos, Özkan Kürşad, Muys Bart (2010): Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests. Ecological Modelling, 221, 1119-1130
Asadollahi F. (1987): Geographical study of plants communities of the north-west forests of Hircanian (Asalem) and its use in natural resources. Journal of Forest and Rang Management, 2: 4–7. (in Persian)
Bates D.M., Watts D.G. (1980): Relative curvature measures of nonlinearity. Journal of the Royal Statistical Society, Series B, 42: 1–16.
Burk T.E., Burkhart H.E. (1984): Diameter Distributions and Yields of Natural Stands of Loblolly Pine. Blacksburg, Virginia Polytechnic Institute and State University, Blacksburg Publishing: 46.
Burkhart H.E., Strub M.R. (1974): A model for simulation of planted loblolly pine stands. In: Fries J. (ed.): Growth Models for Tree and Stand Simulation. Stockholm, Royal College of Forestry, Research Note 30: 128–135.
Buford M.A. (1986): Height–diameter relationship at age 15 in loblolly pine seed sources. Forest Science, 32: 812–818.
Calama Rafael, Montero Gregorio (2004): Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, 34, 150-163
Colbert K.C., Larsen D.R., Lootens J.R. (2002): Height-diameter equations for thirteen Midwestern bottomland hardwood species. Northern Journal of Applied Forestry, 19: 171–176.
Curtis R.O. (1967): Height-diameter-age equations for second-growth Douglas-fir. Forest Science, 13: 365–375.
Diamantopoulou M. J., Özçelik R. (2012): Evaluation of different modeling approaches for total tree-height estimation in Mediterranean Region of Turkey. Forest Systems, 21, 383-
Fallah A. (2009): Determination of the Best Diameter-Height Model for the Norway spruce (Picea abies L. Karst.) in Kelardasht afforestation (North of Iran). Journal of Applied Sciences, 9, 3870-3875
Fang Zixing, Bailey R.L. (1998): Height–diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110, 315-327
Farr Wilbur A., DeMars Donald J., Dealy J. Edward (1989): Height and crown width related to diameter for open-grown western hemlock and Sitka spruce. Canadian Journal of Forest Research, 19, 1203-1207
Huang Shongming, Titus Stephen J., Wiens Douglas P. (1992): Comparison of nonlinear height–diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22, 1297-1304
Krisnawati H., Wang Y., Ades P.K. (2010): Generalized height-diameter model for Acacia mangium Wild. plantations in South Sumatra. Journal of Forest Research, 7: 1–19.
Larson Bruce C. (1986): Development and growth of even-aged stands of Douglas-fir and grand fir. Canadian Journal of Forest Research, 16, 367-372
Larsen D.R., Hann D.W. (1987): Height-diameter Equations for Seventeen Tree Species in Southwest Oregon. Corvallis, Oregon State University, Forest Research Laboratory Research Paper, 49: 16.
Larsen David R. (1994): Adaptable stand dynamics model integrating site-specific growth for innovative silvicultural prescriptions. Forest Ecology and Management, 69, 245-257
Loetsch F., Zöhrer F., Haller K.E. (1973): Forest Inventory. Munich, BLV Verlagsgesellschaft: 469.
Lumbres Roscinto Ian C., Lee Young Jin, Seo Yeon Ok, Kim Sung Ho, Choi Jung Kee, Lee Woo Kyun (2011): Development and validation of nonlinear height–DBH models for major coniferous tree species in Korea. Forest Science and Technology, 7, 117-125
Meyer H.A. (1940): A mathematical expression for height curves. Journal of Forestry, 38: 415–420.
Moffat A. J., Matthews R. W., Hall J. E. (1991): The effects of sewage sludge on growth and foliar and soil chemistry in pole-stage Corsican pine at Ringwood Forest, Dorset, UK. Canadian Journal of Forest Research, 21, 902-909
Olson L.D., Delen D. (2008): Advanced Data Mining Technique. Berli, Heidelberg, Springer: 180.
ÖZÇELİK Ramazan, YAVUZ Hakkı, KARATEPE Yasin, GÜRLEVİK Nevzat, KIRIŞ Rüstem (2014): Development of ecoregion-based height–diameter models for 3 economically important tree species of southern Turkey. TURKISH JOURNAL OF AGRICULTURE AND FORESTRY, 38, 399-412
Parresol Bernard R. (1992): Baldcypress height–diameter equations and their prediction confidence intervals. Canadian Journal of Forest Research, 22, 1429-1434
Pearl R., Reed L. J. (1920): On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation. Proceedings of the National Academy of Sciences, 6, 275-288
Peng C., Zhang L., Liu J. (2001): Developing and validating nonlinear height-diameter models for major tree species of Ontario’s boreal forests. Northern Journal of Applied Forestry, 18: 87–94.
Pourmajidian M.R. (1992): Researches in Relation to Results of Afforestation with Picea abies in Kelardasht Region. [MSc Thesis.] Tehran, Tehran University: 78. (in Persian)
Prodan M. (1968): Forest Biometrics. Oxford, Pergamon Press: 447.
Ratkowsky D.A. (1990): Handbook of Nonlinear Regression. New York, Marcel Dekker: 120.
Ratkowsky David A., Reedy Terry J. (1986): Choosing Near-Linear Parameters in the Four-Parameter Logistic Model for Radioligand and Related Assays. Biometrics, 42, 575-
RICHARDS F. J. (1959): A Flexible Growth Function for Empirical Use. Journal of Experimental Botany, 10, 290-301
Ritchie Martin W., Hann David W. (1986): Development of a tree height growth model for Douglas-fir. Forest Ecology and Management, 15, 135-145
Ritz C., Streibig J. (2008): Nonlinear regression with R. New York, Springer: 148.
Sagheb-talebi K.H., Sajedi T., Yazdian F. (2004): Forests of Iran. Tehran, Research Institute of Forests and Rangelands Publication: 339. (in Persian)
L�pez S�nchez Carlos A., Gorgoso Varela Javier, Castedo Dorado Fernando, Rojo Alboreca Alberto, Soalleiro Roque Rodr�guez, �lvarez Gonz�lez Juan Gabriel, S�nchez Rodr�guez Federico (2003): A height-diameter model for Pinus radiata D. Don in Galicia (Northwest Spain). Annals of Forest Science, 60, 237-245
Schreuder H.T., Hafley W.L., Bannett F.A. (1979): Yield prediction for unthinned natural slash pine stands. Forest Science, 25: 25–30.
Schnute Jon (1981): A Versatile Growth Model with Statistically Stable Parameters. Canadian Journal of Fisheries and Aquatic Sciences, 38, 1128-1140
Sheikholeslami H. (1998): Study of the Effects of Changes in Elevation, Slope and Vegetation Cover in Soil Transformation of the Asalem Region. [MSc Thesis.] Tehran, Tehran University: 175. (in Persian)
Siahipour Z., Rostami T., Taleb S., Taheri K. (2002): Investigation of sustainable Picea abies in afforestation of Guilan province. Iranian Journal of Forest and Poplar Research, 312: 1–53. (in Persian)
Somers G.L., Farrar R.M. (1991): Bio-mathematical growth equations for natural longleaf pine stands. Forest Science, 37: 227–244.
Stage A.R. (1963): A mathematical approach to polymorphic site index curves for grand fir. Forest Science, 9: 167–180.
Stage A.R. (1975): Prediction of Height Increment for Models of Forest Growth. Research Paper INT-164. Ogden, Intermountain Forest and Range Experiment Station, USDA Forest Service: 20.
Stoffels A., van Soeset J. (1953): The main problems in sample plots. 3. height regression. Nederlands Bosbouw Tijdschrift, 25: 190–199.
Van Deusen P.C., Biging G.S. (1985): Development of a tree height growth model for Douglas-fir. Forest Ecology and Management, 15: 135–145.
Watts S.B. (1983): Forestry Handbook for British Columbia. 4th Ed. Vancouver, University of British Columbia: 773.
Winsor C. P. (1932): The Gompertz Curve as a Growth Curve. Proceedings of the National Academy of Sciences, 18, 1-8
Wykoff W.R., Crookston N.L., Stage A.R. (1982): User’s Guide to the Stand Prognosis Model. General Technical Report INT-133. Ogden, Intermountain Forest and Range Experiment Station, USDA Forest Service: 112.
Yang R. C., Kozak A., Smith J. H. G. (1978): The potential of Weibull-type functions as flexible growth curves. Canadian Journal of Forest Research, 8, 424-431
Zeide Boris (1989): Accuracy of equations describing diameter growth. Canadian Journal of Forest Research, 19, 1283-1286
ZHANG L (): Cross-validation of Non-linear Growth Functions for Modelling Tree Height–Diameter Relationships. Annals of Botany, 79, 251-257
download PDF

© 2020 Czech Academy of Agricultural Sciences