ESTIMATING TREE BOLE HEIGHT WITH BAYESIAN ANALYSIS.

Elias Milios, Kyriaki Kitikidou, Elias Pipinis, Athanasios Stampoulidis, Melina Gotsi

Abstract


Aim of study: The classical method for estimating a height-diameter model is based on the Least Squares Method (LSM) and the fit of a regression line. The Bayesian method has an exclusive advantage, compared with the classical method, in that the parameters to be estimated are considered as random variables. In this study, the Simple Linear Regression (SLR) model and the Bayesian model were used to estimate bole height from breast height diameter. Area of study: We used data of the forest stands of Rhodope (north-eastern Greece).  Materials and methods: The variables that we used were the tree bole height and the diameter at breast height. Main results: The results showed that there is an improvement in prediction accuracy with the Bayesian model; however, this didn't lead to narrower confidence intervals of the predicted value, compared to SLR. Research essentials: Narrower confidence intervals are not necessarily achieved with Bayesian methods; confidence intervals' width is related to both statistical analyses and nature of data (in this case, species ecology and structure - composition of the stands where the sampled trees belong).


Keywords


Bayes; regression; tree height; tree bole.

Full Text:

PDF

References


Anholt, B., E., Werner, D., Skelly, 2000: Effect of food and predators on the activity of four larval ranid frogs, Ecology, 81 (12): 3509–3521.

Arbuckle, J., 2012: IBM SPSS Amos 21 User's Guide, IBM Corporation, 653 p., USA.

Assmann, E., 1970: The Principles of Forest Yield Study, Pergamon Press, 506 p., New York, USA.

Batziou, M., E., Milios, K., Kitikidou, 2016: Is diameter at the base of root collar a key characteristic of seedling sprouts in a Quercus pubescens - Quercus frainetto grazed forest in Northeastern Greece? A morphological analysis, New Forests, 48(1): 1-16.

Bullock, B., E., Boone, 2007: Deriving tree diameter distributions using Bayesian model averaging, Forest Ecology and Management, 242, (2-3): 127–132.

Calama, R., G., Montero, 2004: Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain, Canadian Journal of Forest Research, 34(1): 150–163.

Chave, J., C., Andalo, S., Brown, M., Cairns. J., Chambers, D., Eamus, H., Fölster, F., Fromard, N., Higuchi, T., Kira, J., Lescure, B., Nelson, H., Ogawa, H., Puig, B., Riéra, T., Yamakura: 2005), Tree allometry and improved estimation of carbon stocks and balance in tropical forests, Oecologia, 145(1): 87–99.

Clark, J., M., Wolosin, M., Dietze, I., Ibáñez, S., LaDeau, M., Welsh, B., Kloeppel, 2007: Tree growth inference and prediction from diameter censuses and ring widths, Ecological Applications, 17(7): 1942–1953.

Colbert, K., D., Larsen, J., Lootens, 2002: Height-diameter equations for thirteen midwestern bottomland hardwood species., Northern Journal of Applied Forestry, 19(4): 171–176.

Curtis, R., 1967: Height-diameter and height-diameter-age equations for second-growth Douglas-fir, Forest Science, 13: 365–375.

Dafis, S., 1986): Forest ecology (in Greek), Giahoudi-Giapouli, 443 p, Thessaloniki, Greece.

De Valpine, P., A., Hastings, 2002: Fitting population models incorporating process noise and observation error, Ecological Monographs, 72(1): 57–76.

Edwards, A., 1992: Likelihood. Johns Hopkins University Press, 296 p, Baltimore, USA.

FAO, 2006: GreenFacts - Scientific facts on forests. Level 2 - Details on forests, GreenFacts Foundation, 62 p, Brussels, Belgium.

Fekedulgn, D., M., Mac Siurtain, J., Colbert, 1999: Parameter estimation of nonlinear growth models in forestry, Silva Fennica, 33(4): 327–336.

Flewelling, J., R., de Jong, 1994: Considerations in simultaneous curve fitting for repeated height-diameter measurements, Canadian Journal of Forest Research, 24(7): 1408–1414.

Gelman, A., J., Carlin, H., Stern, D., Rubin, 2004, Bayesian Data Analysis, 2nd edition. Chapman and Hall/CRC, 690 p, Boca Raton, USA.

Hann, D., 2006: ORGANON User’s Manual Edition 8.0. Department of Forest Resources, Oregon State University, 129 p, Corvallis, Oregon, USA.

Huang, S., 1999, Ecoregion-based individual tree height-diameter models for lodgepole pine in Alberta, Western Journal of Applied Forestry, 14(4): 186–193.

Hui, C., L., Foxcroft, D., Richardson, S., Macfadyen, 2011: Defining optimal sampling effort for large-scale monitoring of invasive alien plants: a Bayesian method for estimating abundance and distribution, Journal of Applied Ecology, 48(3): 768–776.

Hui, C., M., McGeoch, M., Warren, 2006: A spatially explicit approach to estimating species occupancy and spatial correlation, Journal of Animal Ecology, 75(1): 140–147.

King, D., 1991: Tree allometry, leaf size and adult tree size in old-growth forests, Tree Physiology, 9(3): 369–381.

Kitikidou, K., 2005: Applied Statistics Using SPSS, Tziolas Press, 288 p, Thessaloniki, Greece.

Kitikidou, K., E., Milios, S., Katsogridakis, 2016: Meta-analysis for the volume of Pinus sylvestris in Europe, Revista Chapingo Serie Ciencias Forestales y del Ambiente, 23(1): 22-34.

Korakis, G., 2015: Forest Botany, Hellenic Academic Libraries, 619 p, Athens, Greece.

Lacointe, A., E., Deleens, T., Ameglio, B., Saint-Joanis, C., Lelarge, M., Vandame, G., Song, F., Daudet, 2004).: Testing the branch autonomy theory: a 13C/14C double-labelling experiment on differentially shaded branches, Plant, Cell and Environment, 27: 1159–1168.

Lappi, J., 1991: Calibration of height and volume equations with random parameters, Forest Science, 37: 781–801.

Larsen, D., D., Hann, 1987: Height-Diameter Equations for Seventeen Tree Species in Southwest Oregon. Oregon State University, 16 p, Corvallis, Oregon, USA.

Li, R., B., Stewart, A., Weiskittel, 2012: A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry, Forestry, 85(1): 17–25.

McCarthy, M., 2007: Bayesian Methods for Ecology, Cambridge University Press, 295 p, Cambridge, UK.

Metcalf, C., S., McMahon, J., Clark, 2009: Overcoming data sparseness and parametric constraints in modeling of tree mortality: a new nonparametric Bayesian model, Canadian Journal of Forest Research, 39(9): 1677–1687.

Milios, E., 2000: Dynamics and evaluation of the Rhodope mixed stands in the region of Xanthi (In Greek), PhD thesis, Aristotle University of Thessaloniki, 345 p.

Milios, E., 2004: The influence of stand development process on the height and volume growth of dominant Fagus sylvatica L. sl trees in the central Rhodope Mountains of north-eastern Greece, Forestry, 77(1): 17-26.

Ministry of Agriculture, 1992: Results of the ï¬rst national forest inventory (in Greek), Publication of Department of Forest Mapping, 134 p, Athens, Greece.

Newton, P., I., Amponsah. 2007: Comparative evaluation of five height-diameter models developed for black spruce and jack pine stand-types in terms of goodness-of-fit, lack-of-fit and predictive ability, Forest Ecology and Management, 247(1–3): 149–166.

Nogueira, E., B., Nelson, P., Fearnside, M., França, Ã., Oliveira, 2008): Tree height in Brazil's “arc of deforestationâ€: shorter trees in south and southwest Amazonia imply lower biomass, Forest Ecology and Management, 255(7): 2963–2972.

Nyström, K., G., Ståhl: 2001, Forecasting probability distributions of forest yield allowing for a Bayesian approach to management planning, Silva Fennica, 35(2): 185–201.

Oliver, C., B., Larson, 1996: Forest stand dynamics, 520 p, John Wiley & Sons, Inc., New York, USA.

Peng, C., L., Zhang, J., Liu, 2001: Developing and validating nonlinear height-diameter models for major tree species of Ontario's boreal forests, Northern Journal of Applied Forestry, 18(3): 87–94.

Peng, C., L., Zhang, X., Zhou, Q., Dang, S., Huang, 2004: Developing and evaluating tree height-diameter models at three geographic scales for black spruce in Ontario, Northern Journal of Applied Forestry, 21(2): 83–92.

Penner, M., C., Power, C., Muhairve, R., Tellier, Y., Wang, 1997: Canada’s forest biomass resources: deriving estimates from Canada’s forest inventory. Information Report BC-X-370, Canadian Forest Service, 33 p, Pacific Forestry Centre, Victoria, Canada.

Shen, T., A., Chao, F., Lin, 2003: Predicting the number of new species in further taxonomic sampling, Ecology, 84(3): 798–804.

Huang, S., S., Titus, D., Wiens, 1992:. Comparison of nonlinear height-diameter functions for major Alberta tree species, Canadian Journal of Forest Research, 22(9): 1297–1304.

Temesgen, H., K., Gadow, 2004: Generalized height-dimater models—an application for major tree species in complex stands of interior British Columbia, European Journal of Forest Research, 123(1): 45–51.

Temesgen, H., D., Hann, V., Monleon, 2007: Regional height-diameter equations for major tree species of southwest Oregon, Western Journal of Applied Forestry, 22(3): 213–219, 2007.

Toivonen, H., H., Mannila, A., Korhola, H., Olander, 2001: Applying Bayesian statistics to organism-based environmental reconstruction, Ecological Applications, 11(2): 618–630.

Van Laar, A., A., Akça, 2007: Forest mensuration. Springer, Dordrecht, 384 p, The Netherlands.

Wyckoff, P., J., Clark, 2000: Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches, Canadian Journal of Forest Research, 30(1): 156–167.

Zapata, M., C., Sierra, L., Alleman, 2012: Probability distribution of allometric coefficients and Bayesian estimation of aboveground tree biomass, Forest Ecology and Management, 277: 173–179.

Zhang, Z., A., Duan, J., Zhang, C., Xiang, 2014: Estimating tree height - diameter models with the Bayesian Method, The Scientific World Journal: 1-9.


Refbacks

  • There are currently no refbacks.


   

© 2008 Mathematical and Computational Forestry & Natural-Resource Sciences