An individual-tree linear mixed-effects model for predicting the basal area increment of major forest species in Southern Europe
Abstract
Aims of the study. Assessment of growth is essential to support sustainability of forest management and forest policies. The objective of the study was to develop a species-specific model to predict the annual increment of tree basal area through variables recorded by forest surveys, to assess forest growth directly or in the context of more complex forest growth and yield simulation models.
Area of the study. Italy.
Material and methods. Data on 34638 trees of 31 different forest species collected in 5162 plots of the Italian National Forest Inventory were used; the data were recorded between 2004 and 2006. To account for the hierarchical structure of the data due to trees nested within plots, a two-level mixed-effects modelling approach was used.
Main results. The final result is an individual-tree linear mixed-effects model with species as dummy variables. Tree size is the main predictor, but the model also integrates geographical and topographic predictors and includes competition. The model fitting is good (McFadden’s Pseudo-R2 0.536), and the variance of the random effect at the plot level is significant (intra-class correlation coefficient 0.512). Compared to the ordinary least squares regression, the mixed-effects model allowed reducing the mean absolute error of estimates in the plots by 64.5% in average.
Research highlights. A single tree-level model for predicting the basal area increment of different species was developed using forest inventory data. The data used for the modelling cover 31 species and a great variety of growing conditions, and the model seems suitable to be applied in the wider context of Southern Europe.
Keywords: Tree growth; forest growth modelling; forest inventory; hierarchical data structure; Italy.
Abbreviations used: BA - basal area; BAI – five-year periodic basal area increment; BALT - basal area of trees larger than the subject tree; BASPratio - ratio of subject tree species basal area to stand basal area; BASTratio - ratio of subject tree basal area to stand basal area; CRATIO - crown ratio; DBH – diameter at breast height ; DBH0– diameter at breast height corresponding to five years before the survey year; DBHt– diameter at breast height measured in the survey year; DI5 - five-year, inside bark, DBH increment; HDOM - dominant height; LULUCF - Land Use, Land Use Changes and Forestry; ME - mean error; MAE - mean absolute error; MPD - mean percent deviation; MPSE - mean percent standard error; NFI(s) - National Forest Inventory/ies; OLS - ordinary least squares regression; RMSE - root mean squared error; UNFCCC - United Nation Framework Convention on Climate Change.
Downloads
References
Adame P, Hynynen J, Cañellas I, del Río M, 2008. Individual-tree diameter growth model for rebollo oak (Quercus pyrenaica Willd.) coppices. For Ecol Manag 255: 1011-1022. https://doi.org/10.1016/j.foreco.2007.10.019
Andreassen K, Tomter SM, 2003. Basal area growth models for individual trees of Norway spruce, Scots pine, birch and other broadleaves in Norway. For Ecol Manag 180: 11-24. https://doi.org/10.1016/S0378-1127(02)00560-1
Bevilacqua E, 1999. Growth responses in individual eastern white pine (Pinus strobus L.) trees following partial cutting treatments. Ph.D. University of Toronto.
Bosela M, Gasparini P, Di Cosmo L, Parisse B, De Natale F, Esposito S, Scheer L, 2016. Evaluating the potential of an individual-tree sampling strategy for dendroecological investigations using the Italian National Forest Inventory data. Dendrochronologia 38: 90-97. https://doi.org/10.1016/j.dendro.2016.03.011
Bueno S, Bevilacqua E, 2010. Modeling stem increment in individual Pinus occidentalis Sw. trees in La Sierra, Dominican Republic. Forest systems 19 (2): 170-183. https://doi.org/10.5424/fs/2010192-01312
Burkhart HE, Tomé M, 2012. Modeling forest trees and stands. Springer Science+Business Media Dordrecht. https://doi.org/10.1007/978-90-481-3170-9
Cienciala E, Russ R, Šantrůčková H, Altman J, Kopáček J, Hůnová I, Štěpánek P, Oulehle P, Tumajer J, Ståhl G, 2016. Discerning environmental factors affecting current tree growth in Central Europe. Sci Total Environ 573: 541-554. https://doi.org/10.1016/j.scitotenv.2016.08.115
Crecente-Campo F, Tome' M, Soares P, Dieguez-Aranda U, 2010. A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. For Ecol Manag 259: 943-952. https://doi.org/10.1016/j.foreco.2009.11.036
Di Cosmo L, Gasparini P, Tabacchi G, 2016. A national-scale, stand-level model to predict total above-ground tree biomass from growing stock volume. For Ecol Manag 361: 269-276. https://doi.org/10.1016/j.foreco.2015.11.008
Dobbertin M, 2005. Tree growth as indicator of tree vitality and of tree reaction to environmental stress: a review. Eur J Forest Res 124: 319-333. https://doi.org/10.1007/s10342-005-0085-3
Gasparini P and Tabacchi G (eds), 2011. L'inventario nazionale delle foreste e dei serbatori forestali di Carbonio - Secondo inventario forestale nazionale italiano. Metodi e risultati. MiPAAf, CFS, Consiglio per la Ricerca in Agricoltura, Unità di ricerca per il Monitoraggio e la Pianificazione Forestale. Edagricole, Milano, 2011. pp. 394-395.
Gasparini P, Di Cosmo L, 2016. National Forest Inventory Reports - Italy. In: Vidal C, Alberdi I, Hernandez L and Redmond J (eds)- Assessment of Wood Availability and Use. Springer International Publishing, Cham, Switzerland 2016. pp. 485-506. https://doi.org/10.1007/978-3-319-44015-6_26
Gasparini, P, Tosi, V., Di Cosmo, L., 2010. Country report Italy. In: Tomppo, E., Gschwantner, T, Lawrence, M., McRoberts, R.E. (Eds.), National Forest Inventories - Pathways for Common Reporting. Springer Science + Business Media, pp. 311-331
Gasparini P, Di Cosmo L, Rizzo M, Giuliani D, 2017. A stand-level model derived from National Forest Inventory data to predict periodic annual volume increment of forests in Italy. J Forest Res-JPN 22 (4): 209-217.
Gschwantner T, Lanz A, Vidal C, Bosela M, Di Cosmo L, Fridman J, Gasparini P, Kuliešis A, Tomter S, Schadauer K, 2016. Comparison of methods used in European National Forest Inventories for the estimation of volume increment: towards harmonisation. Ann Forest Sci 73: 807-821. https://doi.org/10.1007/s13595-016-0554-5
INFC, 2007. Le stime di superficie 2005 - Seconda parte. Tabacchi G, De Natale F, Di Cosmo L, Floris A, Gagliano C, Gasparini P, Genchi L, Scrinzi G, Tosi V. Inventario Nazionale delle Foreste e dei Serbatoi Forestali di Carbonio. MiPAF - Corpo Forestale dello Stato - Ispettorato Generale, CRA - ISAFA, Trento. http://www.infc.it
IPCC, 2003. Good Practice Guidance for Land Use, Land Use Change and Forestry. Institute for Global Environmental Strategies, Japan. https://www.ipcc-nggip.iges.or.jp/public/gpglulucf/gpglulucf_files/GPG_LULUCF_FULL.pdf
Jõgiste Kalev, 2000. A Basal area increment model for Norway spruce in mixed stands in Estonia. Scand. J. For.Res. 15: 97-102. https://doi.org/10.1080/02827580050160529
Laubhann D, Sterba H, Reinds GJ, De Vries W, 2009. The impact of atmospheric deposition and climate on forest growth in European monitoring plots: An individual tree growth model. For Ecol Manag 258: 1751-1761. https://doi.org/10.1016/j.foreco.2008.09.050
McFadden D, 1979. Quantitative methods for analysing travel behaviour of individuals: some recent developments. In: Hensher, DA and Stopher, PR (eds) Behavioural travel modelling. London, Croom Helm: 279-318.
McRoberts RE, Tomppo E, Næsset E, 2010. Advances and emerging issues in national forest inventories. Scand J Forest Res 2: 368-381. https://doi.org/10.1080/02827581.2010.496739
Pignatti S, 1995. Le zone di vegetazione in Italia. In Pignatti S (eds) Ecologia vegetale. Utet, Torino: 125-126.
Pokharel B, Dech JF, 2012. Mixed-effects basal area increment models for tree species in the boreal forest of Ontario, Canada using an ecological land classification approach to incorporate site effects. Forestry 85 (2): 255-270. https://doi.org/10.1093/forestry/cpr070
Pretzsch H, 2009. Forest dynamics, growth and yield. Springer. https://doi.org/10.1007/978-3-540-88307-4
R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
Rohner B, Waldner P, Lischke H, Ferretti M, Thürig E, 2018. Predicting individual-tree growth of central European tree species as a function of site, stand, management, nutrient, and climate effects. Eur. J. Forest Res. 137: 29-44. https://doi.org/10.1007/s10342-017-1087-7
Schelhaas MJ, Hengeveld GM, Heidema N, Thürig E, Rohner B, Vacchiano G, Vayreda J, Redmond J, Socha J, Fridman J, Tomter S, Polley H, Barreiro S, Nabuurs JN, 2018. Species-specific, pan-European diameter increment models based on data of 2.3 million trees. For Ecosyst 5: 1-21. https://doi.org/10.1186/s40663-018-0133-3
Snijders TA, 2005. Power and sample size in multilevel modelling. In: Everitt BS, Howell DC (eds) Encyclopedia of statistics in behavioral science. Wiley, Chichester: 1570-1573. https://doi.org/10.1002/0470013192.bsa492
Snowdon P, 1991. A ratio estimator for bias correction in logarithmic regressions. Can. J. For. Res., 21 (1991): 720-724. https://doi.org/10.1139/x91-101
Solberg S, Dobbertin M, Reinds GJ, Lange H, Andreassen K, Fernandez PG, Hildingsson A, de Vries W, 2009. Analyses of the impact of changes in atmospheric deposition and climate on forest growth in European monitoring plots: a stand growth approach. For Ecol Manag 258: 1735-1750. https://doi.org/10.1016/j.foreco.2008.09.057
Spiecker H, 1999. Overview of recent growth trends in European forests. Water Air Soil Pollut 116: 33-46. https://doi.org/10.1023/A:1005205515952
Tomppo E, Schadauer K, McRoberts RE, Gschwantner T, Gabler K, Sthål G, 2010. Introduction. In: Tomppo E, Gschwantner T, Lawrence M, McRoberts RE (eds) National Forest Inventories. Pathways for Common Reporting. Springer: 1-18 https://doi.org/10.1007/978-90-481-3233-1_1
Vospernik S, 2017. Possibilities and limitations of individual-tree growth models - A review on model evaluations. Die Bodenkultur: Journal of Land Management, Food and Environment 68 (2): 103-112. https://doi.org/10.1515/boku-2017-0010
Yue C, Kahle HP, Kohnle U, Zhang Q, Kang X, 2014. Detecting trends in diameter growth of Norway spruce on long-term forest research plots using linear mixed-effects models. Eur J For Res 133: 783-792. https://doi.org/10.1007/s10342-014-0795-5
Weiskittel AR, Hann DW, Kershaw JA, Vanclay JK. 2011. Forest growth and yield modeling. Chichester, UK: Wiley-Blackwell, p. 50. https://doi.org/10.1002/9781119998518
Wykoff WR, 1990. A basal area increment model for individual conifers in the Northern Rocky Mountains. For Sci 36 (4): 1077-1104.
Zhang L., Peng C., Dang Q., 2004. Individual-tree basal area growth models for jack pine and black spruce in northern Ontario. The Forestry Chronicle, 80 (3): 366-374. https://doi.org/10.5558/tfc80366-3
Zeng WS. 2015. Using nonlinear mixed model and dummy variable model approaches to develop origin-based individual tree biomass equations. Trees, 29: 275-283. https://doi.org/10.1007/s00468-014-1112-0
Zuur A, Leno EN, Elphick CS, 2010. A protocol for data exploration to avoid common statistical problems. Mathods in Ecology and Evolution 1:3-14. https://doi.org/10.1111/j.2041-210X.2009.00001.x
© CSIC. Manuscripts published in both the printed and online versions of this Journal are the property of Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a “Creative Commons Attribution 4.0 International” (CC BY 4.0) License. You may read here the basic information and the legal text of the license. The indication of the CC BY 4.0 License must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the published by the Editor, is not allowed.