Effect of stand characteristics and environmental factors on the volume increment of oak in Poland
Wpływ cech drzewostanu i czynników środowiskowych na przyrost miąższości dębu w Polsce
Sylwan 168 (2):71-91, 2024
Available online: 2024-04-18
Open Access (CC-BY)
environmental effect • forest productivity • GAM • NFI • periodic volume increment

Volume increment is a valuable indicator of the growth and performance of stands over time. It allows forest managers to assess forest productivity and indicate changes in growth conditions. In forestry practice, growth and productivity models can be developed by integrating volume increment data with environmental factors. The primary objective of this study was to develop a generalized additive model that would explain the influence of tree characteristics, climate and topography on oak volume increment. Our findings underscored the significant impact of basal area, age, height, and relative spacing index on the periodic annual volume increment (PAIv) of oak in Poland. We found that temperature, precipitation, slope and soil type within the study area also had significant effects on PAIv. The developed model explained approximately 43.8% of the variance of the PAIv. Notably, when applied to specific natural forest regions, the explanatory capacity of the model increased significantly, reaching around 64.4%. For smaller areas such as natural forest regions, PAIv was mainly determined by stand characteristics and less influenced by site factors such as slope and climate. This enhanced accuracy enhances its practical value and underscores its utility in distinct forest management contexts.

Ábri, T., Rédei, K., 2022. Analyses of periodic annual increment by diameter and volume in differently aged black locust (Robinia pseudoacacia L.) stands: Case study. Journal of Forest Science, 68 (6): 213-219. DOI:
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. Ecological Modelling, 221 (8): 1119-1130. DOI:
Albert, M., Nagel, R.V., Sutmöller, J., Schmidt, M., 2018. Quantifying the effect of persistent dryer climates on forest productivity and implications for forest planning: A case study in northern Germany. Forest Ecosystems, 5 (1): 1-21. DOI:
Allen, M., Brunner, A., Antón-Fernández, C., Astrup, R., 2021. The relationship between volume increment and stand density in Norway spruce plantations. Forestry: An International Journal of Forest Research, 94 (1): 151-165. DOI:
Bauwe, A., Jurasinski, G., Scharnweber, T., Schröder, C., Lennartz, B., 2015. Impact of climate change on tree-ring growth of Scots pine, common beech and pedunculate oak in northeastern Germany. iForest – Biogeosciences and Forestry, 9 (1): 11. DOI:
Bayat, M., Bettinger, P., Hassani, M., Heidari, S., 2021. Ten-year estimation of Oriental beech (Fagus orientalis Lipsky) volume increment in natural forests: a comparison of an artificial neural networks model, multiple linear regression and actual increment. Forestry: An International Journal of Forest Research, 94 (4): 598-609. DOI:
Browne, L., Wright, J.W., Fitz-Gibbon, S., Gugger, P.F., Sork, V.L., 2019. Adaptational lag to temperature in valley oak (Quercus lobata) can be mitigated by genome-informed assisted gene flow. Proceedings of the National Academy of Sciences, 116 (50): 25179-25185. DOI:
Bruchwald, A., Rymer-Dudzińska T., Dudek, A., Michalak, K., Wróblewski, L., Zasada, M., 2000. Wzory empiryczne do określania wysokości i pierśnicowej liczby kształtu drzewa. (Empirical formulae for defining height and dbh shape figure of thick wood). Sylwan, 144 (10): 5-13.
Brunner, A., Forrester, D.I., 2020. Tree species mixture effects on stem growth vary with stand density – An analysis based on individual tree responses. Forest Ecology and Management, 473: 118334. DOI:
Budzyńska, K, Stuczyński, T., Zaliwski, A, 2001. Numerical agricultural soil map of Poland at the scale of 1:500 000. Acta Agrophysica, 50: 271-274.
Caignard, T., Kremer, A., Firmat, C., Nicolas, M., Venner, S., Delzon, S., 2017. Increasing spring temperatures favor oak seed production in temperate areas. Scientific Reports, 7 (1): 1-8. DOI:
Cheng, J., Sun, J., Yao, K., Xu, M., Cao, Y., 2022. A variable selection method based on mutual information and variance inflation factor. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 268: 120652. DOI:
Cicsa, A., Tudoran, G.M., Boroeanu, M., Dobre, A.C., Spârchez, G., 2021. Estimation of the productivity potential of mountain sites (mixed beech-coniferous stands) in the Romanian Carpathians. Forests, 12 (5): 549. DOI:
Coops, N.C., Shang, C., Wulder, M.A., White, J.C., Hermosilla, T., 2020. Change in forest condition: Characterizing non-stand replacing disturbances using time series satellite imagery. Forest Ecology and Management, 474: 118370. DOI:
Costa, A., Madeira, M., Oliveira, Â.C., 2008. The relationship between cork oak growth patterns and soil, slope and drainage in a cork oak woodland in Southern Portugal. Forest Ecology and Management, 255 (5-6): 1525-1535. DOI:
Drobyshev, I., Niklasson, M., Eggertsson, O., Linderson, H., Sonesson, K., 2008. Influence of annual weather on growth of pedunculate oak in southern Sweden. Annals of Forest Science, 65 (5): 512-512. DOI:
Eaton, E., Caudullo, G., Oliveira, S., Rigo, D. de, 2016. Quercus robur and Quercus petraea in Europe: Distribution, habitat, usage and threats. Luxembourg: Publication Office of the European Union. Available from: [accessed: 10.03.2023].
Di Filippo, A., Alessandrini, A., Biondi, F., Blasi, S., Portoghesi, L., Piovesan, G., 2010. Climate change and oak growth decline: Dendroecology and stand productivity of a Turkey oak (Quercus cerris L.) old stored coppice in Central Italy. Annals of Forest Science, 67 (7): 706. DOI:
Fortin, M., Van Couwenberghe, R., Perez, V., Piedallu, C., 2019. Evidence of climate effects on the height-diameter relationships of tree species. Annals of Forest Science, 76 (1): 1-20. DOI:
Friedrichs, D.A., Bntgen, U., Frank, D.C., Esper, J., Neuwirth, B., Loffler, J., 2009. Complex climate controls on 20th century oak growth in Central-West Germany. Tree Physiology, 29 (1): 39-51. DOI:
Gadow, K.V., Kotze, H., 2014. Tree survival and maximum density of planted forests – Observations from South African spacing studies. Forest Ecosystems, 1 (1): 1-9. DOI:
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. Journal of Forest Research, 22 (4): 209-217. DOI:
Gauthier, S., Bernier, P., Kuuluvainen, T., Shvidenko, A.Z., Schepaschenko, D.G., 2015. Boreal forest health and global change. Science, 349 (6250): 819-822. DOI:
Gieger, T., Thomas, F.M., 2005. Differential response of two Central-European oak species to single and combined stress factors. Trees – Structure and Function, 19 (5): 607-618. DOI:
Greenwell, B.M., Boehmke, B.C., 2020. Variable importance plots-an introduction to the vip package. The R Journal, 12 (1): 343-366. Available from: [accessed: 17.03.2022].
Groover, A., 2017. Age-related changes in tree growth and physiology. Encyclopedia of Life Sciences, 12 (1): 1-7. DOI:
Hamidi, S.K., Zenner, E.K., Bayat, M., Fallah, A., 2021. Analysis of plot-level volume increment models developed from machine learning methods applied to an uneven-aged mixed forest. Annals of Forest Science, 78 (1): 1-16. DOI:
Hastie, T.J., Tibshirani, R.J., 2017. Generalized additive models. Chapman and Hall/CRC. DOI:
James, G., Witten, D., Hastie, T., Tibshirani, R., 2013. An introduction to statistical learning. In: Springer texts in statistics. New York: Springer, pp. 1-14. DOI:
Johnson, P.S., Shifley, S.R., Rogers, R., 2002. The ecology and silviculture of Oaks. Oxford University Press, 544 pp. Available from: [accessed: 12.04.2023].
Johnson, S.E., Abrams, M.D., 2009. Age class, longevity and growth rate relationships: Protracted growth increases in old trees in the eastern United States. Tree Physiology, 29 (11): 1317-1328. DOI:
Kravkaz-Kuscu, I.S., Sariyildiz, T., Cetin, M., Yigit, N., Sevik, H., Savaci, G., 2018. Evaluation of the soil properties and primary forest tree species in Taskopru (Kastamonu) district. Fresenius Environmental Bulletin, 27 (3): 1613-1617.
Krug, J.H.A., 2019. How can forest management increase biomass accumulation and CO2 sequestration? A case study on beech forests in Hesse, Germany. Carbon Balance and Management, 14 (1): 1-16. DOI:
Larsen, K., 2015. GAM: The predictive modeling silver bullet. Public. Available from: [accessed: 05.03.2023].
Manso, R., Davidson, R., Mclean, J.P., 2022. Diameter, height and volume increment single tree models for improved Sitka spruce in Great Britain. Forestry: An International Journal of Forest Research Forestry, 95 (3): 391-404. DOI:
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? Annals of Forest Science, 76 (1): 1-12. DOI:
Melnychuk, M.C., Peterson, E., Elliott, M., Hilborn, R., 2017. Fisheries management impacts on target species status. Proceedings of the National Academy of Sciences of the United States of America, 114 (1): 178-183. DOI:
Mendes, H., De Fátima Borges, M., Scott, C.L., Frid, C., 2008. Climatic impact on hake recruitment in Iberian Peninsula and implications for fisheries management: An InExFish project study. Halifax: Annual Science Conference. Available from: [accessed: 23.05.2023].
Meredieu, C., Perret, S., Dreyfus, P., 2002. Modelling dominant height growth: Effect of stand density. Workshop on Reality models and parameters estimation: The forestry scenario, Sesimbra, PRT, 2-5 June 2002, pp. 111-121. Available from: [accessed: 23.11.2022].
Murray, L., Nguyen, H., Lee, Y.-F., Remmenga, M.D., Smith, D.W., 2012. Variance inflation factors in regression models with dummy variables. In: W. Song, ed. Conference on Applied Statistics in Agriculture. Kansas State University Libraries, New Prairie Press, pp. 161-177. DOI:
Orwig, D.A., Cogbill, C.V, Foster, D.R., O’keefe, J.F., 2001. Variations in old-growth structure and definitions: Forest dynamics on Wachusett mountain, Massachusetts. Ecological Applications, 11 (2): 437-452. DOI:
Passioura, J.B., 1991. Soil structure and plant growth. Australian Journal of Soil Research, 29 (6): 717-728. DOI:
Petritan, A.M., Biris, I.A., Merce, O., Turcu, D.O., Petritan, I.C., 2012. Structure and diversity of a natural temperate sessile oak (Quercus petraea L.) – European Beech (Fagus sylvatica L.) forest. Forest Ecology and Management, 280: 140-149. DOI:
Pilcher, J.R., Gray, B., 1982. The relationships between Oak tree growth and climate in Britain. The Journal of Ecology, 70 (1): 297. DOI:
Pretzsch, H., 2010. Forest dynamics, growth and yield: From measurement to model. Berlin, Heidelberg: Springer, 664 pp. DOI:
R Core Team, 2021. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available from:
Río, M., Sterba, H., 2009. Comparing volume growth in pure and mixed stands of Pinus sylvestris and Quercus pyrenaica. Annals of Forest Science, 66 (5): 502-502. DOI:
Rohner, B., Bugmann, H., Bigler, C., 2013. Estimating the age-diameter relationship of oak species in Switzerland using nonlinear mixed-effects models. European Journal of Forest Research, 132 (5-6): 751-764. DOI:
Ryan, M.G., Yoder, B.J., 1997. Hydraulic limits to tree height and tree growth: What keeps trees from growing beyond a certain height? BioScience, 47 (4): 235-242. DOI:
Socha, J., Hawryło, P., Pierzchalski, M., Stereńczak, K., Krok, G., Wężyk, P., Tymińska-Czabańska, L., 2020. An allometric area-based approach – A cost-effective method for stand volume estimation based on ALS and NFI data. Forestry: An International Journal of Forest Research, 93 (3): 344-358. DOI:
Socha, J., Tymińska-Czabańska, L., 2019. A method for the development of dynamic site index models using height – Age data from temporal sample plots. Forests, 10 (7): 542. DOI:
Stimm, K., Heym, M., Nagel, R.V., Uhl, E., Pretzsch, H., 2022. Long-term productivity of monospecific and mixed Oak (Quercus petraea [Matt.] Liebl. and Quercus robur L.) Stands in Germany: Growth dynamics and the effect of stand structure. Forests, 13 (5): 724. DOI:
Stokland, J.N., 2021. Volume increment and carbon dynamics in boreal forest when extending the rotation length towards biologically old stands. Forest Ecology and Management, 488: 119017. DOI:
Tomter, S.M., Kuliešis, A., Gschwantner, T., 2016. Annual volume increment of the European forests – description and evaluation of the national methods used. Annals of Forest Science, 73 (4): 849-856. DOI:
Torres, A.B., Lovett, J.C., 2013. Using basal area to estimate aboveground carbon stocks in forests: La Primavera Biosphere’s Reserve, Mexico. Forestry: An International Journal of Forest Research, 86 (2): 267-281. DOI:
Trouillier, M., van der Maaten-Theunissen, M., Scharnweber, T., Wilmking, M., 2020. A unifying concept for growth trends of trees and forests – The ‘Potential Natural Forest’. Frontiers in Forests and Global Change, 3: 581334. DOI:
Tymińska-Czabańska, L., Socha, J., Maj, M., Cywicka, D., Hoang Duong, X.V., 2021. Environmental drivers and age trends in site productivity for oak in southern Poland. Forests, 12 (2): 209. DOI:
Vanclay, J.K., 1994. Modelling forest growth and yield: applications to mixed tropical forests. Wallingford: CAB International, 312 pp.
Viet, H.D.X., Tymińska-Czabańska, L., Socha, J., 2023. Modeling the effect of stand characteristics on Oak volume increment in Poland using generalized additive models. Forests, 14 (1): 123. DOI:
Vospernik, S., Heym, M., Pretzsch, H., Pach, M., Steckel, M., Aldea, J., Brazaitis, G., Bravo-Oviedo, A., Del Rio, M., Löf, M., Pardos, M., Bielak, K., Bravo, F., Coll, L., Černý, J., Droessler, L., Ehbrecht, M., Jansons, A., Korboulewsky, N., Jourdan, M., Nord-Larsen, T., Nothdurft, A., Ruiz-Peinado, R., Ponette, Q., Sitko, R., Svoboda, M., Wolff, B., 2023. Tree species growth response to climate in mixtures of Quercus robur/Quercus petraea and Pinus sylvestris across Europe – a dynamic, sensitive equilibrium. Forest Ecology and Management, 530: 120753. DOI:
Wang, W., Chen, X., Zeng, W., Wang, J., Meng, J., 2019. Development of a mixed-effects individual-tree basal area increment model for Oaks (Quercus spp.) considering forest structural diversity. Forests, 10 (6): 474. DOI:
Weiskittel, A.R., Hann, D.W., Kershaw, J.A., Vanclay, J.K., 2011. Forest growth and yield modeling. John Wiley & Sons, Ltd., 45 pp. DOI:
West, P.W., 2014. Growing plantation forests. Springer International Publishing, 329 pp. DOI:
West, P.W., 2015. Tree and forest measurement. Springer International Publishing, 209 pp. DOI:
Wood, S.N., 2017. Generalized additive models. New York: Chapman and Hall/CRC, 496 pp. DOI:
Wu, S.-H., Chao, C.-T., Huang, B.-H., Luo, M.-X., Duan, X.-G., Liao, P.-C., 2020. Environmental disturbance in natural forest and the effect of afforestation methods on timber volume increment in Pinus sylvestris L. var. mongolica Litv. Global Ecology and Conservation, 24: 1311. DOI:
Xo Viet, H.D., Tymińska-Czabańska, L., Socha, J., 2022. Drivers of site productivity for oak in Poland. Dendrobiology, 88: 81-93. DOI:
Yu, Y., Chen, J.M., Yang, X., Fan, W., Li, M., He, L., 2017. Influence of site index on the relationship between forest net primary productivity and stand age. PlosOne, 12 (5): 177084. DOI:
Zacharski, R., 2018. Training Sets, Test Sets, and 10-fold Cross-validation. KDnuggets. Available from: [accessed: 30.12.2022].
Zhao, D., Kane, M., Borders, B.E., 2010. Development and applications of the relative spacing model for loblolly pine plantations. Forest Ecology and Management, 259 (10): 1922-1929. DOI:
Zielony, R., Kliczkowska, A., 2012. Regionalizacja przyrodniczo-leśna Polski 2010. Warszawa: Centrum Informacyjne Lasów Państwowych, 359 pp.