Vladimir Shanin, Pavel Grabarnik, Maxim Shashkov, Natalya Ivanova, Sergey Bykhovets, Pavel Frolov, Miroslav Stamenov


Most models of forest communities cannot represent the asymmetry of crowns resulting from inter-tree competition. However, this is important for the accurate simulation of mixed and uneven-aged forest stands. In the paper we propose a new model, which is individual-based and spatially-explicit, i.e., taking into account the relative positions and properties of all competing trees in a forest stand. The model uses species-specific coefficients, thus it allows to take into account the different strategies of competition for light. The model operates with the 3D-representation of tree crowns and light transmission through the canopy, with discrete spatial and temporal resolution. It thus enables to represent the asymmetry of the crown shape and biomass distribution in response to the local surrounding of a given tree. In order to estimate the performance of the model in the simulation of aboveground competition, a set of simulation scenarios, representing stands of different spatial structures, ages, and species compositions, was used. Simulations showed the positive effect of species mixture on crown size and light interception efficiency, as well as species- and age-related dependencies of these parameters. Differences in the spatial structure mostly affected the light transmission pattern at the stand level. The importance of crown asymmetry in the increase in light interception efficiency was also shown. Thus, the proposed model allows simulating light absorption by the canopy with a high spatial resolution, using relatively few parameters. The model imitates a mechanism allowing trees to decrease the aboveground competition in forest stands and it also is applicable for simulating aboveground competition in mixed uneven-aged stands.


competition, PAR, crown asymmetry, mixed uneven-aged stands

Full Text:



Anonymous. 1987–2001. Scientific and applied reference book on climate of USSR [Nauchno-prikladnoy spravochnik po klimatu SSSR]. Issues 1–34. Leningrad (Saint Petersburg), Gidrometeoizdat. (In Russian).

Aubin, I., Beaudet, M., & Messier, C. 2000. Light extinction coefficients specific to the understory vegetation of the southern boreal forest, Quebec. Can. J. For. Res. 30: 168–177. doi:10.1139/x99-185

Bobkova, K.S., Urnyshev, A.P., & Urnyshev, V.A. 2000. Vertical distribution of phytomass in spruce forests of European north-east [Vertikal'noe raspredelenie fitomassy v elovykh lesakh evropeiskogo severo-vostoka]. Lesovedenie 3: 49–54. (In Russian).

Bossel, H. 1996. TREEDYN3 forest simulation model. Ecol. Model. 90. 187–227. doi:10.1016/0304-3800(95)00139-5

Brisson, J. 2001. Neighborhood competition and crown asymmetry in Acer saccharum. Can. J. For. Res. 31: 2151–2159. doi:10.1139/x01-161

Canham, C.D. 1988. An index for understory light levels in and around canopy gaps. Ecology,69: 1634–1638. doi:10.2307/1941664

Cavard, X., Bergeron, Y., Chen, H.Y.H., Paré, D., Laganiére, J., & Brassard, B. 2011. Competition and facilitation between tree species change with stand development. Oikos 120:1683–1695. doi:10.1111/j.1600-0706.2011.19294.x

Cescatti, A. 1997a. Modelling the radiative transfer in discontinuous canopies of asymmetric crowns. I. Model structure and algorithms. Ecol. Model. 101(2–3): 263–274. doi:10.1016/S0304-3800(97)00050-1

Cescatti, A. 1997b. Modelling the radiative transfer in discontinuous canopies of asymmetric crowns. II. Model testing and application in a Norway spruce stand. Ecol. Model. 101(2–3): 275–284. doi:10.1016/S0304-3800(97)00055-0

Collalti, A., Perugini, L., Santini, M., Chiti, T., Nolèc, A., Matteucci, G., & Valentini, R. 2014. A process-based model to simulate growth in forests with complex structure: Evaluation and use of 3D-CMCC Forest Ecosystem Modeling a deciduous forest in Central Italy. Ecol. Model. 272: 362–378. doi:10.1016/j.ecolmodel.2013.09.016

Daniels, R.F., Burkhart, H.E., & Clason, T.R. 1986. A comparison of competition measures for predicting growth of loblolly pine trees. Can. J. For. Res. 16: 1230–1237. doi:10.1139/x86-218

Danilov, D.A. & Ischuk, T.A. 2013. Competitive relationships in the pine-spruce stands undergone improvement thinning and complex forest care [Otsenka konkurentnykh vzaimootnosheniy sosny i eli v smeshannykh drevostoyakh chernichnogo tipa lesa, proidennykh rubkami ukhoda i kompleksnym ukhodom za lesom]. Sistemy. Metody. Tekhnologii 1(17): 176–181. (In Russian with English summary).

Duursma, R.A. & Mäkelä, A. 2007. Summary models for light interception and light-use efficiency of non-homogeneous canopies. Tree Physiol. 27: 859–870. doi:10.1093/treephys/27.6.859

Evstigneev, O.I. 2018. Ontogenetic scales of relation of trees to light (on the example of eastern European forests). Russ. J. Ecosyst. Ecol. 3(3). doi:10.21685/2500-0578-2018-3-3

Frolova, G., Frolov, P., Ivanova, N., & Shanin, V. 2018. Analysis of competitive interactions between undergrowth and ground layer vegetation in pine forests of the European part of Russia. In M. Zhiyanski, M. Glushkova, & M. Georgieva (eds.) International scientific conference “90 years Forest research institute – for the society and natureâ€, 24–26 October 2018, Sofia, Bulgaria. Book of abstracts. P. 56.

Galenko, E.P. 1983. Phytoclimate and energetic factors of productivity of coniferous forest of European North [Fitoklimat I energeticheskie factory produktivnosti khvoynogo lesa Evropeyskogo severa]. Leninrad, Nauka. (In Russian).

Gower, S.T., McMurtrie, R.E., & Murty, D. 1996. Aboveground net primary production decline with stand age: potential causes. Trends Ecol. Evol. 11(9): 378–382. doi:10.1016/0169-5347(96)10042-2

Green, D.G. & Sadedin, S. 2005. Interactions matter – complexity in landscapes and ecosystems. Ecol. Complex. 2: 117–130. doi:10.1016/j.ecocom.2004.11.006

Gspaltl, M., Bauerle, W., Binkley, D., & Sterba, H. 2013. Leaf area and light use efficiency patterns of Norway spruce under different thinning regimes and age classes. For. Ecol. Manage. 288: 49–59. doi:10.1016/j.foreco.2011.11.044

Gulbe, Ya.I., Ermolova, L.S., Rozhdestvenskiy, S.G., Utkin, A.I., & Tselniker, Yu.L. 1983. Vertical distribution of leaf surface and light regime in hardwood young stands of southern taiga [Vertikal'noe raspredelenie poverkhnosti list'ev i svetovoy rezhim v listvennykh molodnyakakh yuzhnoi taygi]. Lesovedenie 2: 21–29. (In Russian with English summary).

Haywood, A. 2002. Growth of advanced European beech trees in the transformation phase in the southern Black Forest. [Dissertation] University of Freiburg. 152 p.

Haefner, J.W., Poole, G.C., Dunn, P.V., & Decker, R.T. 1991. Edge effects in computer models of spatial competition. Ecol. Model. 56: 221–244. doi:10.1016/0304-3800(91)90201-B

Illian, J., Penttinen, A., Stoyan, H., & Stoyan, D. 2008. Statistical analysis and modelling of spatial point patterns. John Wiley & Sons. 560 p. ISBN: 978-0-470-01491-2.

Johansson, T. 1989. Irradiance within canopies of young trees of European aspen (Populus tremula) and European birch (Betula pubescens) in stands of different spacings. For. Ecol. Manage. 28: 217–236. doi:10.1016/0378-1127(89)90005-4

Johansson, T. 1996. Estimation of canopy density and irradiance in 20- and 40-year-old birch stands (Betula pubescens Ehrh. and Betula pendula Roth). Trees 10: 223–230. doi:10.1007/BF02185673

Kędra, K. & Gazda, A. 2016. New angular competition index and crown projection model. Abstracts of 2016 IEEE International Conference on Functional-Structural Plant Growth Modeling, Simulation, Visualization and Applications, 7–11 Nov, Qingdao, China. P. 13.

Kolobov, A.N. & Frisman, E.Ya. 2016. Individual-based model of spatio-temporal dynamics of mixed forest stands. Ecol. Complex. 27: 29–39. doi:10.1016/j.ecocom.2015.10.002

Komarov, A., Chertov, O., Zudin, S., Nadporozhskaya, M., Mikhailov, A., Bykhovets, S., Zudina, E., & Zoubkova, E. 2003. EFIMOD 2 – A model of growth and elements cycling in boreal forest ecosystems. Ecol. Model. 170(2–3): 373–392. doi:10.1016/S0304-3800(03)00240-0

Kukumägi, M., Ostonen, I., Kupper, P., Truu, M., Tulva, I., Varik, M., Aosaar, J., Sõber, J., & Lõhmus, K. 2014. The effects of elevated atmospheric humidity on soil respiration components in a young silver birch forest. Agric. For. Meteorol. 194: 167–174. doi:10.1016/j.agrformet.2014.04.003

Lebedev, A.N., Borushko, I.S., & Egorova, A.Yu. (Eds). 1979. Reference book on climate of Western Europe [Klimaticheskiy spravochnik Zapadnoi Evropy]. Leningrad, Gidrometeoizdat. (In Russian). 678 p.

Lebedev, S.V. & Chumachenko, S.I. 2002. Dynamic model of uneven-aged mixed-species forest community: modelling the light regime under the canopy [Dinamicheskaya model' raznovozrastnogo mnogovidovogo lesnogo tsenoza: modelirovanie svetovogo rezhima pod pologom]. In Ecology, monitoring and rational use of natural resources: transactions [Ekologiya, monitoring i ratsional'noe prirodopol'zovanie. Nauchnye trudy]. Issue 318. Moscow, Moscow state forest university. P. 111–118. (In Russian).

Lebedev, S.V. & Chumachenko, S.I. 2011. Individual-based dynamic model of mixed uneven-aged stand (PIXTA) [Poderevnaya model' dinamiki mnogovidovogo raznovozrastnogo nasazhdeniya (PIXTA)]. Vestnik Moskovskogo gosudarstvennogo universiteta lesa – Lesnoy vestnik 7(83): 73–80. (In Russian).

Lintunen, A., Kaitaniemi, P., Perttunen, J., & Sievänen, R. 2013. Analysing species-specific light transmission and related crown characteristics of Pinus sylvestris and Betula pendula using a shoot-level 3D model. Can. J. For. Res. 43: 929–938. doi:10.1139/cjfr-2013-0178

Majasalmi, T., Rautiainen, M., & Stenberg, P. 2014. Modeled and measured fPAR in a boreal forest: Validation and application of a new model. Agric. For. Meteorol. 189–190: 118–124. doi:10.1016/j.agrformet.2014.01.015

Mäkelä, A. & Vanninen, P. 2001. Vertical structure of Scots pine crowns in different age and size classes. Trees 15: 385–392. doi:10.1007/s004680100118

McCree, K.J. 1981. Photosynthetically active radiation. In Encyclopedia of Plant Physiology, vol. 12A. Springer-Verlag, Berlin, P. 41–55.

Mencuccini, M. & Grace, J. 1996. Hydraulic conductance, light interception and needle nutrient concentration in Scots pine stands and their relations with net primary productivity. Tree Physiol. 16: 459–468. doi:10.1093/treephys/16.5.459

Molchanov, A.G. 2000. Photosynthetic utilization efficiency of absorbed photosynthetically active radiation by Scots pine and birch forest stands in the southern Taiga. Tree Physiol. 20: 1137–1148. doi:10.1093/treephys/20.17.1137

Morin, X., Fahse, L., Scherer-Lorenzen, M., & Bugmann, H. 2011. Tree species richness promotes productivity in temperate forests through strong complementarity between species. Ecol. Lett. 14: 1211–1219. doi:10.1111/j.1461-0248.2011.01691.x

Navrátil, M., Špunda, V., Marková, I., & Janous, D. 2007. Spectral composition of photosynthetically active radiation penetrating into a Norway spruce canopy: the opposite dynamics of the blue/red spectral ratio during clear and overcast days. Trees 21: 311–320. doi:10.1007/s00468-007-0124-4.

Olchev, A., Radler, K., Sogachev, A., Panferov, O., & Gravenhorst, G. 2009. Application of a three-dimensional model for assessing effects of small clear-cuttings on radiation and soil temperature. Ecol. Model. 220: 3046–3056. doi:10.1016/j.ecolmodel.2009.02.004

Oleksyn, J., Reich, P.B., Rachwal, L., Tjoelker, M.G., & Karolewski, P. 2000. Variation in aboveground net primary production of diverse European Pinus sylvestris populations. Trees 14: 415–421. doi:10.1007/PL00009775

Olofsson, P. & Eklundh, L. 2007. Estimation of absorbed PAR across Scandinavia from satellite measurements. Part II: Modeling and evaluating the fractional absorption. Remote Sens. Environ. 110: 240–251. doi:10.1016/j.rse.2007.02.020

Ovhed, M. & Holmgren, B. 1995. Spectral Quality and Absorption of solar radiation in a mountain birch forest, Abisko, Sweden. Arctic Alpine Res. 27(4): 380–388. doi:10.1080/00040851.1995.12003135

OzolinÄius, R., MikÅ¡ys, V., & Stakénas, V. 1996. Above-ground phytomass and light regime in Norway spruce stands planted with different initial density. Biomass Bioenerg. 11(2/3): 201–206. doi:10.1016/0961-9534(96)00015-3

Peng, C., Liu, J., Dang, Q., Apps, M.J., & Jiang, H. 2002. TRIPLEX: a generic hybrid model for predicting forest growth and carbon and nitrogen dynamics. Ecol. Model. 153: 109–130. doi:10.1016/S0304-3800(01)00505-1

Perttunen, J. 2009. The LIGNUM functional-structural tree model. [Dissertation] Systems Analysis Laboratory, Helsinki University of Technology. 52 p.

Piñeiro, G., Perelman, S., Guerschman, J.P., Paruelo, J.M. 2008. How to evaluate models: observed vs. predicted or predicted vs. observed? Ecol. Model. 216: 316–322. doi:10.1016/j.ecolmodel.2008.05.006

Pretzsch, H., Biber, P., & Ďurský, J. 2002. The single tree-based stand simulator SILVA: construction, application and evaluation. For. Ecol. Manage. 162: 3–21. doi:10.1016/S0378-1127(02)00047-6

Pretzsch, H. 2014. Canopy space filling and tree crown morphology in mixed-species stands. For. Ecol. Manage. 327: 251–264. doi:10.1016/j.foreco.2014.04.027

Pretzsch, H. & Schütze, G. 2016. Effect of tree species mixing on the size structure, density, and yield of forest stands. Eur. J. For. Res. 135: 1–22. doi:10.1007/s10342-015-0913-z

Pugachevskiy, A.V. 1992. Coenopopulations of spruce: structure, dynamics, regulating factors [Tsenopopulyatsii eli: struktura, dinamika, faktory regulyatsii]. Minsk, Navuka i tekhnika. (In Russian).

Rautiainen, M. & Stenberg, P. 2005. Simplified tree crown model using standard forest mensuration data for Scots pine. Agric. For. Meteorol. 128: 123–129. doi:10.1016/j.agrformet.2004.09.002

Renaud, V., Innes, J.L., Dobbertin, M., & Rebetez, M. 2011. Comparison between open-site and below-canopy climatic conditions in Switzerland for different types of forests over 10 years (1998−2007). Theor. Appl. Climatol. 105: 119–127. doi:10.1007/s00704-010-0361-0

Renshaw, E. 1985. Computer simulation of Sitka spruce: spatial branching models for canopy growth and root structure. Math. Med. Biol. 2: 183–200. doi:10.1093/imammb/2.3.183

Ross, J. 1981. The radiation regime and architecture of plant stands. Dr W. Junk Publishers, The Hague. 420 p. doi:10.1007/978-94-009-8647-3

Rouvinen, S. & Kuuluvainen, T. 1997. Structure and asymmetry of tree crowns in relation to local competition in a natural mature Scots pine forest. Can. J. For Res. 27:. 890–902. doi:10.1139/x97-012

Schröter, M., Härdtle, W., & von Oheimb, G. 2012. Crown plasticity and neighborhood interactions of European beech (Fagus sylvatica L.) in an old-growth forest. Eur. J. For. Res. 131: 787–798. doi:10.1007/s10342-011-0552-y

Seidl, R., Rammer, W., Scheller, R.M., & Spies, T.A. 2012. An individual-based process model to simulate landscape-scale forest ecosystem dynamics. Ecol. Model. 231: 87–100. doi:10.1016/j.ecolmodel.2012.02.015

Shanin, V.N., Shashkov, M.P., Ivanova, N.V., & Grabarnik, P.Ya. 2016. The effect of aboveground competition on spatial structure and crown shape of the dominating canopy species of forest stands of European Russia [Vliyanie konkurentsii v pologe lesa na prostranstvennuyu strukturu drevostoev i formu kron dominantov drevesnogo yarusa na primere lesov evropeiskoi chasti Rossii]. Russ. J. Ecosyst. Ecol. 1(4). doi:10.21685/2500-0578-2016-4-5 (In Russian with English summary).

Shanin, V.N., Grabarnik, P.Ya., Bykhovets, S.S., Chertov, O.G., Priputina, I.V., Shashkov, M.P., Ivanova, N.V., Stamenov, M.N., Frolov, P.V., Zubkova, E.V., & Ruchinskaya, E.V. 2019. Parameterization of productivity model for the most common trees species in European part of Russia for simulation of forest ecosystem dynamics [Parametrizatsiya modeli produktsionnogo protsessa dlya dominiruyushchikh vidov derev'ev Evropeyskoy chasti RF v zadachakh modelirovaniya dinamiki lesnykh ekosistem]. Math. Biol. Bioinformatics 14(1). doi: 10.17537/2019.14.54 (In Russian with English summary).

Shashkov, M., Ivanova, N., Shanin, V., & Grabarnik, P. 2019. Ground surveys versus UAV photography: the comparison of two tree crown mapping techniques. In I. Bychkov, V. Voronin (eds). Information Technologies in the Research of Biodiversity. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. P. 48–56. doi: 10.1007/978-3-030-11720-7_8

Shvidenko, A.Z., Schepaschenko, D.G., Nilsson, S., & Buluy, Yu.I. 2008. Tables and models of growth and productivity of forests of major forest forming species of Northern Eurasia (standard and reference materials). Second edition, supplemented. Moscow, Federal Agency Of Forest Management, International Institute For Applied Systems Analysis. 886 p.

Sterba, H, Blab, A, & Katzensteiner, K 2002. Adapting as individual tree growth model for Norway spruce (Picea abies L. Karst.) in pure and mixed species stands. For. Ecol. Manage. 159: 101–110. doi:10.1016/S0378-1127(01)00713-7

Stoll, P. & Schmid, B. 1998. Plant foraging and dynamic competition between branches of Pinus sylvestris in contrasting light environments. J. Ecol. 86: 934–945. doi:10.1046/j.1365-2745.1998.00313.x

Tahvanainen, T. & Forss, E. 2008. Individual tree models for the crown biomass distribution of Scots pine, Norway spruce and birch in Finland. For. Ecol. Manage. 255: 455–467. doi:10.1016/j.foreco.2007.09.035

Thorpe, H.C., Astrup, R., Trowbridge, A., & Coates, K.D. 2010. Competition and tree crowns: a neighborhood analysis of three boreal tree species. For. Ecol. Manage. 259: 1586–1596. doi:10.1016/j.foreco.2010.01.035

Tran, Q.T., Tainar, D., & Safar, M. 2009. Reverse k nearest neighbor and reverse farthest neighbor search on spatial networks. In A. Hameurlain, J. Küng, & R. Wagner (eds.). Transactions on large-scale data- and knowledge-centered systems. 374 p. doi:10.1007/978-3-642-03722-1.

Tselniker, Yu.L., Malkina, I.S., Gurtsev, A.I., & Nikolayev, D.K. 1999. Quantitative estimation of light regime based on morphostructural indicators of crowns of spruce saplings [Kolichestvennaya otsenka svetovogo rezhima po morfostrukturnym pokazatelyam kron podrosta eli]. Lesovedenie 4: 64–69. (In Russian).

Usoltsev, V.A. 2013a. Structure of tree biomass-height profiles: studying a system of regularities [Vertikal'no-fraktsionnaya struktura fitomassy derev'ev. Issledovanie zakonomernostey]. Ekaterinburg, Ural State Forest Engineering University. 602 p. (In Russian with English summary).

Usoltsev, V.A. 2013b Production and competitive relations of trees: studying a system of regularities [Produktsionnye pokazateli i konkurentnye otnosheniya derev'ev. Issledovanie zavisimostei]. Ekaterinburg, Ural State Forest Engineering University. 553 p. (In Russian with English summary).

Usoltsev, V.A. 2016a Single-tree biomass of forest-forming species in Eurasia: database, climate-related geography, weight tables [Fitomassa model'nykh derev'ev lesoobrazuyushchikh porod Evrazii: baza dannykh, klimaticheski obuslovlennaya geografiya, taksatsionnye normativy]. Ekaterinburg, Ural State Forest Engineering University. 336 p. (In Russian with English summary).

Usoltsev, V.A. 2016b. Biological productivity of forest-forming species in Eurasia's climatic gradients (as related to supporting decision-making processes in forest management) [Biologicheskaya produktivnost' lesoobrazuyushchikh porod v klimaticheskikh gradientakh Evrazii (k menedzhmentu biosfernykh funktsiy lesov)]. Ekaterinburg, Ural State Forest Engineering University. 384 p. (In Russian with English summary).

Uri, V., Lõhmus, K., Ostonen, I. Tullus, H., Lastik, R., & Vildo, M. 2007. Biomass production, foliar and root characteristics and nutrient accumulation in young silver birch (Betula pendula Roth.) stand growing on abandoned agricultural land. Eur. J. For. Res. 126(4): 495–506. doi:10.1007/s10342-007-0171-9

Uria-Diez, J. & Pommerening, A. 2017. Crown plasticity in Scots pine (Pinus sylvestris L.) as a strategy of adaptation to competition and environmental factors. Ecol. Model. 356: 117–126. doi:10.1016/j.ecolmodel.2017.03.018

Varik, M., Kukumägi, M., Aosaar, J., Becker, H., Ostonen, I., Lõhmus, K. & Uri, V. 2015. Carbon budgets in fertile silver birch (Betula pendula Roth) chronosequence stands. Ecol. Eng. 77: 284–296. doi:10.1016/j.ecoleng.2015.01.041

Walter, J.-M.N. & Himmler, C.G. 1996. Spatial heterogeneity of a Scots pine canopy: an assessment by hemispherical photographs. Can. J. For. Res. 26: 1610–1619. doi:10.1139/x26-181

Widlowski, J.-L., Verstraete, M., Pinty, B., & Gobron, N. 2003. Allometric relationships of selected European tree species. EC Joint Research Centre, Technical Report EUR 20855 EN, Ispra, Italy. 61 p.

Wu, H., Sharp, P.J., Walker, J., & Penridge, L.K. 1985. Ecological field theory: a spatial analysis of resource interference among plants. Ecol. Model. 29: 215–243. doi:10.1016/0304-3800(85)90054-7

Xiao, C.-W., Yuste, J.C., Janssens, I.A., Roskams, P., Nachtergale, L., Carrara, A., Sanchez, B.Y., & Ceulemans, R. 2003. Above- and belowground biomass and net primary production in a 73-year-old Scots pine forest. Tree Physiol. 23: 505–516. doi:10.1093/treephys/23.8.505

Yarmishko, V.T. 1999. Vertical structure of aboveground biomass profiles of Pinus sylvestris L. at northern range limit under atmospheric pollution [Vertikal'no-fraktsionnaya struktura nadzemnoy fitomassy Pinus sylvestris L. na severnom predele rasprostraneniya v usloviyakh atmosfernogo zagryazneniya]. Rastitel'nye resursy 35(1): 3–13. (In Russian).


  • There are currently no refbacks.


© 2008 Mathematical and Computational Forestry & Natural-Resource Sciences