Parameterization of productivity model for the most common trees species in european part of Russia for simulation of forest ecosystem dynamics

V. N. Shanin ; P. Ya. Grabarnik ; S. S. Bykhovets ; O. G. Chertov ; I. V. Priputina ; M. P. Shashkov ; N. V. Ivanova ; M. N. Stamenov ; P. V. Frolov ; E. V. Zubkova ; E. V. Ruchinskaya

Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 1, pp. 54-76.

Résumé

The proposed model is the version of well-known biomass production model 3-PG (Physiological Principles Predicting Growth), which allows for calculation of biomass production in dependence of consumed soil nitrogen and available solar radiation. The model utilizes the concept of modifiers, i.e. functions describing the effect of tree age and environmental factors (air temperature and humidity, soil moisture, carbon dioxide concentration) on productivity. To make the model applicable to mixed forests of European Russia, the substantial modifications were implemented. In particular, more detailed response functions to air temperature, soil moisture and absorbed nitrogen were introduced. We also implemented new procedure of calculation of light use efficiency taking into account the difference between shade-tolerant and shade-intolerant tree species. The rank distribution equation was used for the description of an increment allocation to different tree biomass compartments. Model parameters were estimated for the 12 most common tree species of European Russia. The model was implemented as sub-routine for calculation of biomass production in forest ecosystem model EFIMOD 2. The model performance was tested against the wide range of environmental conditions.

Bibliographie

[1] A. N. Kolobov, E. Ya. Frisman, Matematicheskaya biologiya i bioinformatika, 11:2 (2016), 323–335 | DOI | MR

[2] M. D. Korzukhin, “K ekologo-fiziologicheskoi modeli lesnoi dinamiki”, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 9, Gidrometeoizdat, L., 1986, 259–276

[3] V. N. Kudeyarov (red.), Modelirovanie dinamiki organicheskogo veschestva v lesnykh ekosistemakh, Nauka, M., 2007, 380 pp.

[4] S. I. Chumachenko, V. N. Korotkov, M. M. Palenova, D. V. Politov, Ecol. Model., 170:2-3 (2003), 345–362 | DOI

[5] A. Olchev, K. Radler, A. Sogachev, O. Panferov, G. Gravenhorst, Ecol. Model., 220:21 (2009), 3046–3056 | DOI

[6] G. R. Larocque, A. Komarov, O. Chertov, V. Shanin, J. Liu, J. S. Bhatti, W. Wang, C. Peng, H. H. Shugart, W. Xi, J. A. Holm, “Process-based models: a synthesis of models and applications to address environmental and management issues”, Ecological forest management handbook, ed. G. R. Larocque, CRC Press, Boca Raton, 2016, 223–266 | DOI

[7] S. Marconi, T. Chiti, A. Nolè, R. Valentini, A. Collalti, Forests, 8:6 (2017), 220 | DOI

[8] R. Seidl, W. Rammer, R. M. Scheller, T. A. Spies, Ecol. Model., 231 (2012), 87–100 | DOI

[9] A. S. Komarov, O. G. Chertov, S. L. Zudin, M. A. Nadporozhskaya, A. V. Mikhailov, S. S. Bykhovets, E. V. Zudina, E. V. Zoubkova, Ecol. Model., 170:2-3 (2003), 373–392 | DOI

[10] A. S. Komarov, O. G. Chertov, S. S. Bykhovets, I. V. Priputina, V. N. Shanin, E. O. Vidyagina, V. G. Lebedev, K. A. Shestibratov, Matematicheskaya biologiya i bioinformatika, 10:2 (2015), 398–415 | DOI

[11] I. V. Priputina, G. G. Frolova, S. S. Bykhovets, V. N. Shanin, V. G. Lebedev, K. A. Shestibratov, Matematicheskaya biologiya i bioinformatika, 11:2 (2016), 245–262 | DOI

[12] V. N. Shanin, A. S. Komarov, R. Mäkipää, Eur. J. For. Res, 133:2 (2014), 273–286 | DOI

[13] V. Shanin, S. Valkonen, P. Grabarnik, R. Mäkipää, For. Ecol. Manag., 378 (2015), 193–205 | DOI

[14] V. N. Shanin, L. K. Rocheva, M. P. Shashkov, N. V. Ivanova, S. V. Moskalenko, E. R. Burnasheva, Izvestiya Rossiiskoi akademii nauk. Seriya biologicheskaya, 2015, no. 3, 316–325 | DOI

[15] V. N. Shanin, M. P. Shashkov, N. V. Ivanova, P. Ya. Grabarnik, Russ. J. Ecosyst. Ecol., 1:4 (2016) | DOI | Zbl

[16] X. Morin, L. Fahse, M. Scherer-Lorenzen, H. Bugmann, Ecol. Lett., 14:12 (2011), 1211–1219 | DOI

[17] H. Pretzsch, For. Ecol. Manag, 327 (2014), 251–264 | DOI

[18] S. N. Sannikov, N. S. Sannikova, Sibirskii lesnoi zhurnal, 2014, no. 1, 25–34

[19] M. Loreau, A. Hector, Nature, 412 (2001), 72–76 | DOI

[20] M. Mina, M. O. Huber, D. I. Forrester, E. Thürig, B. Rohner, J. Ecol., 103:3 (2018), 1106–1119 | DOI

[21] H. Pretzsch, Forest dynamics, growth and yield: from measurement to model, Springer-Verlag, Berlin, 2010, 664 pp. | DOI

[22] J. J. Landsberg, R. H. Waring, For. Ecol. Manag, 95:3 (1997), 209–228 | DOI

[23] C. Peng, J. Liu, Q. Dang, M. J. Apps, H. Jiang, Ecol. Model, 153:1-2 (2002), 109–130 | DOI

[24] V. N. Shanin, M. P. Shashkov, N. V. Ivanova, S. S. Bykhovets, P. Ya. Grabarnik, “Model konkurentsii za svet mezhdu derevyami v smeshannykh drevostoyakh borealnoi zony s uchetom asimmetrii kron”, Nauchnye osnovy ustoichivogo upravleniya lesami:, Materialy II Vserossiiskoi nauchnoi konferentsii (s mezhdunarodnym uchastiem), TsEPL RAN, M., 2016, 62–63

[25] V. N. Shanin, M. P. Shashkov, N. V. Ivanova, S. S. Bykhovets, P. V. Frolov, P. Ya. Grabarnik, “Model konkurentsii za svet v smeshannykh drevostoyakh borealnoi zony”, Matematicheskoe modelirovanie v ekologii, Materialy Pyatoi Natsionalnoi nauchnoi konferentsii s mezhdunarodnym uchastiem (16-20 oktyabrya 2017 g.), IFKhiBPP RAN, Puschino, 2017, 252–254

[26] A. Mäkelä, P. Hari, F. Berninger, H. Hänninen, E. Nikinmaa, Tree Physiol, 24:4 (2004), 369–376 | DOI

[27] A. Mäkelä, M. Pulkkinen, P. Kolari, F. Lagergren, P. Berbigier, A. Lindroth, D. Loustau, E. Nikinmaa, T. Vesala, P. Hari, Glob. Change Biol., 14:1 (2008), 92–108 | DOI

[28] B. Y. Amichev, M. Johnston, K. C. J. van Rees, Biomass Bioenergy, 34:5 (2010), 687–702 | DOI

[29] E. Dreyer, X. Le Roux, P. Montpied, F. A. Daudet, F. Masson, Tree Physiol., 21:4 (2001), 223–232 | DOI

[30] B. E. Medlyn, E. Dreyer, D. Ellsworth, M. Forstreuter, P. C. Harley, M. U.F. Kirschbaum, X. Le Roux, P. Montpied, J. Strassemeyer, A. Walcroft, K. Wang, D. Loustau, Plant Cell Environ, 25:9 (2002), 1167–1179 | DOI

[31] Niinemets, V. Oja, O. Kull, Plant Cell Environ, 22:12 (1999), 1497–1513 | DOI

[32] M. D. Korzukhin, N. N. Vygodskaya, I. M. Milyukova, F. A. Tatarinov, Yu. L. Tselniker, Fiziologiya rastenii, 51:3 (2004), 341–354

[33] M. D. Korzukhin, Yu. L. Tselniker, S. M. Semenov, Meteorologiya i gidrologiya, 2008, no. 12, 56–69

[34] M. D. Korzukhin, Yu. L. Tselniker, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 22 (2009), 92–123

[35] M. D. Korzukhin, Yu. L. Tselniker, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 23 (2010), 249–268

[36] Yu. L. Tselniker, M. D. Korzukhin, G. G. Suvorova, L. S. Yankova, L. D. Kopytova, A. K. Filippova, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 21 (2007), 265–292

[37] Yu. L. Tselniker, M. D. Korzukhin, S. M. Semenov, Lesovedenie, 2010, no. 2, 36–45

[38] A. V. Olchev, Yu. A. Kurbatova, A. V. Varlagin, N. N. Vygodskaya, Lesovedenie, 2008, no. 3, 3–13 | MR

[39] A. V. Olchev, Yu. A. Kurbatova, F. A. Tatarinov, A. G. Molchanov, A. V. Varlagin, I. I. Gorshkova, N. N. Vygodskaya, Uspekhi sovremennoi biologii, 129:6 (2009), 565–578

[40] V. B. Pridacha, V. K. Bolondinskii, A. V. Olchev, T. A. Sazonova, Izvestiya RAN. Seriya biologicheskaya, 2017, no. 2, 114–119 | DOI

[41] G. D. Farquhar, S. von Caemmerer, J. A. Berry, Planta, 149 (1980), 78–90 | DOI

[42] P. G. Jarvis, Philos. T. Roy. Soc. Lon. B, 273:927 (1976), 593–610 | DOI

[43] R. F. Appleby, W. J. Davies, Oecologia, 56:1 (1983), 30–40 | DOI

[44] T. Gebauer, Water turnover in species-rich and species-poor deciduous forests: xylem sap flow and canopy transpiration, Dissertation, Biodiversity and Ecology Series B, 4, Georg-August-Universität, Göttingen, 2010, 146 pp. | DOI

[45] V. I. Kharuk, S. T. Im, I. A. Petrov, M. L. Dvinskaya, E. V. Fedotova, K. J. Ranson, Reg. Environ. Change, 17:3 (2017), 803–812 | DOI

[46] R. Seidl, M. J. Lexer, D. Jäger, K. Hönninger, Tree Physiol, 25:7 (2005), 939–951 | DOI

[47] P. J. Hanson, D. E. Todd, J. S. Amthor, Tree Physiol, 21:6 (2001), 345–358 | DOI

[48] S. D. Wullschleger, P. J. Hanson, “Sensitivity of sapling and mature-tree water use to altered precipitation regimes”, North American temperate deciduous forest responses to changing precipitation regimes, eds. P. J.Hanson, S. D. Wullschleger, Springer, New York, 2003, 87–98 | DOI

[49] E. V. Shein, Kurs fiziki pochv, Izdatelstvo MGU, M., 2005, 432 pp. | MR

[50] K. E. Saxton, W. J. Rawls, Soil Sci. Soc. Am. J., 70 (2006), 1569–1578 | DOI

[51] N. Bréda, A. Granier, F. Barataud, C. Moyne, Plant Soil, 172:1 (1995), 17–27 | DOI

[52] C. Dulamsuren, M. Hauck, M. Bader, D. Osokhjargal, S. Oyungerel, S. Nyambayar, M. Runge, C. Leuschner, Tree Physiol, 29:1 (2008), 99–110 | DOI

[53] A. Geßler, C. Keitel, J. Kreuzwieser, R. Matyssek, W. Seiler, H. Rennenberg, Trees, 21:1 (2007), 1–11 | DOI

[54] T. M. Hinkley, J. P. Lassoie, S. W. Running, For. Sci, 24:S1 (1978), a0001–z0001 | DOI | MR

[55] P. Köcher, T. Gebauer, V. Horna, C. Leuschner, Ann. For. Sci., 66:1 (2009), 101 | DOI

[56] D. Lemoine, J. P. Peltier, G. Marigo, Ann. For. Sci., 58:7 (2001), 723–731 | DOI

[57] M. J. Lexer, K. Hönninger, For. Ecol. Manag., 144:1-3 (2001), 43–65 | DOI

[58] Ü. Niinemets, F. Valladares, Ecol. Monogr., 76:4 (2006), 521–547 | DOI

[59] T. G. Ranney, R. E. Bir, W. A. Skroch, Tree Physiol, 8:4 (1991), 351–360 | DOI

[60] D. A. Way, J. C. Domec, R. B. Jackson, Plant Cell Environ, 36:1 (2013), 103–115 | DOI

[61] S. S. Bykhovets, A. S. Komarov, Pochvovedenie, 2002, no. 4, 443–452

[62] B. J. Cosby, G. M. Hornberger, R. B. Clapp, T. R. Ginn, Water Resour. Res., 20:6 (1984), 682–690 | DOI

[63] C. R. Schwalm, A. Ek, Ecol. Model, 179:3 (2004), 317–348 | DOI

[64] K. S. Bobkova, Biologicheskaya produktivnost khvoinykh lesov Evropeiskogo Severo-Vostoka, Nauka, L., 1987, 156 pp.

[65] A. D. Vakurov, A. F. Polyakova, “Krugovorot azota i mineralnykh elementov v nizkoproduktivnykh elnikakh severnoi taigi”, Krugovorot khimicheskikh veschestv v lesu, Nauka, M., 1982, 20–43

[66] D. A. Vakurov, A. F. Polyakova, “Krugovorot azota i mineralnykh elementov v 35-letnem osinnike”, Krugovorot khimicheskikh veschestv v lesu, Nauka, M., 1982, 44–54

[67] R. I. Vinokurova, O. V. Lobanova, Vestnik Povolzhskogo gosudarstvennogo tekhnologicheskogo universiteta. Seriya: Les. Ekologiya. Prirodopolzovanie, 2011, no. 2, 76–83

[68] V. N. Vtorova, “Osobennosti vertikalnogo raspredeleniya khimicheskogo sostava strukturnykh komponentov eli i sosny v Podmoskove”, Kompleksnye biogeotsenoticheskie issledovaniya v lesakh Podmoskovya, Nauka, M., 1982, 5–20

[69] A. A. Dymov, K. S. Bobkova, V. V. Tuzhilkina, D. A. Rakina, “Izvestiya vysshikh uchebnykh zavedenii”, Lesnoi zhurnal, 2012, no. 3, 7–18

[70] N. I. Kazimirov, R. M. Morozova, Biologicheskii krugovorot veschestv v elnikakh Karelii, Nauka, L., 1973, 175 pp.

[71] I. V. Karmanova, T. N. Sudnitsina, N. A. Ilina, Prostranstvennaya struktura slozhnykh sosnyakov, Nauka, M., 1987, 100 pp.

[72] N. V. Lukina, V. V. Nikonov, Kh. Raitio, Lesovedenie, 1994, no. 6, 10–21

[73] V. B. Lukyanets, Lesovedenie, 1980, no. 1, 52–57 | MR

[74] A. I. Matvienko, Vliyanie azota na mineralizatsiyu ugleroda v pochvakh pod listvennitsei sibirskoi i sosnoi obyknovennoi, dis. kand. biol. nauk: 03.02.08, Krasnoyarsk, 2017, 147 pp.

[75] E. S. Migunova, Lesa i lesnye zemli (kolichestvennaya otsenka vzaimosvyazei), Ekologiya, M., 1993, 364 pp.

[76] A. A. Molchanov, A. F. Polyakova, “Produktivnost organicheskoi massy v sosnyakakh sfagnovykh”, Produktivnost organicheskoi i biologicheskoi massy lesa, Nauka, M., 1974, 43–77

[77] A. A. Molchanov, A. F. Polyakova, “Kharakteristika osnovnykh tipov lesa”, Osnovnye tipy biogeotsenozov severnoi taigi, Nauka, M., 1977, 44–203

[78] R. M. Morozova, “Khimicheskii sostav rastenii elovykh i berezovykh lesov Karelii”, Lesnye rastitelnye resursy Yuzhnoi Karelii, Kareliya, Petrozavodsk, 1971, 57–66

[79] R. M. Morozova, Mineralnyi sostav rastenii lesov Karelii, Goskomizdat, Petrozavodsk, 1991, 100 pp.

[80] Yu. E. Novitskaya, Osobennosti fiziologo-biokhimicheskikh protsessov v khvoe i pobegakh eli v usloviyakh Severa, Nauka, L., 1971, 117 pp.

[81] L. M. Nosova, L. B. Kholopova, “Osobennosti obmena veschestv mezhdu rastitelnostyu i pochvoi v iskusstvennykh nasazhdeniyakh sosny na dernovo-podzolistykh pochvakh”, Obschie problemy biogeotsenologii, Nauka, M., 1990, 252–266

[82] N. V. Oskina, “Soderzhanie azota i zolnykh elementov v nadzemnoi fitomasse kultur sosny obyknovennoi Vladimirskoi, Ulyanovskoi i Kuibyshevskoi oblastei”, Biologicheskaya produktivnost lesov Povolzhya, Nauka, M., 1982, 7–11

[83] T. A. Rabotnov, “Azot v nazemnykh biogeotsenozakh”, Strukturno-funktsionalnaya organizatsiya biogeotsenozov, Nauka, M., 1980, 69–90

[84] N. P. Remezov, L. N. Bykova, K. M. Smirnova, Potreblenie i krugovorot azota i zolnykh elementov v lesakh Evropeiskoi chasti SSSR, Izdatelstvo Moskovskogo universiteta, M., 1959, 284 pp.

[85] N. P. Remezov, P. S. Pogrebnyak, Lesnoe pochvovedenie, Lesnaya promyshlennost, M., 1965, 324 pp.

[86] T. V. Reshetnikova, Vestnik Krasnoyarskogo gosudarstvennogo agrarnogo universiteta, 2011, no. 12, 74–81

[87] G. V. Rusanova, “Biologicheskaya produktivnost i soderzhanie khimicheskikh elementov v fitomasse elnika-zelenomoshnika”, Produktivnost i krugovorot elementov v fitotsenozakh severa, Nauka, L., 1975, 30–51

[88] N. I. Smeyan, T. A. Romanova, N. I. Turenkov, S. A. Tikhonov, K. V. Balkhanova, “Podzolistye pochvy Belorusskoi SSR”, Podzolistye pochvy zapada Evropeiskoi chasti SSSR, Kolos, M., 1977, 31–109

[89] D. P. Stolyarov, V. N. Poluboyarinov, V. N. Minaev, N. N. Dekatov, G. N. Nekrasova, Rekomendatsii po otsenke stroeniya, tovarnoi struktury i kachestva drevesiny raznovozrastnykh elnikov s tselyu organizatsii vyborochnogo khozyaistva, NII lesnogo khozyaistva, L., 1989, 56 pp.

[90] N. E. Sudachkova, I. L. Milyutina, G. P. Semenova, Khvoinye borealnoi zony, 2003, no. 1, 54–60

[91] A. V. Khavronin, V. M. Kretinin, L. V. Dubovskaya, “Biologicheskaya akkumulyatsiya pitatelnykh elementov v polezaschitnykh lesnykh polosakh na obyknovennom chernozeme”, Mezhvuzovskii sbornik, Voprosy lesnoi biogeotsenologii, ekologii i okhrany prirody v stepnoi zone, 2, Kuibyshevskii gosudarstvennyi universitet, Kuibyshev, 1977, 42–49

[92] G. Bauer, E. D. Schulze, M. Mund, Tree Physiol, 17:12 (1997), 777–786 | DOI

[93] K. L.Bocock, J. Ecol., 52:2 (1964), 273–284 | DOI

[94] M. Dannenmann, J. Simon, R. Gasche, J. Holst, P. S. Naumann, I. Kögel-Knabner, H. Knicker, H. Mayer, M. Schloter, R. Pena, A. Polle, H. Rennenberg, H. Papen, Soil Biol. Biochem., 41:8 (2009), 1622–1631 | DOI

[95] S. E. Hobbie, J. Oleksyn, D. M. Eissenstat, P. B. Reich, Oecologia, 162:2 (2010), 505–513 | DOI

[96] M. Nahm, A. Matzarakis, H. Rennenberg, A. Geßler, Trees, 2007, no. 21, 79 | DOI

[97] Ü. Niinemets, Int. J. Plant Sci., 159:2 (1998), 318–330 | DOI

[98] A. D. Peuke, H. Rennenberg, Trees, 18:6 (2004), 639–648 | DOI

[99] M. Trémolières, A. Schnitzler, J. M. Sánchez-Pérez, D. Schmitt, Ann. For. Sci., 56:8 (1999), 641–650 | DOI

[100] L. Vesterdal, I. K. Schmidt, I. Callesen, L. O. Nilsson, P. Gundersen, For. Ecol. Manag, 255:1 (2008), 35–48 | DOI

[101] R. H. Waring, J. J. Landsberg, M. Williams, Tree Physiol, 18:2 (1998), 129–134 | DOI

[102] N. C. Coops, R. H. Waring, B. E. Law, Ecol. Model, 183:1 (2005), 107–124 | DOI

[103] P. Friedlingstein, I. Fung, E. Holland, J. John, G. Brasseur, D. Erickson, D. Schimel, Global Biogeochem. Cy., 9:4 (1995), 541–556 | DOI

[104] J. J. Swenson, R. H. Waring, W. Fan, N. Coops, Can. J. For. Res., 35:7 (2005), 1697–1707 | DOI

[105] R. J. Norby, E. H. DeLucia, B. Gielen, C. Calfapietra, C. P. Giardina, J. S. King, J. Ledford, H. R. McCarthy, D. J.P. Moore, R. Ceulemans, P. De Angelis, A. C. Finzi, D. F. Karnosky, M. E. Kubiske, M. Lukac, K. S. Pregitzer, G. E. Scarascia-Mugnozza, W. H. Schlesinger, R. Oren, PNAS, 102:50 (2005), 18052–18056 | DOI

[106] R. H. Waring, J. F. Franklin, Science, 204 (1979), 1380–1386 | DOI

[107] H. K. M. Bugmann, A. M. Solomon, Ecol. Appl., 10:1 (2000), 95–114 | DOI

[108] W. M. Jolly, R. Nemani, S. Running, Glob. Change Biol., 11:4 (2005), 619–632 | DOI

[109] I. A. Poletaev, Zhurnal obschei biologii, 40:6 (1979), 915–925

[110] V. Z. Antonopoulos, J. Plant Nutr. Soil Sc., 162:6, 667–675, 1999 | 3.0.CO;2-D class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[111] K. I. Paul, P. J. Polglase, A. M. O-Connell, J. C. Carlyle, P. J. Smethurst, P. K. Khanna, Eur. J. Soil Sci., 54:1 (2003), 39–47 | DOI

[112] P. V. Frolov, E. V. Zubkova, “Modelirovanie dinamiki biomassy rastenii travyanisto-kustarnichkovogo yarusa lesnykh ekosistem”, Sokhranenie lesnykh ekosistem: problemy i puti ikh resheniya, materialy Vserossiiskoi nauchno-prakticheskoi konferentsii (g. Kirov, 15–19 maya 2017 g.), eds. N. P.Savinykh, O. N. Perestoronina, E. A. Domnina, S. V. Shabalkina, M. N. Shakleina, OOO Izdatelstvo «Raduga-PRESS», Kirov, 2017, 334–339

[113] O. Räim, E. Kaurilind, L. Hallik, E. Merilo, Plant Biol, 14:2 (2012), 306–314 | DOI

[114] K. S. Bobkova, E. P. Galenko, S. V. Zagirova, A. I. Patov, Lesovedenie, 2007, no. 3, 23–31

[115] O. V. Smirnova (red.), Vostochnoevropeiskie lesa: istoriya v golotsene i sovremennost, v. 1, Nauka, M., 2004, 479 pp.

[116] V. A. Usoltsev, Fitomassa lesov Severnoi Evrazii: normativy i elementy geografii, UrO RAN, Ekaterinburg, 2002, 762 pp.

[117] A. Z. Shvidenko, D. G. Schepaschenko, S. Nilsson, Yu. I. Bului, Tablitsy i modeli rosta i produktivnosti osnovnykh lesoobrazuyuschikh porod Severnoi Evrazii (normativno-spravochnye materialy), Federalnoe agentstvo lesnogo khozyaistva. Mezhdunarodnyi institut prikladnogo sistemnogo analiza, M., 2008, 886 pp.

[118] A. Praciak (ed.), The CABI encyclopedia of forest trees, CABI, Oxfordshire, 2013, 536 pp.

[119] B. Mandelbrot, Inform. Control, 4:2-3 (1961), 198–216 | DOI | MR | Zbl

[120] A. S. Isaev, T. M. Ovchinnikova, V. G. Sukhovolskii, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 21 (2007), 232–250

[121] A. S. Komarov, L. K. Ginzhul, V. N. Shanin, S. S. Bykhovets, K. S. Bobkova, M. A. Kuznetsov, A. V. Manov, A. F. Osipov, Izvestiya Rossiiskoi akademii nauk. Seriya biologicheskaya, 2017, no. 6, 76–84 | DOI

[122] V. A. Usoltsev, Fitomassa modelnykh derevev lesoobrazuyuschikh porod Evrazii: baza dannykh, klimaticheski obuslovlennaya geografiya, taksatsionnye normativy, Uralskii gosudarstvennyi lesotekhnicheskii universitet, Ekaterinburg, 2016, 336 pp.

[123] H. S. Helmisaari, K. Makkonen, S. Kellomäki, E. Valtonen, E. Mälkönen, For. Ecol. Manag, 165:1-3 (2002), 317–326 | DOI

[124] V. D. Stakanov, Lesovedenie, 1990, no. 4, 25–32

[125] E. A. Thurm, P. Biber, H. Pretzsch, Trees, 31:1 (2017), 349–365 | DOI

[126] M. Weemstra, F. J. Sterck, E. J. W. Visser, T. W. Kuyper, L. Goudzwaard, L. Mommer, Plant Soil, 415:1-2 (2017), 175–188 | DOI

[127] V. Shanin, R. Mäkipää, M. Shashkov, N. Ivanova, K. Shestibratov, S. Moskalenko, L. Rocheva, P. Grabarnik, K. Bobkova, A. Manov, A. Osipov, E. Burnasheva, M. Bezrukova, Eur. J. For. Res., 134:6 (2015), 1055–1074 | DOI

[128] B. N. Ugolev (red.), Spravochnik po drevesine, Lesnaya promyshlennost, M., 1989, 296 pp.

[129] G. Alberti, P. Candido, A. Peressotti, S. Turco, P. Piussi, G. Zerbi, Ann. For. Sci., 62:8 (2005), 831–836 | DOI

[130] T. De Jaegere, S. Hein, H. A. Claessens, Forests, 7:3 (2016), 56 | DOI

[131] D. Diaconu, M. Wassenberg, H. Spiecker, For. Ecosyst., 3:6 (2016) | DOI

[132] I. J. Díaz-Maroto, T. Sylvain, Wood Res, 61:5 (2016), 683–695

[133] K. Giagli, J. Baar, M. Fajstavr, V. Gryc, H. Vavrčík, BioResources, 13:1 (2018), 804–819 | DOI

[134] V. Gryc, H. Vavrčík, Gomola. J. For. Sci., 54:9 (2008), 418–425 | DOI

[135] J. Hamada, A. Pétrissans, F. Mothe, J. Ruelle, M. Pétrissans, P. Gérardin, Ann. For. Sci., 73:2 (2016), 277–286 | DOI

[136] H. Heräjärvi, R. Junkkonen, Balt. For., 12:1 (2006), 2–8

[137] T. Jyske, H. Mäkinen, P. Saranpää, Silva Fenn., 42:3 (2008), 439–455 | DOI

[138] T. Kärki, Holz Roh. Werkst., 59:1-2 (2001), 79–84 | DOI

[139] M. Kiaei, A. Samariha, Am.-Euras. J. Agric. Environ. Sci., 11:2 (2011), 257–260

[140] R. Lal, M. Suleimenov, B. A. Stewart, D. O. Hansen, P. Doraiswamy, Climate change and terrestrial carbon sequestration in Central Asia, CRC Press, London, 2007, 512 pp. | DOI

[141] J. Liepiņš, J. Ivanovs, A. Lazdiņš, J. Jansons, K. Liepiņš, Silva Fenn., 51:5 (2017), 7798 | DOI

[142] K. Luostarinen, Silva Fenn., 46:5 (2012), 707–716 | DOI

[143] K. Luostarinen, E. Verkasalo, Birch as sawn timber and in mechanical further processing in Finland. A literature study, Silva Fennica Monographs, 1, 2000, 40 pp.

[144] H. Mäkinen, P. Saranpää, S. Linder, Can. J. For. Res., 32:2 (2002), 185–194 | DOI

[145] P. S. Mederski, M. Bembenek, Z. Karaszewski, D. F. Giefing, E. Sulima-Olejniczak, M. Rosińska, A. Łacka, Drewno, 58:195 (2015) | DOI

[146] M. Skarvelis, G. Mantanis, Wood Res, 58:1 (2013), 123–130

[147] A. Tomczak, T. Jelonek, M. Jakubowski, Annals of Warsaw University of Life Sciences – SGGW Forestry and Wood Technology, 76 (2011), 144–148

[148] A. Viherä-Aarnio, P. Velling, Silva Fenn., 51:4 (2017), 7731 | DOI

[149] U. Zaja̧czkowska, P. Kozakiewicz, Holzforschung, 70:10 (2016), 993–1002 | DOI

[150] S. Y. Zhang, R. E. Owoundi, G. Nepveu, F. Mothe, J. F. Dhôte, Can. J. For. Res., 23:12 (1993), 2587–2593 | DOI

[151] D. Zianis, P. Muukkonen, R. Mäkipää, M. Mencuccini, “Biomass and stem volume equations for tree species in Europe”, Silva Fennica Monographs, no. 4, 2005, 1–2, 5–63

[152] A. A. Uranov, “Nauchnye doklady vysshei shkoly”, Biologicheskie nauki, 1975, no. 2, 7–33

[153] O. Chertov, A. Komarov, C. Shaw, S. Bykhovets, P. Frolov, V. Shanin, P. Grabarnik, I. Priputina, E. Zubkova, M. Shashkov, Ecol. Model., 345 (2017), 125–139 | DOI

[154] O. Chertov, C. Shaw, M. Shashkov, A. Komarov, S. Bykhovets, V. Shanin, P. Grabarnik, P. Frolov, O. Kalinina, I. Priputina, E. Zubkova, Ecol. Model., 345 (2017), 140–149 | DOI

[155] A. Komarov, O. Chertov, S. Bykhovets, C. Shaw, M. Nadporozhskaya, P. Frolov, M. Shashkov, V. Shanin, P. Grabarnik, I. Priputina, E. Zubkova, Ecol. Model., 345 (2017), 113–124 | DOI

[156] L. Khanina, M. Bobrovsky, A. Komarov, A. Mikhajlov, For. Ecol. Manag., 248:1-2 (2007), 80–94 | DOI

[157] V. N. Shanin, S. S. Bykhovets, P. V. Frolov, I. V. Priputina, G. G. Frolova, E. O. Vidyagina, V. G. Lebedev, K. A. Shestibratov, EFIMOD-fbp imitatsionnaya model prognozirovaniya ekologicheskikh effektov lesnykh plantatsii na osnove derevev s zadannymi kharakteristikami (biotekhnologicheskikh form berezy i osiny), svidetelstvo o gosudarstvennoi registratsii programmy dlya EVM No 2017612595 ot 01.03.2017