Models of tree dynamics and tree community dynamics: progressing from two-dimensional to three-dimensional models

V. V. Galitskii

Matematičeskaâ biologiâ i bioinformatika, Tome 7 (2012) no. 1, pp. 54-80.

Résumé

The browse of the works fulfilled within the frames of the approach according to «a principle of a minimum visual angle», i.e. step-by-step moving from a minimum image of the modelled object to more and more detailed is presented. Models of dynamics of plants in view of their usage in models of communities are considered. Two-dimensional models of dynamics of a biomass quite adequately describe productional process, for example, explaining effect of an after grass. Using in models of the community consisting of such models of plants, considering the area occupied by community as a resource and applying thus Voronoii mosaic, we receive the tool for research of the main process of dynamics of community — a competition. The role of space structure of community in dynamics of a competition is considered for a uniform community as an example. With usage of two-dimensional model of community it is shown that so-called «The rule $-3/2$» describes dependence between phytomass (but not biomasses) with community denseness in a course of communities thinning. At the three-dimensional modelling a decomposing of biomass dynamics of a tree into the sum of biomass dynamics of sections amounting the tree it is offered. Analysis of sectional model allows to explain a number of effects observed in the nature and to describe dynamics of allocation of a biomass on the heights which are associating with some species. The sectional construction of model was spread to system of branches of a tree, and the model of branches had demonstrated boundedness of number of orders and time of life of branches of a tree. Analysis of system of branches of ordinary spruce with usage of model together with the published natural data has shown that natural values of times of life of branches of a spruce are impossible without taking into account in model of known peculiarities of a spruce — an initial growth inhibition and presence of inter-verticil branches. The mechanism and its model exposition for process of replacement of skeletal (regular) branches of a spruce by inter-verticil is offered. Values of parameters of model for natural data are gained. Analysis of sectional model of a tree shows, that death of tree in community is invoked not directly by disadvantage of resources, but the weakening of growth of height because of that. The synchronous sectional model of trees' community dynamics is described.

Bibliographie

[1] Monsi M., Saeki T., “Uber den Lichtfaktor in den Pflanzengeselschaften und seine Bedeutung fur die Stoffproduction”, Jap. J. Bot., 14:1 (1953), 22–52

[2] Khilmi G.F., Teoreticheskaya biogeofizika lesa, Izd. AN SSSR, M., 1957, 266 pp.

[3] Bikhele Z.N., Moldau Kh.A., Ross Yu.K., Matematicheskoe modelirovanie transpiratsii i fotosinteza rastenii pri nedostatke pochvennoi vlagi, Gidrometeoizdat, L., 1980

[4] Hogeweg P., Hesper B., “Crowns crowding: an individual oriented model of the Acanthaster phenomenon”, Acanthaster phenomenon, Lecture Notes in Math. Biol., ed. Bradbury R., Springer, 1990, 169–187

[5] Munro D.D., “Forest growth models. A prognosis”, Growth Models for Tree and Stand Simulation, Research notes — Dept. of Forest Yield Research, 30, ed. Fries J., Royal College of Forestry, Stockholm, 1974, 7–21

[6] Dale V.H., Doyle T.W., Shugart H.H., “A comparison of tree growth models”, Ecol. Model., 29 (1985), 145–169 | DOI

[7] Galitskii V.V., Tyuryukanov A.N., “O metodologicheskikh predposylkakh modelirovaniya v biogeotsenologii”, A. N. Tyuryukanov. Izbrannye trudy, Izd. REFIA, 2001, 94–108

[8] Ramenskii L.G., “K metodike sravnitelnoi obrabotki i sistematizatsii spiskov rastitelnosti i drugikh ob'ektov, opredelyaemykh neskolkimi neskhodno deistvuyuschimi faktorami”, Izbrannye raboty. Problemy i metody izucheniya rastitelnogo pokrova, Nauka, L., 1971, 34–56

[9] Galitskii V.V., “Modelirovanie soobschestva rastenii: individualno-orientirovannyi podkhod. I. Model rasteniya”, Izv. AN. Ser. biol., 1999, no. 5, 539–546

[10] Bertallanfy L. von, “A quantitative theory of organic growth”, Human Biology, 10:2 (1938), 181–213

[11] Galitskii V.V., Komarov A.S., “O modelirovanii rosta rastenii”, Izv. AN SSSR. Ser. biolog., 1979, no. 5, 714–723

[12] Galitskii V.V., “The 2D modeling of tree community: from «microscopic» description to macroscopic behavior”, For. Ecol. and Manag., 183 (2003), 95–111 | DOI

[13] Sovetskii entsiklopedicheskii slovar, 2-e izd., Sov. entsiklopediya, M., 1983, 1600 pp.

[14] Makela A., Hari P., “Stand growth model based on carbon uptake and allocation in individual trees”, Ecol. Model., 33 (1986), 315–331 | DOI

[15] Botkin D.B., Janak J.F., Wallis J.R., “Some ecological consequences of a computer model forest growth”, J. Ecology, 60:3 (1972), 849–872 | DOI

[16] Poletaev I.A., “O matematicheskikh modelyakh elementarnykh protsessov v biogeotsenozakh”, Problemy kibernetiki, 16, Nauka, M., 1966, 175–177

[17] Galitskii V.V., “O kollektivnom samougnetenii v odnorodnom rastitelnom soobschestve i kolebatelnykh izmeneniyakh biomassy ego chlenov”, DAN, 246:4 (1979), 1013–1015

[18] Galitskii V.V., “O vliyanii otchuzhdeniya chasti fitomassy na rost rasteniya”, Izv. AN SSSR. Ser. biol., 1984, no. 6, 823–833

[19] Abaturov B.D., Bioproduktsionnyi protsess v nazemnykh ekosistemakh, Nauka, M., 1979

[20] Galitskii V.V., “Modelirovanie soobschestva rastenii: individualno-orientirovannyi podkhod. II. Model soobschestva”, Izv. AN. Ser. biol., 2000, no. 2, 178–185

[21] Miroshnichenko G.N., “Teoriya i metodika izucheniya vnutrividovoi konkurentsii u rastenii”, Botan. zhurn., 40:3 (1955), 408–410

[22] Voronoi G.F., “Issledovaniya o primitivnykh paralleloedrakh”, Sobranie sochinenii, v. 2, Izd. AN USSR, Kiev, 1952, 239–368

[23] Galitskii V.V., Mironenko E.V., Mozaika Voronogo na ploskosti. Algoritm postroeniya, ONTI NTsBI, Puschino, 1981, 26 pp.

[24] Galitskii V.V., “O modelirovanii produktsionnogo protsessa v rastitelnom soobschestve”, Modelirovanie biogeotsenoticheskikh protsessov, ed. Galitskii V.V., Nauka, M., 1981, 104–118

[25] Galitsky V.V., “On modelling the plant community dynamics”, Cybernetics and Systems Research, ed. Trappl R., North-Holland, Amsterdam, 1982, 667–682

[26] Galitskii V.V., Abaturov A.V., “Ranzhirovanie skhodnykh drevostoev po intensivnosti konkurentsii putem analiza ikh konturnykh planov”, DAN, 347:3 (1996), 421–423

[27] Abaturov A.V., Galitskii V.V., “O mashinnoi obrabotke planov drevostoev”, Ekologiya, 1995, no. 3, 184–192

[28] Galitskii V.V., “O dinamike integralnoi mery konkurentsii v soobschestvakh rastenii razlichnoi stepeni odnorodnosti”, Izv. AN. Ser. biol., 2006, no. 2, 156–164 | Zbl

[29] Galitskii V.V., “Dynamics of competition in uniform communities of trees”, Comm. Ecol., 7 (2006), 69–80 | DOI

[30] White J., “Demographic factors in populations of plants”, Demography and evolution in plant populations, University of California Press, Berkeley, 1980, 21–48

[31] Yoda K.T., Kira T., Ogawa H., Hozumi K., “Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants. XI)”, Journal of the Institute of Polytechnics, Osaka City University, 14 (1963), 107–129 (Ser. D)

[32] Zeide B., “Analysis of the 3/2 power law of self-thinning”, For. Sci., 33:2 (1987), 517–537

[33] Weller D.E., “A reevaluation of the $-3/2$ power rule of plant self-thinning”, Ecol. Monogr., 57 (1987), 23–43 | DOI

[34] Lonsdale W.M., “The self-thinning rule: dead or alive”, Ecol., 71:4 (1990), 1373–1388 | DOI

[35] Norberg R.A., “Theory of growth geometry of plants and self-thinning of plant populations: geometric similarity, elastic similarity, and different growth modes of plant parts”, Am. Nat., 131 (1988), 220–256 | DOI

[36] Galitskii V.V., “Modelnyi analiz pravila $-3/2$ dlya soobschestva rastenii”, DAN, 362 (1998), 840–843

[37] Mohler C.L., Marks P.L., Sprugel D.G., “Stand structure and allometry of trees during self-thinning of pure stands”, J. Ecol., 66 (1978), 599–614 | DOI

[38] Sprugel D.G., “Density, biomass, productivity, and nutrient-cycling changes during stand development in wave-regenerated balsam fir forests”, Ecol. Model., 54 (1984), 165–186

[39] Galitskii V.V., “O dinamike raspredeleniya po vysote biomassy svobodno rastuschego dereva. Modelnyi analiz”, DAN, 407:4 (2006), 564–566

[40] Galitskii V.V., “Sektsionnaya struktura dereva. Modelnyi analiz vertikalnogo raspredeleniya biomassy”, Issledovano v Rossii, 2008, no. 128, 1309–1320 ; URL: (дата обращения: 11.09.2011) http://zhurnal.ape.relarn.ru/articles/2007/128.pdf | Zbl

[41] Barthelemy D., Caraglio Y., “Plant Architecture: A Dynamic, Multilevel and Comprehensive Approach to Plant Form. Structure and Ontogeny”, Ann. Bot., 99 (2007), 375–407 | DOI

[42] Tselniker Yu.L., “Struktura krony eli”, Lesovedenie, 1994, no. 4, 35–44

[43] Galitskii V.V., “Sektsionnaya struktura dereva. Modelnyi analiz vertikalnogo raspredeleniya biomassy”, Zhurn. Obsch. Biol., 71:1 (2010), 19–29 | MR

[44] Serebryakova T.I., Voronin N.S., Elenevskii A.G., Batygina T.B., Shorina N.I., Savinykh N.P., Botanika s osnovami fitotsenologii: Anatomiya i morfologiya rastenii, Akademkniga, M., 2006, 543 pp.

[45] Timiryazev K.A., Zhizn rasteniya, 8-e izd., M. i S. Sabashnikovy, M., 1914, 360 pp.

[46] Corana A., Marchesi M., Martini C., Ridella S., “Minimizing Multimodal Functions of Continuous Variables with the ‘Simulated Annealing Algorithm’”, ACM Trans. Math. Soft., 13:3 (1987), 262–280 | DOI | MR | Zbl

[47] Kazimirov N.I., Elniki Karelii, Nauka, L., 1971, 139 pp.

[48] Kramer P.J., Kozlowski T.T., Physiology of trees, McGraw-Hill, N.Y., 1960, 642 pp.

[49] Treskin P.P., “Zakonomernosti morfogeneza skeletnoi chasti krony vzrosloi eli”, Struktura i produktivnost elovykh lesov yuzhnoi taigi, Nauka, L., 1973, 222–240

[50] Galitskii V.V., “Nesvobodnyi rost dereva. q3D-model”, Issledovano v Rossii, 2006, no. 019, 191–199; URL: (дата обращения: 11.09.2011) http://zhurnal.ape.relarn.ru/articles/2006/019.pdf

[51] Galitskii V.V., “Sinkhronnaya kvazitrekhmernaya sektsionnaya model dinamiki biomassy soobschestva derevev”, Issledovano v Rossii, 2006, no. 158, 1464–1471 ; URL: (дата обращения: 11.09.2011) http://zhurnal.ape.relarn.ru/articles/2006/158.pdf | Zbl

[52] Weigelt A., Jolliffe P., “Indices of plant competition”, J. Ecol., 91 (2003), 707–720 | DOI

[53] Galitskii V.V., “Modelnyi analiz dinamiki dalnego transporta assimilyatov svobodno rastuschego dereva”, Matematicheskaya biologiya i bioinformatika, 4:1 (2009), 1–20 ; URL: (дата обращения: 11.09.2011) http://www.matbio.org/downloads/Galitskii2009(4_1).pdf