Computational Biology and Bioinformatics
Volume 2, Issue 3, June 2014, Pages: 43-51
Received: Jun. 26, 2014;
Accepted: Jul. 8, 2014;
Published: Jul. 20, 2014
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Trashcheev Rostislav, Institute of Fundamental Problems of Biology of the Russian Academy of Sciences, Pushchino, Russia
Boranbayev Askar, Nazarbayev University, Astana, Republic of Kazakhstan
Boranbayev Seilkhan, L. N. Gumilyov Eurasian National University, Astana, Republic of Kazakhstan
Sarancha Dmitry, Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia
Lyulyakin Oleg, Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia
Yurezanskaya Yulia, Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia
This article describes a mathematical modeling method of an ecological biology system; this method uses computers. Hypotheses about the leading mechanisms of fluctuations for tundra animals population’s number are formulated. An analysis of difference and differential equations and their manifestations in the community model “vegetation – lemmings – arctic foxes” and in an individual-oriented model of a lemming population are performed. This method uses research results including a full set of operations, namely from a substantiation of an object choice, a selection and processing of a biological information to the construction of a set of interconnected models. The given approach is used in the analysis of animal fluctuations by means of the tundra community models “vegetation – lemmings – arctic foxes”, “vegetation – reindeer”, and the individual-oriented model of the lemming population.
Analytic and Simulation Modeling of Plant-Animal Populations in Russian Tundra, Computational Biology and Bioinformatics.
Vol. 2, No. 3,
2014, pp. 43-51.
J. Forrester, Word Dynamics, Massachusetts Wright – Allen Press Inc., Cambridge, 1971.
C.J. Topping, T. Dalkvist, and V. Grimm, “Post-hoc pattern-oriented testing and tuning of an existing large model: lessons from the field vole”, Plos One, vol. 7, no. 9, Article Number: e45872, 2012.
V. N. Glushkov and D. A. Sarancha, “A complex mathematical modeling method for biological objects. Modeling the tundra community”, Automation and Remote Control, vol. 74, no. 2, pp. 240–251, 2013.
S.N. Boranbayev, D.A. Sarancha, R. Taberkhan, and R.V. Trashcheev, “Applying of combined methods for initiation of mathematical modeling of biogeocenosis in the different region of Kazakhstan (individual-oriented models)”, Bulletin of Gumilyov’s Eurasian National University, Special Issue, pp.133–142, 2012.
D.A. Sarancha, O.P. Lyulyakin, and R.V. Trashcheev, “Interaction of simulation and analytic methods in modeling of ecological and biological objects”, Russian Journal of Numerical Analysis and Mathematical Modeling, vol. 27, no. 5, pp. 479–492, 2012.
F. B. Chernyavskyi and A. N. Lazutkin, The Cycles Lemmings and Voles in the North, Magadan: Russian Academy of Sciences, Far East Branch, North-East Scientific Center, Institute of Biological Problems in the North, 2004.
D.A. Sarancha, Kolichestvennye metody v ekologii. Biofizicheskie aspekty i matematicheskoe modelirovanie (Quantitative Methods in Ecology: Biophysical Aspects and Mathematical Modeling), Moscow: Mosk. Fiz.-Tekh. Inst., 1997.
J. Murray, Mathematical Biology, vol.1, Springer-Verlag, New York, 2007.
J. J. Nieto, M. J. Pacifico, and J. L. Vieitez, “Long-term and short-term dynamics of microtus epiroticus: a Yoccoz-Birkeland model”, Siam Journal on Applied Dynamical Systems, vol. 11, no. 4, pp. 1499–1532, 2012.
E. V. Nedostupov, D. A. Sarancha, E. N. Chigerev, and Yu. S. Yurezanskaya, “Some properties of one-dimensional unimodal mappings”, Doklady Mathematics, vol. 81, no. 1, pp. 16–21, 2010.
V.A. Orlov, D.A. Sarancha, and O.A. Shelepova, “Mathematical-model of the numerical dynamics of lemmings (Lemmus, Dicrostonyx) and its application for describing the populations of West Taimyr”, Soviet Journal of Ecology, vol. 17, no. 2, pp.97–104, 1986.
F.A. Pitelka and G.O. Batzli, “Population cycle of lemmings near Barrow, Alaska: a history review”, Acta Theriologica, vol. 52, no. 3, pp. 323–336, 2007.
V. D. Perminov and D. A. Sarancha, “On some ap-proach to solving population ecology problems”, Matem. Mod., vol. 15, no. 11, pp. 121–128, 2003.
A.I. Lobanov, D.A. Sarancha, and T.K. Starozhilova, “Seasonality in the Lotka–Volterra model”, Biofizika, vol. 47, no. 2, pp. 325–330, 2002.
V.N. Lopatin and B.D. Abaturov, “Mathematical Modeling of Тrophically Dependent Cycle of Reindeer (Rangifer Tarandus) Population”, Zoologichesky Zhurnal, vol. 79, no. 4, pp. 452–460, 2000.
B.D. Abaturov, “On the mechanisms of natural regulation of the relationship between herbivorous mammals and vegetation”, Zoologichesky Zhurnal, 1975, vol. 54, no. 5, pp. 342–351, 1975.
A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, 2nd ed., Chapman & Hall/CPC, Boca Raton, 2003.