Skip to main content
SpringerLink
Log in

On the Calibration of an Autonomous Model of the Biological Population of the Tundra Lemming

  • COMPLEX SYSTEMS BIOPHYSICS
  • Published:
Biophysics Aims and scope Submit manuscript

Abstract

An autonomous model of a phenomenological type was designed for a biological population of lemmings in complex studies of tundra communities. The population dynamics is described in the model by a difference equation, which relates the population sizes observed in 2 consecutive years and depends on three parameters of biological and ecological nature. A combination of parameter values included in the equation determines a class of one-dimensional unimodal mappings of a dynamical system. Bifurcation properties, asymptotics, and stability of trajectories were studied both analytically and numerically in the class. The problem of model identification is the main focus. The method of identification sets was proposed for calibrating the model. The method is based on the approximation and visualization of small-dimensional projections of a multidimensional graph of the error function specified in a space of three environmental and two population parameters. An example model identification was performed using data on a tundra lemming population of the Taimyr Peninsula. Two biological and ecological parameters were shown to allow a stable location distribution in this case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. V. Volterra, Lessons in the Mathematical Theory of the Struggle for Life (Gauthier-Villars, Paris, 1931; Nauka, Moscow, 1976).

  2. A. J. Lotka, Elements of Physical Biology (Williams and Wilkins, Baltimor, 1925).

  3. P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis (Princeton Univ. Press, Princeton, 2003).

    MATH  Google Scholar 

  4. A. N. Kolmogorov, in Problems in Cybernetics (Nauka, Moscow, 1972), Vol. 25, pp. 100–106 [in Russian].

  5. G. Yu. Riznichenko and A. B. Rubin, Mathematical Models of Biological Production Processes (Moscow State Univ., Moscow, 1993) [in Russian].

    Google Scholar 

  6. Yu. M. Svirezhev and D. O. Logofet, Stability of Biological Communities (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  7. A. D. Bazykin, Mathematical Biophysics of Interacting Populations (Nauka, Moscow, 1985) [in Russian].

    MATH  Google Scholar 

  8. S. V. Fomin and M. B. Berkenblit, Mathematical Problems in Biology (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  9. V. A. Orlov, D. A. Sarancha, and O. A. Shelepova, Ekologiya 2, 43 (1986).

    Google Scholar 

  10. F. A. Pitelka and G. O. Batzli, Acta Theriol. 52 (3), 323 (2007).

    Article  Google Scholar 

  11. F. B. Chernyavskii, Priroda, № 10, 34 (2002).

    Google Scholar 

  12. O. F. Sadykov and I. E. Benenson, Population Dunamics of Small Mammals: Concepts, Hypotheses, Models (Nauka, Moscow, 1992) [in Russian].

    Google Scholar 

  13. T. Oksanen, L. Oksanen, J. Dahlgren, et al., Evol. Ecol. Res. 10, 415 (2008).

    Google Scholar 

  14. V. N. Glushkov and D. A. Sarancha, Avtomatika i Telemekhanika 2, 94 (2013).

    Google Scholar 

  15. D. A. Sarancha, Quantitative Methods in Ecology: Biophysical Aspects and Mathematical Modeling (MFTI, Moscow, 1996).

    Google Scholar 

  16. V. A. Kostitsyn, Evolution of the Atmosphere, Biosphere, and Climate (Nauka, Moscow, 1984) [in Russian].

    Google Scholar 

  17. G. K. Kamenev, N. A. Lysenko, O. P. Lyulyakin, et al., Methods of Mathematical Modeling for Analyzing Ecological Objects (RAS Comput. Center, Moscow, 2015) [in Russian].

    Google Scholar 

  18. E. V. Nedostupov, D. A. Sarancha, E. N. Chigirev, et al., Dokl. Akad. Nauk 430 (1), 23 (2010).

    Google Scholar 

  19. N. V. Belotelov, I. V. Dmitriev, and D. A. Sarancha, in Biomodeling, Ed. by Yu. P. Ivanilov (RAS Comput. Center, Moscow, 1993), pp. 111–154 [in Russian].

    Google Scholar 

  20. G. K. Kamenev, O. P. Lyulyakin, D. A. Sarancha, et al., Russ. J. Numer. Anal. Math. Model. 31 (5), 253 (2016).

    Article  Google Scholar 

  21. Yu. Ilyashenko and W. Li, Nonlocal Bifurcations (Am. Math. Soc., Providence, RI, 1999).

    MATH  Google Scholar 

  22. G. K. Kamenev, Tr. Inst. Sist. Anal. Ross. Akad. Nauk 68 (2), 26 (2018).

    Google Scholar 

  23. G. K. Kamenev, D. A. Sarancha and V. O. Polya-novsky, Biophysics (Moscow) 63 (4), 596 (2018).

    Article  Google Scholar 

  24. G. K. Kamenev, Mat. Model. 22 (9), 116 (2010).

    Google Scholar 

  25. G. K. Kamenev, A Method for Analyzing Uncertainty Arising in Identification of Model Parameters (RAS Comput. Center, Moscow, 2010) [in Russian].

    Google Scholar 

  26. G. K. Kamenev, in Proceedings of the Department of Mathematical Modeling of Economic Systems, Computing Center of Russian Academy of Siences, Ed. by I. G. Pospelov (RAS Comput. Center, Moscow, 2017), pp. 94–142 [in Russian]. https://doi.org/10.13140/RG.2.2.33808.46086

  27. G. K. Kamenev, in OPM2018: Proc. 9th Moscow Conf. on Operation Research, Ed. by F. E. Ereshko (MAKS Press, Moscow, 2018), Vol. 2, pp. 175–179.

  28. G. K. Kamenev, Dokl. Akad. Nauk 359 (3), 319 (1998).

    MathSciNet  Google Scholar 

  29. G. K. Kamenev, Zh. Vychisl. Mat. Mat. Fiz. 56 (11) 1872 (2016). https://doi.org/10.7868/S0044466916110089

    Article  Google Scholar 

  30. G. K. Kamenev, Mat. Model. 29 (8), 29 (2017).

    MathSciNet  Google Scholar 

  31. G. K. Kamenev and D. L. Kondrat’ev, Mat. Model. 4 (3), 105 (1992).

    MathSciNet  Google Scholar 

  32. G. K. Kamenev, Zh. Vychisl. Mat. Mat. Fiz. 41 (11), 1751 (2001).

    Google Scholar 

  33. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (Univ. of Illinois Press, Urbana, IL, 1949).

    MATH  Google Scholar 

  34. A. V. Lotov, V. A. Bushenkov, and G. K. Kamenev, Interactive Decision Maps. Approximation and Visualization of Pareto Frontier (Kluwer, Boston, 2004).

    Book  Google Scholar 

  35. Y. I. Kokorev and V. A. Kuksov, Ornis Suecica 12 (3), 139 (2002).

    Google Scholar 

  36. L. M. Shilyaeva, personal communication (Research Institute of Game Management and Fir Farming, Kirov, 1978).

  37. G. K. Kamenev, D. A. Sarancha, and V. O. Polya-novskii, in Modeling the Coevolution of Nature and Society: Problems and Experience. To the 100th Anniversary of the Birth of Academician N. N. Moiseev, Ed. by I. G. Posperlov (RAS Comput. Center, Moscow, 2017), pp. 327–335 [in Russian].

    Google Scholar 

  38. G. K. Kamenev, in Modeling the Coevolution of Nature and Society: Problems and Experience. To the 100th Anniversary of the Birth of Academician N. N. Moiseev, Ed. by I. G. Posperlov (RAS Comput. Center, Moscow, 2017), pp. 315–326 [in Russian].

    Google Scholar 

  39. D. Ehrich, N. M. Schmidt, G. Gauthier, et al., J. Human Environ. 49, 786 (2020). https://doi.org/10.1007/s13280-019-01198-7

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, 119333, Moscow, Russia

    G. K. Kamenev & D. A. Sarancha

  2. Engelhardt Institute of Molecular Biology, Russian Academy of Sciences, 119991, Moscow, Russia

    V. O. Polyanovsky

Authors
  1. G. K. Kamenev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Sarancha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. O. Polyanovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to G. K. Kamenev or V. O. Polyanovsky.

Ethics declarations

Conflict of interests. The authors declare that they have no conflict of interest.

This work does not contain any studies involving animals or human subjects performed by any of the authors.

Additional information

Translated by T. Tkacheva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamenev, G.K., Sarancha, D.A. & Polyanovsky, V.O. On the Calibration of an Autonomous Model of the Biological Population of the Tundra Lemming. BIOPHYSICS 65, 1007–1016 (2020). https://doi.org/10.1134/S0006350920060068

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0006350920060068

Search

Navigation