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The dynamics of the lynx–hare system: an application of the Lotka–Volterra model

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Abstract

The Lotka–Volterra model of predator–prey dynamics was used for approximation of the wellknown empirical time series on the lynx–hare system in Canada that was collected by the Hudson Bay Company in 1845–1935. The model was assumed to demonstrate satisfactory data approximation if the sets of deviations of the model and empirical data for both time series satisfied a number of statistical criteria (for the selected significance level). The frequency distributions of deviations between the theoretical (model) trajectories and empirical datasets were tested for symmetry (with respect to the Y-axis; the Kolmogorov–Smirnov and Lehmann–Rosenblatt tests) and the presence or absence of serial correlation (the Swed–Eisenhart and “jumps up–jumps down” tests). The numerical calculations show that the set of points of the space of model parameters, when the deviations satisfy the statistical criteria, is not empty and, consequently, the model is suitable for describing empirical data.

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References

  1. 1.

    D. A. MacLulich, Fluctuations in the Numbers of Varying Hare (Lepus americanus) (Univ. of Toronto Press, Toronto, 1937).

  2. 2.

    C. S. Elton and M. Nicholson, J. Anim. Ecol. 11, 215 (1942).

  3. 3.

    M. E. Gilpin, Am. Nat. 107 (957), 727 (1973).

  4. 4.

    M. Gilpin, Samarskaya Luka: Probl. Glob. Region. Ekol. 19 (3), 177 (2010).

  5. 5.

    G. S. Rozenberg, Samarskaya Luka: Probl. Glob. Region. Ekol. 19 (3), 180 (2010).

  6. 6.

    V. Volterra, Mathematical Theory of Struggle for Life (Nauka, Moscow, 1976) [in Russian].

  7. 7.

    V. Volterra, Lecons sur la theorie mathematique de la lutte pour la vie (Gauthiers-Villars, Paris, 1931).

  8. 8.

    A. I. Lotka, J. Am. Chem. Soc. 42 (8), 1595 (1920).

  9. 9.

    A. I. Lotka, Elements of Physical Biology (Williams & Wilkins, Baltimore, 1925).

  10. 10.

    F. J. Ayala, M. E. Gilpin, and J. G. Ehrenfeld, Theor. Pop. Biol. 4, 331 (1973).

  11. 11.

    M. E. Gilpin and F. J. Ayala, Proc. Nat. Acad. Sci. USA. 70 (12), 3590 (1973).

  12. 12.

    L. V. Nedorezov, Zh. Obshch. Biol. 73 (2), 114 (2012).

  13. 13.

    L. V. Nedorezov, Population Dynamics: Analysis, Modelling, Forecast 1 (1), 47 (2012).

  14. 14.

    L. V. Nedorezov, Chaos and Order in Population Dynamics: Modeling, Analysis, and Forecast (Lambert Acad. Publ., Saarbrücken, 2012).

  15. 15.

    L. V. Nedorezov, Biophysics (Moscow) 60 (3), 457 (2015).

  16. 16.

    L. V. Nedorezov, Biophysics (Moscow) 60 (5), 862 (2015).

  17. 17.

    L. N. Bol’shev and N. V. Smirnov, Mathematical Statistical Tables (Nauka, Moscow, 1983) [in Russian].

  18. 18.

    I. Like and J. Laga, Basic Statistical Tables (SNTL, Prague, 1978; Finansy i Statistika, Moscow 1985).

  19. 19.

    M. Hollander and D. A. Wolfe, Nonparametric Statistical Methods (New York, Wiley, 1973; Finansy i Statistika, Moscow, 1983).

  20. 20.

    N. R. Draper and H. Smith, Applied Regression Analysis, 2nd ed. (Wiley, New York, 1981; Finansy i Statistika, Moscow, 1986), Vol.1.

  21. 21.

    N. R. Draper and H. Smith, Applied Regression Analysis, 2nd ed. (Wiley, New York, 1981; Finansy i Statistika, Moscow, 1987), Vol. 2.

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Correspondence to L. V. Nedorezov.

Additional information

Original Russian Text © L.V. Nedorezov, 2016, published in Biofizika, 2016, Vol. 61, No. 1, pp. 178–184.

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Nedorezov, L.V. The dynamics of the lynx–hare system: an application of the Lotka–Volterra model. BIOPHYSICS 61, 149–154 (2016) doi:10.1134/S000635091601019X

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Keywords

  • the Lotka–Volterra model
  • model parameter estimation
  • deviation analysis