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Recurrence as a Basis for the Assessment of Predictability of the Irregular Population Dynamics

Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)

Abstract

I give a brief overview of a number of methods that are aimed to assess predictability of population dynamics. Besides, a few examples of using the methods based on the recurrence nature of fluctuations of the population size in order to evaluate numerically the horizon of predictability time series resulted from both field observations and mathematical modeling of population dynamics are given in this paper.

Keywords

  • Predictability
  • Population dynamics

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References

  1. S. Laplace, Essai Philosophique sur Les Probabilités (Courcier, Paris, 1814)

    MATH  Google Scholar 

  2. H. Poincaré, Sur le problème des trois corps. Bull. Astron. 8, 12–24 (1891)

    Google Scholar 

  3. E. Ott, Chaos in Dynamical Systems (Cambridge University, Cambridge, 2002)

    CrossRef  Google Scholar 

  4. H. Poincaré, Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13, 1–270 (1890)

    MathSciNet  MATH  Google Scholar 

  5. O.I. Petchey, M. Pontarp, T.M. Massie, S. Kéfi, A. Ozgul, M. Weilenmann, G.M. Palamara, F. Altermatt, B. Matthews, J.M. Levine, D.Z. Childs, B.J. McGill, M.E. Schaepman, B. Schmid, P. Spaak, A.P. Beckerman, F. Pennekamp, I.S. Pearse, The ecology forecast horizon, and examples of its uses and determinants. Ecol. Lett. 18, 597–611 (2015)

    CrossRef  Google Scholar 

  6. R.V. Solé, J. Bascompte, Self-Organization in Complex Ecosystems (Princeton University, Princeton, 2006)

    CrossRef  Google Scholar 

  7. F. Pannekamp, M.W. Adamson, O.I. Petchey, J.-C. Poggiale, M. Aguiar, B.W. Kooi, D.B. Botkin, D.L. DeAngelis, The practice of prediction: what can ecologists learn from applied, ecology-related fields? Ecol. Complex. 32(Part B), 156–167 (2017)

    CrossRef  Google Scholar 

  8. F.R.S. Lighthill, The recently recognized failure of predictability in Newtonian dynamics. Proc. R. Soc. Lond. A 407, 35–50 (1986)

    CrossRef  Google Scholar 

  9. H. Kantz, A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185, 77–87 (1994)

    CrossRef  Google Scholar 

  10. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (Cambridge University, Cambridge, 1997)

    MATH  Google Scholar 

  11. M.T. Rosenstein, J.J. Collins, C.J. De Luca, A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D 65, 117–134 (1993)

    MathSciNet  CrossRef  Google Scholar 

  12. G. Boffetta, M. Cencini, M. Falcioni, A. Vulpiani, Predictability: a way to characterize complexity. Phys. Rep. 356, 367–474 (2002)

    MathSciNet  CrossRef  Google Scholar 

  13. P. Turchin, Complex Population Dynamics. A Theoretical/Empirical Synthesis (Princeton University, Princeton, 2003)

    MATH  Google Scholar 

  14. L. Becks, F.M. Hilker, H. Malchow, K. Jürgens, H. Arndt, Experimental demonstration of chaos in a microbial food web. Nature 435, 1226–1229 (2005)

    CrossRef  Google Scholar 

  15. D. Kaplan, L. Glass, Understanding Nonlinear Dynamics (Springer, New York, 1995)

    CrossRef  Google Scholar 

  16. A.B. Medvinsky, A.V. Rusakov, Chaos and order in stateless societies: intercommunity exchange as a factor impacting the population dynamical patterns. Chaos Solitons Fractals 44, 390–400 (2011)

    MathSciNet  CrossRef  Google Scholar 

  17. A.B. Medvinsky, Chaos and predictability in population dynamics. Nonlinear Dynamics Psychol. Life Sci. 13, 311–326 (2009)

    MathSciNet  Google Scholar 

  18. A.E. Bobyrev, V.A. Burmensky, E.A. Kriksunov, A.B. Medvinsky, M.M. Melnik, N.I. Nurieva, A.V. Rusakov, The analysis of commercial fish population size oscillations in Lake Peipus. Biofizika 57, 140–145 (2012)

    Google Scholar 

  19. S.M. Henson, R.F. Costantino, J.M. Cushing, R.A. Desharnais, B. Dennis, A.A. King, Lattice effects observed in chaotic dynamics of experimental populations. Science 294, 602–605 (2001)

    CrossRef  Google Scholar 

  20. A.B. Medvinsky, A.V. Rusakov, N.I. Nurieva, Integer-based modeling of population dynamics: competition between attractors limits predictability. Ecol. Complex. 14, 108–116 (2013)

    CrossRef  Google Scholar 

  21. W.E. Ricker, Stock and recruitment. J. Fish. Res. Board Can. 11, 559–623 (1954)

    CrossRef  Google Scholar 

  22. P. Turchin, A.D. Taylor, Complex dynamics in ecological time series. Ecology 73, 289–305 (1992)

    CrossRef  Google Scholar 

  23. P. Turchin, S.P. Ellner, Living on the edge of chaos: population dynamics of Fennoscandian voles. Ecology 81, 3099–3116 (2000)

    CrossRef  Google Scholar 

  24. J.-P. Eckmann, S. Oliffson Kamphorst, D. Ruelle, Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–977 (1987)

    CrossRef  Google Scholar 

  25. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Recurrense plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)

    MathSciNet  CrossRef  Google Scholar 

  26. A.B. Medvinsky, B.V. Adamovich, A. Chakraborty, E.V. Lukyanova, T.M. Mikheyeva, N.I. Nurieva, N.P. Radchikova, A.V. Rusakov, T.V. Zhukova, Chaos far away from the edge of chaos: a recurrence quantification analysis of plankton time series. Ecol. Complex. 23, 61–67 (2015)

    CrossRef  Google Scholar 

  27. A.B. Medvinsky, B.V. Adamovich, R.R. Aliev, A. Chakraborty, E.V. Lujyanova, T.M. Mikheyeva, L.V. Nikitina, N.I. Nurieva, A.V. Rusakov, T.V. Zhukova, Temperature as a factor affecting fluctuations and predictability of the abundance of lake bacterioplankton. Ecol. Complex. 32, 90–98 (2017)

    CrossRef  Google Scholar 

  28. D.A. Vasseur, Assessing the impact of environmental variability on trophic systems using an allometric frequency-resolved approach, in The Impact of Environmental Variability on Ecological Systems, ed. by D. A. Vasseur, K. S. Mc Cann, (Springer, Dordrecht, 2007), pp. 49–60

    CrossRef  Google Scholar 

  29. A.B. Medvinsky, S.V. Petrovskii, I.A. Tikhonova, H. Malchow, B.-L. Li, Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44, 311–370 (2002)

    MathSciNet  CrossRef  Google Scholar 

  30. O.L. Zhdanova, A.E. Kuzin, E.I. Skaletskaya, E.Y. Frisman, Why the population of the northern fur seals (Callorhinus ursinus) of Tyuleniy Island does not recover following the harvest ban: analysis of 56 years of observation data. Ecol. Model. 363, 57–67 (2017)

    CrossRef  Google Scholar 

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Acknowledgments

The author is deeply grateful to anonymous reviewers. This work was partly supported by the Russian Foundation for Basic Research (grant # 17-04-00048).

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Medvinsky, A.B. (2019). Recurrence as a Basis for the Assessment of Predictability of the Irregular Population Dynamics. In: Berezovskaya, F., Toni, B. (eds) Advanced Mathematical Methods in Biosciences and Applications. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-15715-9_6

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