Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots
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Alexander B. Medvinsky
,
Alexey V. Rusakov
Abstract
The quantitative analysis of recurrence plots while applied to mathematical models was shown to be an effective tool in recognizing a frontier between deterministic chaos and random processes. In nature, however, unlike mathematical models, deterministic processes are closely intertwined with random influences. As a result, the non-structural distributions of points on the recurrence plots, which are typical of random processes, are inevitably superimposed on the aperiodic structures characteristic of chaos. Taking into account that the stochastic impacts are an inherent feature of the dynamics of populations in the wild, we present here the results of the analysis of recurrence plots in order to reveal the extent to which irregular phytoplankton oscillations in the Naroch Lakes, Belarus, are susceptible to stochastic impacts. We demonstrate that numerical assessments of the horizon of predictability Tpr of the dynamics under study and the average number Pd of the points that belong to the diagonal segments on the recurrence plots can furnish insights into the extent to which the dynamics of both model and phytoplankton populations are affected by random components. Specifically, a comparative analysis of the values of Tpr and Pd for the time series of phytoplankton and the time series of random processes allows us to conclude that random components of the phytoplankton dynamics in the Naroch Lakes do not prevent recognition of chaotic nature of these dynamics.
Acknowledgement
The authors thank anonymous reviewer for meaningful comments on the earlier version of this paper.
Funding: This work was partially supported by the Russian Foundation for Basic Research (grant No. 17-04-00048).
References
[1] B. V. Adamovich, A. B. Medvinsky, L. V. Nikitina, N. P. Radchikova, T. M. Mikheyeva, R. Z. Kavalevskaya, Yu. K. Veras, A. Chakraborty, A. V. Rusakov, N. I. Nurieva, and T. V. Zhukova, Relations between variations in the bacterioplankton abundance and the lake trophic state: Evidence from the 20-year monitoring. Ecological Indicators97 (2019), 120–129.10.1016/j.ecolind.2018.09.049Suche in Google Scholar
[2] N. Boccara, Modeling Complex Systems. Springer, New York, 2004.Suche in Google Scholar
[3] T. Coulson, P. Rohani, and M. Pascual, Skeletons, noise and population growth: the end of an old debate? Trends in Ecology and Evolution19 (2004), 359-364.10.1016/j.tree.2004.05.008Suche in Google Scholar
[4] W. W. Fox, An exponential surplus yield model for optimizing in exploited fish populations. Transactions of the American Fisheries Society99 (1970), 80–88.10.1577/1548-8659(1970)99<80:AESMFO>2.0.CO;2Suche in Google Scholar
[5] B. Gompertz, On the nature of the function expressive of the low of mortality, and on a new method of determining the value of life contingencies. Philosophical Transactions of the Royal Society27 (1825), 513–585.Suche in Google Scholar
[6] K. Higgins, A. Hastings, J. N. Sarvela, and L. W. Botsford, Stochastic dynamics and deterministic skeletons: Population behavior of Dungeness crab. Science276 (1997), 1431–1435.10.1126/science.276.5317.1431Suche in Google Scholar
[7] H. Kantz and T. Schreiber, Nonlinear Time Series Analysis. Cambridge University Press, Cambridge, 1997.Suche in Google Scholar
[8] L. Lacasa and R. Toral, Description of stochastic and chaotic time series using visibility graphs. Physical Review E82 (2010), No. 036120, 11 p.10.1103/PhysRevE.82.036120Suche in Google Scholar
[9] N. Marwan, A historical review of recurrence plots. The European Physical Journal Special Topics. The European Physical Journal Special Topics164 (2008), 3–12.10.1140/epjst/e2008-00829-1Suche in Google Scholar
[10] R. M. May, Biological populations with non-overlapping generations: stable points, stable cycles, and chaos. Science186 (1974), 645–647.10.1126/science.186.4164.645Suche in Google Scholar
[11] R. M. May, Simple mathematical models with very complicated dynamics. Nature261 (1976), 459–467.10.1038/261459a0Suche in Google Scholar
[12] A. B. Medvinsky, B. V. Adamovich, R. R. Aliev, A. Chakraborty, E. V. Lukyanova, T. M. Mikheyeva, L. V. Nikitina, N. I. Nurieva, A. V. Rusakov, and T. V. Zhukova, Temperature as a factor affecting fluctuations and predictability of the abundance of lake bacterioplankton. Ecological Complexity32 (2017), 90–98.10.1016/j.ecocom.2017.10.002Suche in Google Scholar
[13] E. Ott, Chaos in Dynamical Systems. Cambridge University Press, Cambridge, 2002.10.1017/CBO9780511803260Suche in Google Scholar
[14] O. L. 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, and I. S. Pearse, The ecological forecast horizon, and examples of its uses and determinants. Ecology Letters18 (2015), 597–611.10.1111/ele.12443Suche in Google Scholar PubMed PubMed Central
[15] M. G. Ravetti, L. C. Carpi, B. A. Gonçalves, A. Frery, and O. A. Rosso, Distinguishing noise from chaos: Objective versus subjective criteria using horizontal visibility graph. PLOS ONE9 (2014), No. e108004, 15 p.10.1371/journal.pone.0108004Suche in Google Scholar PubMed PubMed Central
[16] W. E. Ricker, Stock and recruitment. Journal of the Fisheries Research Board of Canada11 (1954), 559–623.10.1139/f54-039Suche in Google Scholar
[17] O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, and M. A. Fuentes, Distinguishing noise from chaos. Physical Review Letters99 (2007), 154102 (4 p.).10.1103/PhysRevLett.99.154102Suche in Google Scholar PubMed
[18] R. V. Solé and J. Bascompte, Organization in Complex Ecosystems. Princeton University Press, Princeton, 2006.10.1515/9781400842933Suche in Google Scholar
[19] P. Turchin, Complex Population Dynamics. A Theoretical/Empirical Synthesis. Princeton University Press, Princeton, 2003.Suche in Google Scholar
[20] J. M. G. Vilar and J. M. Rubi, Determinants of population responses to environmental fluctuations. Scientific Reports8 (2018), No. 887, 10 p.10.1038/s41598-017-18976-6Suche in Google Scholar PubMed PubMed Central
[21] C. L. Webber Jr. and N. Marwan (Eds.), Recurrence Quantification Analysis. Theory and Best Practices. Springer, Cham, 2015.10.1007/978-3-319-07155-8Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots
- Stochastic and deterministic kinetic energy backscatter parameterizations for simulation of the two-dimensional turbulence
- Neural networks for topology optimization
- Eulerian modelling of compressible three-fluid flows with surface tension
Artikel in diesem Heft
- Frontmatter
- Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots
- Stochastic and deterministic kinetic energy backscatter parameterizations for simulation of the two-dimensional turbulence
- Neural networks for topology optimization
- Eulerian modelling of compressible three-fluid flows with surface tension
