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Stochastic effects in mean-field population growth: The quasi-Gaussian approximation to the case of a Taylor’s law-distributed substrate

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  • Khalin, Andrey A.
  • Postnikov, Eugene B.
  • Ryabov, Alexey B.

Abstract

We analyze the effect of the stochastic growth rates, which may originate from heterogeneity of resource distribution on the average unrestricted growth of an ensemble of non-interacting sub-populations of consumers with Holling I and II functional responses, assuming normal (Gaussian) and anomalous (Tweedie) density distributions of resources. We show that the variation in the resource availability between the sub-population habitats leads to a non-Malthusian dynamics of the initial phase of the average biomass growth, and that this phase of growth can be successfully approximated using quasi-Gaussian approach. This conclusion is illustrated by numerical simulations.

Suggested Citation

  • Khalin, Andrey A. & Postnikov, Eugene B. & Ryabov, Alexey B., 2018. "Stochastic effects in mean-field population growth: The quasi-Gaussian approximation to the case of a Taylor’s law-distributed substrate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 166-173.
    • Handle: RePEc:eee:phsmap:v:511:y:2018:i:c:p:166-173
    DOI: 10.1016/j.physa.2018.07.052
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    References listed on IDEAS

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    1. Cohen, Joel E., 2013. "Taylor’s power law of fluctuation scaling and the growth-rate theorem," Theoretical Population Biology, Elsevier, vol. 88(C), pages 94-100.
    2. Johansen, Anders & Sornette, Didier, 2001. "Finite-time singularity in the dynamics of the world population, economic and financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 465-502.
    3. De Lauro, E. & De Martino, S. & De Siena, S. & Giorno, V., 2014. "Stochastic roots of growth phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 207-213.
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    Cited by:

    1. Eugene B. Postnikov & Andrey A. Khalin & Anastasia I. Lavrova & Olga A. Manicheva, 2019. "Resazurin Assay Data for Mycobacterium tuberculosis Supporting a Model of the Growth Accelerated by a Stochastic Non-Homogeneity," Data, MDPI, vol. 4(1), pages 1-8, February.

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