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Taylor’s power law of fluctuation scaling and the growth-rate theorem

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  • Cohen, Joel E.

Abstract

Taylor’s law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations’ growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:88:y:2013:i:c:p:94-100
    DOI: 10.1016/j.tpb.2013.04.002
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    Cited by:

    1. Carpenter, Samuel & Callens, Scout & Brown, Clark & Cohen, Joel E. & Webb, Benjamin Z., 2023. "Taylor’s law for exponentially growing local populations linked by migration," Theoretical Population Biology, Elsevier, vol. 154(C), pages 118-125.
    2. Jiang, Jiang & DeAngelis, Donald L. & Zhang, Bo & Cohen, Joel E., 2014. "Population age and initial density in a patchy environment affect the occurrence of abrupt transitions in a birth-and-death model of Taylor's law," Ecological Modelling, Elsevier, vol. 289(C), pages 59-65.
    3. 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.
    4. Cohen, Joel E., 2014. "Stochastic population dynamics in a Markovian environment implies Taylor’s power law of fluctuation scaling," Theoretical Population Biology, Elsevier, vol. 93(C), pages 30-37.
    5. Joel E. Cohen & Christina Bohk & Roland Rau, 2018. "Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(29), pages 773-842.

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