IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v88y2013icp94-100.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S004058091300035X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2013.04.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:88:y:2013:i:c:p:94-100. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.