IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v289y2014icp59-65.html
   My bibliography  Save this article

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

Author

Listed:
  • Jiang, Jiang
  • DeAngelis, Donald L.
  • Zhang, Bo
  • Cohen, Joel E.

Abstract

Taylor's power law describes an empirical relationship between the mean and variance of population densities in field data, in which the variance varies as a power, b, of the mean. Most studies report values of b varying between 1 and 2. However, Cohen (2014a) showed recently that smooth changes in environmental conditions in a model can lead to an abrupt, infinite change in b. To understand what factors can influence the occurrence of an abrupt change in b, we used both mathematical analysis and Monte Carlo samples from a model in which populations of the same species settled on patches, and each population followed independently a stochastic linear birth-and-death process. We investigated how the power relationship responds to a smooth change of population growth rate, under different sampling strategies, initial population density, and population age. We showed analytically that, if the initial populations differ only in density, and samples are taken from all patches after the same time period following a major invasion event, Taylor's law holds with exponent b=1, regardless of the population growth rate. If samples are taken at different times from patches that have the same initial population densities, we calculate an abrupt shift of b, as predicted by Cohen (2014a). The loss of linearity between log variance and log mean is a leading indicator of the abrupt shift. If both initial population densities and population ages vary among patches, estimates of b lie between 1 and 2, as in most empirical studies. But the value of b declines to ∼1 as the system approaches a critical point. Our results can inform empirical studies that might be designed to demonstrate an abrupt shift in Taylor's law.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ecomod:v:289:y:2014:i:c:p:59-65
    DOI: 10.1016/j.ecolmodel.2014.06.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380014003044
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ecolmodel.2014.06.022?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.

    References listed on IDEAS

    as
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Meng Xu & Joel E Cohen, 2019. "Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-25, December.
    2. Guan, Qingqing & Chen, Jun & Wei, Zhicheng & Wang, Yuxia & Shiyomi, Masae & Yang, Yungui, 2016. "Analyzing the spatial heterogeneity of number of plant individuals in grassland community by using power law model," Ecological Modelling, Elsevier, vol. 320(C), pages 316-321.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kelsey Chalmers & Elizabeth M Kita & Ethan K Scott & Geoffrey J Goodhill, 2016. "Quantitative Analysis of Axonal Branch Dynamics in the Developing Nervous System," PLOS Computational Biology, Public Library of Science, vol. 12(3), pages 1-25, March.
    2. 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.
    3. Alessia Naccarato & Federico Benassi, 2018. "On the relationship between mean and variance of world's human population density: A study using Taylor's power law," Letters in Spatial and Resource Sciences, Springer, vol. 11(3), pages 307-314, October.
    4. 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.
    5. 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.
    6. Federico Benassi & Alessia Naccarato & Luca Salvati, 2023. "Testing Taylor’s Law in Urban Population Dynamics Worldwide with Simultaneous Equation Models," Economies, MDPI, vol. 11(2), pages 1-17, February.
    7. 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.

    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:ecomod:v:289:y:2014:i:c:p:59-65. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: http://www.journals.elsevier.com/ecological-modelling .

    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.