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Stochastic population dynamics in a Markovian environment implies Taylor’s power law of fluctuation scaling

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  • Cohen, Joel E.

Abstract

Taylor’s power law of fluctuation scaling (TL) states that for population density, population abundance, biomass density, biomass abundance, cell mass, protein copy number, or any other nonnegative-valued random variable in which the mean and the variance are positive, variance=a(mean)b,a>0, or equivalently log variance=loga+b×log mean. Many empirical examples and practical applications of TL are known, but understanding of TL’s origins and interpretations remains incomplete. We show here that, as time becomes large, TL arises from multiplicative population growth in which successive random factors are chosen by a Markov chain. We give exact formulas for a and b in terms of the Markov transition matrix and the values of the successive multiplicative factors. In this model, the mean and variance asymptotically increase exponentially if and only if b>2 and asymptotically decrease exponentially if and only if b<2.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:93:y:2014:i:c:p:30-37
    DOI: 10.1016/j.tpb.2014.01.001
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    References listed on IDEAS

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    1. You-Gan Wang & Yuning Zhao, 2007. "A Modified Pseudolikelihood Approach for Analysis of Longitudinal Data," Biometrics, The International Biometric Society, vol. 63(3), pages 681-689, September.
    2. 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.
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    Cited by:

    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. 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.
    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. 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.

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