 Stochastic population dynamics in a Markovian environment implies Taylor’s power law of fluctuation scalingJoel E. Cohen Theoretical Population Biology, 2014, vol. 93, issue C, 30-37 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. Keywords: Markov chain; Taylor’s law; Power law; Fluctuation scaling; Random evolution; Variance function (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:93:y:2014:i:c:p:30-37 DOI: 10.1016/j.tpb.2014.01.001 Access Statistics for this article Theoretical Population Biology is currently edited by Jeremy Van Cleve More articles in Theoretical Population Biology from Elsevier |
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