title: Taylor's power law of fluctuation scaling and the growth-rate theorem.
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.
authors.affiliation: Laboratory of Populations, Rockefeller University, 1230 York Avenue, Box 20, New York, NY 10065, USA; Laboratory of Populations, Earth Institute, Columbia University, New York, USA. Electronic address: joel.cohen@rockefeller.edu.
authors.forename: Joel E
authors.initials: JE
authors.lastname: Cohen
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D011158:Population Growth
keywords: Exponential growth; GR; Lewontin–Cohen model; Population density; Population growth rate; TL; Taylor’s law; Variance; growth-rate theorem