Taylor's law and abrupt biotic change in a smoothly changing environment
 Joel E. Cohen
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Abstract
Taylor's law (TL), widely verified in empirical ecology, states that the variance of population density approximates a power function of the mean population density, with exponent denoted b. A model of multiplicative increments in population density, where the increments are determined by a Markovian environment, predicts TL with an explicit formula for b. We give a simple theoretical example where, unexpectedly, smooth changes in environmental autocorrelation lead to an abrupt, infinite discontinuity in b. As the daily probability of change in environmental state increases from 0 to 1, b rises from 2 slowly at first, then explodes to +∞ when the population becomes critical, drops to ∞, and rises again to 2. In this model, an exponent b of large magnitude (positive or negative) signals the proximity of a population's criticality and of a singularity in b. A comparable realworld singularity in b could adversely affect fisheries, forestry, agriculture, conservation, and public health.
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 Title
 Taylor's law and abrupt biotic change in a smoothly changing environment
 Journal

Theoretical Ecology
Volume 7, Issue 1 , pp 7786
 Cover Date
 20140201
 DOI
 10.1007/s120800130199z
 Print ISSN
 18741738
 Online ISSN
 18741746
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Markovian environment
 Regime change
 Power spectra
 Population density
 Fluctuation scaling
 Authors

 Joel E. Cohen ^{(1)}
 Author Affiliations

 1. Laboratory of Populations, The Rockefeller University and Columbia University, 1230 York Avenue, Box 20, New York, NY, 10065, USA