ORIGINAL PAPER

Theoretical Ecology

, Volume 7, Issue 1, pp 77-86

Taylor's law and abrupt biotic change in a smoothly changing environment

  • Joel E. CohenAffiliated withLaboratory of Populations, The Rockefeller University and Columbia University Email author 

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 real-world singularity in b could adversely affect fisheries, forestry, agriculture, conservation, and public health.

Keywords

Markovian environment Regime change Power spectra Population density Fluctuation scaling