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Aaron King

       Aaron A. King, Ph.D.

      Assistant Professor of Ecology & Evolutionary Biology and Mathematics
      University of Michigan
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UM Library 		Experimental support of the scaling rule for demographic stochasticity

Experimental support of the scaling rule for demographic stochasticity

Robert A. Desharnais, R. F. Costantino, J. M. Cushing, Shandelle M. Henson, Brian Dennis, and Aaron A. King

Ecology Letters, 9:437-457.

Abstract

 Clarification of the deterministic signal as habitat size is increased A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two quantitative measures, we extend the scaling rule to situations in which population densities fluctuate due to nonlinear deterministic dynamics. These measures are applied to populations of the flour beetle Tribolium castaneum that display chaotic dynamics in both a 20g and 60g habitat. Populations cultured in the larger habitat exhibit a clarification of the deterministic dynamics which follows the inverse square root rule. Lattice effects, a deterministic phenomenon caused by the discrete nature of individuals, can cause deviations from the scaling rule when population numbers are small. The scaling rule is robust to the probability distribution used to model demographic variation among individuals.