Aaron A. King, Ph.D.

Nelson G. Hairston Collegiate Professor of Ecology, Evolutionary Biology,
Complex Systems, and Mathematics, University of Michigan
External Professor, Santa Fe Institute
Fellow of the American Association for the Advancement of Science

Experimental support of the scaling rule for demographic stochasticity

R. A. Desharnais, R. F. Costantino, J. M. Cushing, S. M. Henson, B. Dennis, and A. A. King
Ecology Letters 9:  537–547, 2006.

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 20-g and 60-g habitats. 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.

The official version of the paper is here.   Please contact Prof. King if you'd like a reprint.

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