Experimental support of the scaling rule for demographic stochasticity

Ecology Letters
R A DesharnaisAaron A King

Abstract

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.

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Citations

Mar 25, 2011·Journal of the Royal Society, Interface·John M DrakeBlaine D Griffen
Jun 12, 2008·Proceedings. Biological Sciences·Blaine D Griffen, John M Drake
Jan 15, 2009·Proceedings. Biological Sciences·Blaine D Griffen, John M Drake
Nov 23, 2006·Proceedings of the National Academy of Sciences of the United States of America·Daniel C ReumanJoel E Cohen
Apr 5, 2011·The American Naturalist·Aline Magdalena LeeSteinar Engen
Feb 14, 2013·Theoretical Population Biology·Edwin van Leeuwen, Rampal S Etienne
Jun 19, 2012·Mathematical Biosciences·Alex Skvortsov, Branko Ristic
Jun 19, 2008·The Journal of Animal Ecology·Blaine D Griffen, John M Drake
Feb 13, 2013·The Journal of Animal Ecology·Elodie VerckenXavier Fauvergue
Sep 16, 2010·The Journal of Animal Ecology·Bernt-Erik SaetherRobert P Freckleton
Nov 14, 2013·Ecology and Evolution·John M Drake, Blaine D Griffen
Sep 20, 2018·Ecology Letters·Robert A DesharnaisJoel E Cohen
Mar 25, 2021·The Journal of Animal Ecology·Tad DallasAlan Hastings

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