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Population fluctuations, power laws and mixtures of lognormal distributions

Summary: Population fluctuations, power laws and mixtures of
lognormal distributions
A number of investigators have invoked a cascading local interaction model to
account for power-law-distributed fluctuations in ecological variables. Invoking such
a model requires that species be tightly coupled, and that local interactions among
species influence ecosystem dynamics over a broad range of scales. Here we reanalyse
bird population data used by Keitt & Stanley (1998, Dynamics of North American
breeding bird populations. Nature, 393, 257260) to support a cascading local
interaction model. We find that the power law they report can be attributed to mixing
of lognormal distributions. More tentatively, we propose that mixing of distributions
accounts for other empirical power laws reported in the ecological literature.
Self-organised criticality, bird population dynamics, power laws.
Ecology Letters (2001) 4 : 13
Keitt & Stanley (1998) report that year-to-year fluctua-
tions of North American breeding bird populations
adhere to a power law distribution of event sizes. Power
law scaling can arise in inanimate systems as a result of
local interactions among particles that propagate through


Source: Allen, Andrew P. - National Center for Ecological Analysis and Synthesis, University of California at Santa Barbara


Collections: Environmental Sciences and Ecology