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Individual-based chaos: Extensions of the discrete logistic model

Gibson, William T. and Wilson, William G. (2013) Individual-based chaos: Extensions of the discrete logistic model. Journal of Theoretical Biology, 339 (S1). pp. 84-92. ISSN 0022-5193. doi:10.1016/j.jtbi.2013.09.001.

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Simple models of density-dependent population growth such as the discrete logistic map provide powerful demonstrations of complex population dynamics. Yet it is unclear whether the dynamics observed in such idealized systems would be present, under realistic conditions, in the context of demographic stochasticity, which is well known to exist in finite natural populations. Here, using a set of simple, individual-based models (IBM's) and their population-level iterative map counterparts, we computationally investigate the contribution of demographic stochasticity to density-dependent population dynamics in a simple model of seed production and recruitment. Notably, for a sufficiently large lattice, even in the presence of demographic stochasticity, many of the qualitative features of these idealized maps – including bifurcations – are still present. Demographic stochasticity and the constraints imposed by a finite lattice size appear to produce mixed dynamics that are partially stochastic, yet qualitatively similar to the deterministic models. The mechanistic assumptions and lattice sizes required to generate these dynamics cast doubt on whether they might be observable in annual plant populations. Nevertheless, we cannot rule out the theoretical possibility that such dynamics might be observable in ecological communities having similar mechanistic properties.

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Additional Information:© 2013 Elsevier Ltd. Available online 11 September 2013. We thank Boris Rubinstein and Bo Chen for helpful comments and discussion. We are grateful to HHMI for financial support. WTG is a fellow of the Jane Coffin Childs Foundation for Medical Research.
Funding AgencyGrant Number
Howard Hughes Medical Institute (HHMI)UNSPECIFIED
Jane Coffin Childs FoundationUNSPECIFIED
Subject Keywords: Chaos; Logistic growth; Population dynamics; Demographic stochasticity; Individual-based model (IBM)
Issue or Number:S1
Record Number:CaltechAUTHORS:20131213-134740690
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Official Citation:William T. Gibson, William G. Wilson, Individual-based chaos: Extensions of the discrete logistic model, Journal of Theoretical Biology, Volume 339, 21 December 2013, Pages 84-92, ISSN 0022-5193, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43001
Deposited By: Ruth Sustaita
Deposited On:13 Dec 2013 22:05
Last Modified:10 Nov 2021 16:31

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