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Theoretical Ecology

, Volume 4, Issue 4, pp 449–465 | Cite as

Simplification of structured population dynamics in complex ecological communities

  • Axel G. Rossberg
  • Keith D. Farnsworth
Original Paper

Abstract

Goldstone’s idea of slow dynamics resulting from spontaneously broken symmetries is applied to Hubbell’s neutral hypothesis of community dynamics, to efficiently simplify stage-structured multi-species models—introducing the quasi-neutral approximation (QNA). Rather than assuming population-dynamical neutrality in the QNA, deviations from ideal neutrality, thought to be small, drive dynamics. The QNA is systematically derived to first and second order in a two-scale singular perturbation expansion. The total reproductive value of species, as computed from the effective life-history parameters resulting from the non-linear interactions with the surrounding community, emerges as the new dynamic variables in this aggregated description. Using a simple stage-structured community-assembly model, the QNA is demonstrated to accurately reproduce population dynamics in large, complex communities. Further, the utility of the QNA in building intuition for management problems is illustrated by estimating the responses of a fish stock to harvesting and variations in fecundity.

Keywords

Reproductive value Lotka–Volterra model Fisheries management Neutral theory of biodiversity Goldstone mode 

Notes

Acknowledgements

The authors acknowledge discussion and comments on this work by Ken Haste Andersen, Martin Pedersen and J.A.J. (Hans) Metz. This Beaufort Marine Research Award is carried out under the Sea Change Strategy and the Strategy for Science Technology and Innovation (2006–2013), with the support of the Marine Institute, funded under the Marine Research Sub-Programme of the Ireland’s National Development Plan 2007–2013.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Biological SciencesQueen’s University BelfastBelfastUK

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