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Journal of Mathematical Biology

, Volume 47, Issue 3, pp 235–248 | Cite as

On the concept of attractor for community-dynamical processes II: the case of structured populations

  • Mats GyllenbergEmail author
  • F.J.A. Jacobs
  • J.A.J. Metz
Article

Abstract.

In Part I of this paper Jacobs and Metz (2003) extended the concept of the Conley-Ruelle, or chain, attractor in a way relevant to unstructured community ecological models. Their modified theory incorporated the facts that certain parts of the boundary of the state space correspond to the situation of at least one species being extinct and that an extinct species can not be rescued by noise. In this part we extend the theory to communities of physiologically structured populations. One difference between the structured and unstructured cases is that a structured population may be doomed to extinction and not rescuable by any biologically relevant noise before actual extinction has taken place. Another difference is that in the structured case we have to use different topologies to define continuity of orbits and to measure noise. Biologically meaningful noise is furthermore related to the linear structure of the community state space. The construction of extinction preserving chain attractors developed in this paper takes all these points into account.

Keywords

 Environmental noise Pseudoorbit Chain attractor Weak-topology Physiologically structured populations Community dynamics Extinction 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Department of Ecology and Evolutionary BiologyUniversity of TennesseeKnoxvilleU.S.A
  3. 3.Institute for Evolutionary and Ecological SciencesLeiden University, The Netherlands and Adaptive Dynamics Network, IIASA, 2361 Laxenburg, Austria.GP LeidenThe Netherlands

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