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Counter-Examples about Lower- and Upper-Bounded Population Growth


  • Jacques Demongeot
  • Jules Waku


For a unimodal growth function f having its maximum at a critical state xc, the interval bounding the population size asymptotically is usually presented as being equal to [f○2(xc), f(xc)]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f○2(xc)), f(xc)], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.

Suggested Citation

  • Jacques Demongeot & Jules Waku, 2005. "Counter-Examples about Lower- and Upper-Bounded Population Growth," Mathematical Population Studies, Taylor & Francis Journals, vol. 12(4), pages 199-209.
  • Handle: RePEc:taf:mpopst:v:12:y:2005:i:4:p:199-209
    DOI: 10.1080/08898480500301785

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