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Finding all multiple stable fixpoints of n-species Lotka–Volterra competition models

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  • Lischke, Heike
  • Löffler, Thomas J.

Abstract

One way to explore assembly of extant and novel communities from species pools, and by that biodiversity and species ranges, is to study the equilibrium behavior of dynamic competition models such as the Lotka–Volterra competition (LVC) model. We present a novel method (COMMUSTIX) to determine all stable fixpoints of the general LVC model with abundances x from a given pool of n species. To that purpose, we split the species in potentially surviving species (xi>0) and in others going extinct (xi=0). We derived criteria for the stability of xi=0 and for the equilibrium of xi>0 to determine possible combinations of extinct and surviving species by iteratively applying a mixed binary linear optimization algorithm.

Suggested Citation

  • Lischke, Heike & Löffler, Thomas J., 2017. "Finding all multiple stable fixpoints of n-species Lotka–Volterra competition models," Theoretical Population Biology, Elsevier, vol. 115(C), pages 24-34.
    • Handle: RePEc:eee:thpobi:v:115:y:2017:i:c:p:24-34
    DOI: 10.1016/j.tpb.2017.02.001
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