Transitional regimes as early warning signals in resource dependent competition models

Irina Kareva, Faina Berezovskaya, Carlos Castillo-Chavez

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In this paper a question of " how much overconsumption a renewable resource can tolerate" is addressed using a mathematical model, where individuals in a parametrically heterogeneous population not only compete for the common resource but can also contribute to its restoration. Through bifurcation analysis a threshold of system resistance to over-consumers (individuals that take more than they restore) was identified, as well as a series of transitional regimes that the population goes through before it exhausts the common resource and thus goes extinct itself, a phenomenon known as " the tragedy of the commons" It was also observed that (1) for some parameter domains a population can survive or go extinct depending on its initial conditions, (2) under the same set of initial conditions, a heterogeneous population survives longer than a homogeneous population and (3) when the natural decay rate of the common resource is high enough, the population can endure the presence of more aggressive over-consumers without going extinct.

Original languageEnglish (US)
Pages (from-to)114-123
Number of pages10
JournalMathematical Biosciences
Issue number2
StatePublished - Dec 2012


  • Resource overconsumption
  • Tipping points
  • Tragedy of the commons
  • Transitional regimes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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