Abstract

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
Volume240
Issue number2
DOIs
StatePublished - Dec 2012

Fingerprint

Competition Model
Early Warning
Restoration
Mathematical models
Resources
Dependent
Population
Initial conditions
Renewable Resources
renewable resources
Bifurcation Analysis
Decay Rate
Theoretical Models
mathematical models
deterioration
Mathematical Model
Series

Keywords

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

ASJC Scopus subject areas

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

Cite this

Transitional regimes as early warning signals in resource dependent competition models. / Kareva, Irina; Berezovskaya, Faina; Castillo-Chavez, Carlos.

In: Mathematical Biosciences, Vol. 240, No. 2, 12.2012, p. 114-123.

Research output: Contribution to journalArticle

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