### 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 language | English (US) |
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Pages (from-to) | 114-123 |

Number of pages | 10 |

Journal | Mathematical Biosciences |

Volume | 240 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2012 |

### Keywords

- 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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## Cite this

*Mathematical Biosciences*,

*240*(2), 114-123. https://doi.org/10.1016/j.mbs.2012.06.001