Article,

DOI: http://dx.doi.org/10.1016/j.mbs.2012.06.001

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. Â\copyright 2012.

- (mathematics);
- (organic);
- adaptation;
- analysis;
- article;
- bifurcation
- bifurcation;
- common
- commons;
- competition
- competition;
- conditions;
- consumer;
- decay
- decay;
- dynamics
- dynamics;
- early
- ecosystem;
- heterogeneous
- humans;
- initial
- management;
- mathematical
- model;
- models,
- natural
- numerical
- of
- overconsumption;
- partitioning;
- point;
- population
- populations;
- regimes,
- renewable
- resistance;
- resource
- resource,
- resource;
- resources;
- restoration,
- survival,
- system
- system;
- the
- theoretical;
- tipping
- tragedy
- transitional