Transitional regimes as early warning signals in resource dependent competition models.
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.
Mathematical, Computational Modeling Sciences Center, P.O. Box 871904, Arizona State University, Tempe, AZ 85287, USA.
Irina
I
Kareva
Faina
F
Berezovskaya
Carlos
C
Castillo-Chavez
D017753:Ecosystem; D006801:Humans; D008962:Models, Theoretical; D011157:Population Dynamics