Bifurcations in Mathematical Models of Niche Construction

A question of “how much overconsumption a renewable resource can tolerate”, which is related to a phenomenon known as “the tragedy of the commons”, is addressed using a mathematical model, where individuals in a population not only compete for the common resource but can also contribute to its restoration. The considered model can realize one of two pure strategies for interaction with the resource, namely using the resource to increase proliferation or to increase environmental capacity and become better competitors, with a full spectrum of possible intermediate strategies. 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. We observe that just knowing the rules according to which the interactions occur is not enough to make accurate predictions about which strategy will come to dominate; one also needs to know the initial composition of the population. We also come to the conclusion that within the frameworks of the model there is no optimal strategy to avoid the tragedy of the commons.