A Resource Dependent Competition Model

There have been five major mass extinction events and a number of smaller extinction events throughout geological time. Each of these events characterises a widespread decrease in species diversity. The largest of these was the End-Permian extinction which saw about 90% of species go extinct. Extinction may be caused by a variety of factors such as asteroid impacts, CO₂ driven ocean acidification, large igneous provinces, global warming/cooling, and oceanic anoxic events. All of these factors cause stress on the environment.

The ability of a species to avoid extinction is dependent on its environmental tolerances, i.e., the ability of a species to tolerate, or survive, changes in environmental conditions.

In population biology one way in which species may become extinct is through competition. The classical theory of competitive exclusion does not consider the type of interaction between species. We create a new mathematical model of competition between species in which the maximum population of a species is dependent on the availability of resources (or food supply) and competition is in the form of competition for these resources. We find this model always leads to stable coexistence. Another way in which populations can go extinct is through extreme oscillations in predator-prey systems; we explain how this can occur and illustrate this with a specific realistic predator-prey model that we then couple to our competition model.