Mathematical Conservation Ecology: A One-predator–Two-prey System as Case Study

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Abstract
A method is presented to analyse the long-term stochastic dynamics of a biological population that is at risk of extinction. From the full ecosystem the method extracts the minimal information to describe the long-term dynamics of that population by a stochastic logistic system. The method is applied to a one-predator-two-prey model. The choice of this example is motivated by a study on the near-extinction of a porcupine population by mountain lions whose presence is facilitated by mule deer taking advantage of a change in land use. The risk of extinction is quantified by the expected time of extinction of the population.

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