Persistence despite perturbation for . . .

... an ed f ne nis iste rtu th interacting populations. Namely, a model is either persistent despite perturbations or not. When it is not persistent, it follows that all initial conditions are prone to extinction due to perturbations of the appropriate type. For frequent small perturbations, this method of the minimal conditions to ensure the long-term survivorship immune systems. The first step in this simplification often involves making a decision whether to focus on determi-nistic or stochastic processes underlying the system consequently, is a relative notion depending on the intent of tions. In contrast to the aforementioned stochastic models, these deterministic models may have population trajectories that persist indefinitely. While this persistence for infinite ARTICLE IN PRESStime cannot occur in reality, one can view these persistent trajectories as implying long-term survival for populations experiencing weak demographic noise