ABSTRACT
In recent years mathematical ecology has become a very active field of research. There are both practical and theoretical reasons for all the activity. The practical interest is mostly based on concerns about the impact of human interference and environmental change on natural communities. The theoretical interest is based partly on the practical interest and partly on the fact that the appropriate analytic methods have recently become available. The essential applied problem is to understand how the interactions of biological species with each other and their environment influence their coexistence, extinction, population size, and other vital phenomena. This chapter considers the pros and cons of these three alternative definitions of survival and coexistence. All have the advantage that they allow a conclusion of coexistence even when there is no globally stable positive equilibrium. The idea of uniform persistence is the most qualitative and thus most natural from the theoretical viewpoint of dynamical or semi-dynamical systems.
