Persistence and extinction of populations

Survival analyses of populations are developed in discrete growth processes and continuous growth processes. Persistence and extinction attributes of age-independent and age-dependent discrete population models are explored on both a finite and infinite time horizon. Conditions for persistence and extinction are found. De compositions of the initial population size axes into intervals where populations are persistent at time N and intervals leading to extinction at time n, where n < N, are found for age-independent discrete population models and two age class discrete population models. Persistence criteria of a class of continuous age-structured population models with separable mortality function and fertility function are established by investigation of asymptotic behaviors of solutions of a first order partial differential equation. Continuous population models with several age classes are studied as well by considering sets of ordinary differential equations. Finally, the connection between individual dynamics and population dynamics is discussed briefly.