Scalar Population Models

The main focus of this chapter is on the introduction of single-species population models and their analysis. Of fundamental interest in population dynamics is how population size changes in time. Is the population increasing, decreasing, fluctuating, or even chaotic? Is it in danger of extinction or will it persist? What are the characteristics of the population’s trajectory? Will it stabilize at an equilibrium state or will it be subject to crash-and-boom sustained oscillations? The answers to these questions require an understanding of the basic demographic processes of birth and death and possibly other processes by which individuals might arrive or depart from the population, such as immigration and/or emigration. In this chapter, we consider models in which a single, aggregate state variable is used to characterize the population.