Population Models of Extinction

In the previous chapter we discussed the basics of population dynamics, whose models describe the average population size, which changes over time. In this chapter, we will consider population extinction by adding random movement in the population size. The study of extinction in conservation ecology and population genetics has a long history, and it is not the purpose of this chapter to summarize the many extant studies. Instead, the goal is to understand their essential aspects intuitively and thereby be able to perform some useful calculations on our own. To this end, the derivation of the relevant formulas has been considered in detail. If the reader is familiar with these derivations, they are encouraged to skip this chapter and move on to the next, which deals with case studies. First, we will present a model of the birth-death process, followed by a model of the stochastic process. Two diffusion process models play an important role in the stochastic process, and the ultimate goal of the chapter is to derive the mean time to extinction (MTE) using these diffusion process models.