2: Age-structured Populations
Determining the age-structure of a population helps governments plan economic development. Age-structure theory can also help evolutionary biologists better understand a species’s life-history. An age-structured population occurs because offspring are born to mothers at different ages. If average per capita birth and death rates at different ages are constant, then a stable age-structure arises. However, a rapid change in birth or death rates can cause the age-structure to shift distributions. In this section, we develop the theory of age-structured populations using both discrete- and continuous-time models. We also present two interesting applications: (1) modeling age-structure changes in China and other countries as these populations age, and; (2) modeling the life cycle of a hermaphroditic worm. We begin this section, however, with one of the oldest problems in mathematical biology: Fibonacci’s rabbits. This will lead us to a brief digression about the golden mean, rational approximations and flower development, before returning to our main topic.