Delay-Differential Equations for Structured Populations

Abstract

This chapter develops an approach to continuous-time models that emphasizes the stage structure of a population. The key motivating idea is that, in many situations, biological differences among individuals within a stage may be unimportant in comparison with interstage differences. For example, the rate of egg production by adult insects may depend on their age, but much insight into population dynamics may be obtained from models that recognize only the distinction between nonreproductive individuals (juveniles) and reproductive individuals (adults). Likewise, an organism’s susceptibility to parasitism may depend on its size but with a range of sizes at which the organism is not vulnerable. It is reasonable to explore the qualitative effects of the invulnerable class before investigating the detailed, quantitative consequences of the size structure.