In the previous chapter, we first discussed the linear difference equation model Pt+1 = λPt, which results in exponential growth or decay. After criticizing this model for not being realistic enough, we looked at nonlinear models that could result in quite complicated dynamics.

However, there is another way our models in the last chapter were simplistic – they treated all individuals in a population identically. In most populations, there are actually many subgroups whose vital behavior can be quite different. For instance, in humans, the death rate for infants is often higher than for older children. Also, children before the age of puberty contribute nothing to the birth rate. Even among adults, death rates are not constant, but tend to rise with advancing age.

In nonhuman populations, the differences can be more extreme. Insects go through a number of distinct life stages, such as egg, larva, pupa, and adult. Death rates may vary greatly across these different stages, and only adults are capable of reproducing. Plants also may have various stages they pass through, such as dormant seed, seedling, nonflowering, and flowering. How can a mathematical model take into account the subgroup structure that we would expect to play a large role in determining the overall growth or decline of such populations?