Numerical solution of structured population models

Abstract

Numerical methods are presented for a general age-structured population model with demographic rates depending on age and the total population size. The accuracy of these methods is established by solving problems for which alternate solution techniques are available and are used for comparison. The methods reliably solve test problems with a variety of dynamic behavior. Simulations of a blowfly population exhibit cyclic fluctuations, whereas a simulated squirrel population reaches a stable age distribution and stable equilibrium population size. Life-history attributes are easily studied from the computed solutions, and are discussed for these examples. Recovery of a stressed population back to equilibrium is examined by computing the transition in age structure, and the transient behavior of other properties of the population such as the per capita growth rate, the average age, and the generation length.