Linear, age-structured models and their long-term dynamics

Abstract

The chapter describes age-structured models that are linear (i.e. without density dependence). Like simple (non-age-structured) linear models they eventually either increase to infinity or decrease to zero. They are only appropriate when density dependence is not an important factor, such as recently introduced populations or those that have declined to low abundance. The chapter steps through several different ways of formulating such models. First are Lotka’s renewal equation and the M’Kendrick/von Foerster equation, both continuous time, continuous age models. Next is the Leslie matrix, which operates in discrete age and time. Solutions to linear matrix equations, such as the Leslie matrix, can be written in a general way in terms of eigenvalues and eigenvectors. These form the basis of analyses of dynamic stability throughout the book. Practically speaking, the Leslie matrix approach is the primary model used in modern ecology.