18 Pages

Mathematical models for age-structured population dynamics: An overview

WithG. Di Cola, G. Gilioli, J. Baumgärtner

The overview on structured population models starts with the presentation of deterministic models (section 2). On this ground models with physiological variables (section 3) and, subsequently, stochastic models (section 4) are introduced. In the second section the continuous von Förster and the discrete Leslie model are shown to be the basic approaches to represent the dynamics of age-structured populations. The up-wind scheme of the von Förster model and the sojourn time models are related. For illustration purposes a sojourn time model and a Leslie model has been chosen. In the third section physiological variables are introduced into structured population models by considering a variable for mass or mass equivalents and/or by using physiological time and age rather than chronological time and age. Both possibilities have been considered in the illustrative example. In the fourth section macroscopic and microscopic stochastic models are introduced. The former are based either on diffusion processes or on time distributed delays. Microscopic models are often considered to be biologically more appealing than macroscopic models, they have recently received considerable attention in population ecology. To illustrate these approaches we primarily refer to structured population models developed by the authors.