Studying the Dynamics of Structured Population Models: A Versatile Technique and Its Application to Daphnia

Abstract

We introduce a versatile model formulation, called the escalator boxcar train, that can be used to study the dynamics of populations structured by age, size, or any other physiological trait. Spanning the entire spectrum between the classical, age-structured, Leslie matrix models and continuous-time, physiologically structured population models, it combines the computational ease of the matrix models with the flexibility of the continuous-time models: it allows the population dynamics to depend on an arbitrary number of individual characteristics and can account for nonlinear interactions of the population with its (fluctuating) environment, for density dependence in individual behavior, and for a continuous reproduction process. Application of the technique to a model for the dynamics of a Daphnia population reveals that a food-dependent maturation delay induces a very specific type of population cycle, in which the demography of the population plays a major role. The influence of "growth-curve plasticity," that is, the change in size at each age with a change in food density, on individual feeding behavior (at higher food densities individuals are larger and hence eat more) is a potential mechanism to stabilize the dynamics. The influence of growth-curve plasticity on reproduction (primarily the increase in maturation delay with a decrease in food density) greatly destabilizes the system.