A generic approach to demographic, equilibrium, and evolutionary analysis of structured population models based on continuous-time, arbitrarily complex individual life histories
Many problems in ecology and evolution revolve around how individual life history influences population and community dynamics or, vice versa, how population and community dynamics influence life histories. Structured population models are well suited to address such questions since they are formulated using rules that describe the life history of individuals. Dynamics of the population emerge by bookkeeping the fates of its individuals. In 1911 Sharpe and Lotka formulated one of the first structured population models using an integral equation describing how the population birth rate depends on the population age distribution. Later representatives of this model class used partial differential instead of integral equations, characterized individuals by their body size or physiological traits instead of their age, and accounted for density dependence and population feedback on individual life history. These models are now generally referred to as physiologically structured population models (PSPMs) and have as their defining characteristic a clear distinction between the state of the individual organism and the state of the environment it lives in. Together, these determine the rates of reproduction, development and mortality. PSPMs account for density dependent, population feedback through changes in the environment that individuals experience. In contrast to the more familiar matrix or integral projection models, the individual life history is described in continuous time, for example, by a dynamic energy budget model for individual body size and energy reserves. PSPMs have proved to be remarkably powerful tools, but the mathematical sophistication of the PSPM formalism has impeded their wide use by ecologists.
In recent years, a general methodology has been developed to carry out demographic, equilibrium (bifurcation) and evolutionary analysis of physiologically structured population models. In its simplest form, the method boils down to the numerical evaluation of the Sharpe-Lotka integral equation. Even more recently, this methodology has been implemented in a software package that allows for full analysis of physiologically structured population models from the specification of the key ingredients of an individual’s life history: its development, reproduction, and mortality, and its interactions with its environment. In this presentation I will give a brief introduction to the general methodology and illustrate with a few examples how the software package can be used for demographic, equilibrium and evolutionary analysis of this general class of structured population models.