A Gentle Introduction to Structured Population Models: Three Worked Examples

In population models the basic unit is the individual. Therefore it is the task of the model builder to translate his/her knowledge about mechanisms on the individual level into models for the change in the number of such individuals.Generally, if one talks to an experimental ecologist (s)he has all kinds of alluring stories to tell about such mechanisms. However, as soon as it comes to writing down equations usually all that remains is but a handwaving reference when some mathematically convenient relationship between, say, death rate and population size is pulled mit of the hat. The main reason for this unsatisfactory state of affairs probably is that applied mathematics seems to revolve around differential equation models which in the simplest case of ordinary differential equations necessarily start at a rather high phenomenologicallevel. And biologists cannot but comply (but see e.g. MCKENDRICK (1926) for an early exception!). What clearly is needed, therefore, is a model1ing methodology which in principle can accomodate any necessary amouot of biological detail and yet is sufficiently near to the mainstream of applied mathematics that its toolscan be brought to bear. This is the backgrouod to our elforts as set forward in these notes.