Population Dynamics Modeling

Abstract

Until now, we have dealt with deductive modeling exclusively, i.e., all our models were created on the basis of a physical understanding of the processes that we wished to capture. Therefore, this type of modeling is also frequently referred to as physical modeling. As we proceed to more and more complex systems, less and less meta-knowledge is available that would support physical modeling. Furthermore, the larger uncertainties inherent in most physical parameters of such systems make physical models less and less accurate. Consequently, researchers in fields such as biology or economics often prefer an entirely different approach to modeling. They make observations about the system under study and then try to fit a model to the observed data. This modeling approach is called inductive modeling. The structural and parametric assumptions behind inductive models are not based on physical intuition, but on factual observation. This chapter illustrates some of the virtues and vices associated with inductive modeling and lists the conditions under which either of the two approaches to modeling is more adequate than the other. This chapter documents how population dynamics models are created, discusses the difference between structural and behavior complexity of models in general, introduces the concept of chaotic motion, and addresses a rather difficult issue, namely, the question of self-organization within systems.