Multi-level Modeling of Populations

Many systems are too complex to represent with a single, detailed model because the model simply becomes too cumbersome . This is especially true when reasoning about populations composed of many interacting individuals . A fully-detailed model of such a system would have to model all the interactions between a potentially enormous number of individuals. Frequently, however, these interactions fall into only a few classes. We claim that when this occurs population systems are profitably modeled at three levels . At the highest level we represent the gross properties of the population as a whole. We also provide restricted means for modeling any direct influences the population's environment may have upon them, such as the constraint that the volume of a gas must equal the volume of its container. At the aggregate level, we model the statistical nature of a population explicitly . Changes to the membership of a population are modeled with sinks and sources. For example, evaporation of a liquid can be modeled as a sink with a threshold on kinetic energy of the molecules. This allows us to deduce the cooling effect of evaporation. The most detailed level describes the properties of individual members of the population . This level includes a set of models that describe all possible interactions that an individual may have with other individuals and with the population's environment. For example, one model might describe a gas molecule's collisions with other molecules, while another model would represent a colision with a container wall . Changes in individual properties due to interactions at the individual level 'This research was funded in part by National Science Foundation Grants IRI-8902010 and IRI-8957302, and a cash donation from the Xerox corporation . Multi-level Modeling of Populations Franz G. Amador & Daniel S . Weld* Department of Computer Science and Engineering, FR-35 University of Washington