ABSTRACT
Nevertheless, the study of the simple modules in isolation is useful because it has proven difficult to deduce the population level consequences of individual level processes using verbal reasoning alone. Population processes involve the interaction of phenomena occurring at two different levels of organization and two distinct time scales. The individual and population levels of organization interact through the sampling processes inherent in reproduction or socialization. The day-to-day ecological time scale, on which processes of change act (e.g., selective mortality), interacts with the long-run evolutionary time scale on which adaptations of particular kinds are or are not produced. Even the simplest examples of evolutionary processes are thus rather complex. Mathematics makes it relatively easy to consistently and systematically trace the implications of a given set of assumptions, even when the processes modelled are probabilistic or quantitative. Simple, but formal, models are a useful mental prosthesis to reduce the handicap of a certain kind of cognitive limitation. It is important to realize that such models serve a rather narrow function, the testing of explanations for logical consistency. While they are tremendously useful in this role, they are only a supplement to other theoretical and empirical tools in the social and biological sciences, not a replacement for them.
