As one might expect, the applications of catastrophe theory in biology tend to occupy a position on the spectrum somewhere between those in physics and those in the social sciences. We do not usually know the dynamic, but we do generally have at least some idea of the processes involved. As a result, we are often in a position to judge whether or not the conditions necessary for catastrophe theory to be applicable are likely to be satisfied, and this puts us on much firmer ground than in the social sciences. Indeed, one of the aims of applying catastrophe theory in biology is to help us in the task of deducing the mechanism.

The two examples that we discuss in this chapter differ from those in Chapters 5 and 6 in an important respect. So far we have seen catastrophe theory applied to problems which had previously been studied by other methods. Here, in contrast, we have two case studies of catastrophe theory in action. In both cases, new results were obtained and (which should satisfy those who see it as the sole criterion for the usefulness of theory in science) further experiments were suggested.

The movement of a frontier

This is one of the first real applications of catastrophe theory. We begin with the statement and proof in more or less the same form as that originally given by Zeeman (1974). We then discuss part of the rest of that paper in order to see precisely what it is that the analysis accomplishes.