The science of economics often takes a pummeling in the press, largely because this field is so intertwined with the messy business of policy. But from a pure research perspective, the way economists successfully handle extremely heterogeneous systems with some relatively simple mathematical models offers some lessons for biologists.
While reading this piece (Paul Krugman talking about his research career), I was struck by how biologists are faced with similar problems:
Robert Solow used to tell his students that there were two kinds of theorists: those who like to generalize, and those who like to look for illuminating special cases. I fall very strongly into the latter camp. Indeed, I have elevated the creation of special cases into a sort of personal art form. In constant-returns models, it is often possible once you have made the big untrue assumptions up front to derive results of considerable generality. For example, the Heckscher-Ohlin-Samuelson model does not depend on any assumptions about the degree of substitutability between capital and labor. You may want to look at, say, a Leontief or a Cobb-Douglas technology as an interesting example, but you don’t have to. In increasing-returns models, by contrast, there are very few general results. Even with two goods, two countries, and one factor of production one easily bogs down in a complex taxonomy. So what do you do?
My answer has been to rely heavily on those suggestive special cases. The process works like this: start with an informal verbal story, often one drawn from casual empiricism or from non-mainstream economic literature. Then try to build the simplest possible model that will illustrate that story. In the course of the model-building the story tends to change along with your intuition, but at the end of the process you have a simple model that is a very special case, but that makes a lot of intuitive sense and effectively gives you a language to discuss things that previously were off limits. The intuition can then also serve as the basis for empirical work, although to be honest I have never been a very persistent econometrician.
How do you find special cases that work, that allow you to go where no modeler has gone before? Any way you can. At various times I have assumed particular functional forms; symmetry; two states of nature where you might expect to find a continuum, or a continuum of goods where the traditional models have two; and in some cases relied on numerical examples where pencil and paper fail. It’s a sort of blitzkrieg approach to theory: instead of trying to advance on a broad front, one tries to get as far as possible along a narrow corridor of advance, taking advantage of any weak points you can find.
“Illuminating special cases”: unlike physicists, biologists can’t make very many generalizations, and even when they can, those generalizations are not quantitative, not expressed by a small set of equations. If you want to understand the molecular basis of quantitative traits, the functioning of genetic networks, the information transducing properties of signaling pathways, the logic behind patterns of developmental gene expression, you need to find illuminating special cases – these questions cannot be answered with a set of general principles, largely thanks to evolutionary history.
What’s more interesting here is the idea that it is still fruitful to apply simple mathematical models to these special cases. Math doesn’t need to be limited to general principles (e.g. Maxwell’s laws), or huge, detailed models that try to incorporate everything known about complex systems.
Simple quantitative models can lead to a core, qualitative insight into what makes your illuminating case work, and with this core insight in hand, you can use what you’re learned in one case to understand what’s going on in another situation.
The Finch and Pea 