ABSTRACT Informal models have always been used in biology to guide thinking and devise experiments. In recent years, formal mathematical models have also been widely introduced. It is sometimes suggested that formal models are inherently superior to informal ones and that biology should develop along the lines of physics or economics by replacing the latter with the former. Here I suggest to the contrary that progress in biology requires a better integration of the formal with the informal. In a series of previous essays, I discussed how formal mathematical models have played a far more significant role in biology than most biologists typically appreciate The word "model" has many meanings in biology. We speak of model organisms as institutionalized representatives of particular phyla. We occasionally build physical models, as Crick and Watson did for DNA. Mostly, however, a model refers to some form of symbolic representation of our assumptions about reality, and that is the sense in which I will use the word here. An informal model is one in which the symbols are mental, verbal, or pictorial, perhaps a scrawl of blobs and arrows on the whiteboard; in contrast, a formal model is one in which the symbols are mathematical. Informal models pervade biology. They help to guide our thinking, and experimentalists rely on them to design experiments. The model may turn out to be nonsense, and an experiment may reveal that, but one has to start somewhere. It is sometimes claimed that one starts with data, from which a model is constructed. But why those data? And how should those data be interpreted? The answers reveal informal models that precede the acquisition of data. Models, whether informal or formal, allow us to capture assumptions and to undertake reasoning. Informal models have two classes of assumptions: those that are explicit in the model itself, or foreground assumptions; and those that are only implicit but potentially significant, or background assumptions. In molecular biology, a foreground assumption might be that blob X is an activated enzyme, which implements an informal arrow. A background assumption might be that X has multiple posttranslational modifications, which influence activation but differ depending on the organism. Whether a particular fact is in the foreground or relegated to the background depends on the problem at hand and the questions being asked. This allows us to tolerate much ambiguity. Does X mean chicken X or fl
