While I was writing Multiscale Structure in Eco-Evolutionary Dynamics, I found myself having a frustrating time reading through big chunks of the relevant literature. The mathematics in the mathematical biology was easier than a lot of what I’d had to deal with in physics, but the arguments were hard to follow. At times, it was even difficult to tell what was being argued about. A blog post by John Baez, on “biology as information dynamics,” called this frustration back to mind—not because it was unclear itself, but rather because it touched on the source of the fog.
I think the basic cause of the trouble is the following:
The application of mathematics to biological evolution is rooted, historically, in statistics rather than in dynamics. Consequently, a lot of model-building starts with tools that belong, essentially, to descriptive statistics (e.g., linear regression). This is fine, but then people turn around and discuss those models in language that implies they have constructed a dynamical system. This makes life quite difficult for the student trying to learn the subject by reading papers! The problem is not the algebra, but the assumptions. And that always makes for a thorny situation.