A few weeks ago an interesting article was published in PLOS Biology, Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology. Importantly the authors emphasize the importance of ‘proof-of-concept’ mathematical models, which lay out verbal logic in a way that might expose contradictions. The emptiness of many verbal models was well illustrated to me in Jerry Coyne and H. Allen Orr’s survey of “models” in Speciation. There wasn’t even an internal check on the speculative frenzy. Mathematical models are also analogy killers, which is usually a good thing because people often end up obfuscating rather than illuminating when they have to make recourse to these verbal structures. Since I promoted Mathematical Models of Social Evolution a few weeks ago, I thought I’d also higlight Sarah Otto and Troy Day’s A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. It really covers all the bases, though it might be heavy-going for some.

Speaking of math and biology, Lior Pachter has a non-jeremiad post up, The two cultures of mathematics and biology, which is worth reading in full. It’s a fact that many biologists are the sort of scientists who have the attitude toward math which takes the form, “yes, some equations for statistical testing, just not too much.” But things are a changing. I’ve never talked to a biologist who has complained that they had to take too much math, rather, it’s always the other way around. With the explosion in genomics some level of mathematical fluency now extends beyond population biological fields within ecology and genetics. As an example, a friend who was trained as a biochemist told me that he had to take a course on graph theory as a postdoc to keep up with the demands of his research. But one portion of Lior’s post caught my attention:

Biologists have their papers cited by thousands, and their results have a real impact on society; in many cases diseases are cured as a result of basic research. Mathematicians are lucky if 10 other individuals on the planet have any idea what they are writing about.

But these aren’t comparable! Just because a paper is cited thousands of times doesn’t mean that those citing understand the paper. Case in point, W. D. Hamilton’s papers are often cited, but not understood to any formal depth. With the mathematicization of population genomics and phyologenomics I’ve seen the problems of specialization and incomprehensibility which are common in math and theoretical physics creeping into biology. A few years ago I mentioned offhand to an acquaintance how difficult some of the mathematical and statistical logic in his papers were. He named a half a dozen young researchers who he was confident could vet said papers. When I brought this conversation up with one of those very researchers he admitted to me that some of the work he was asked to “peer review” was so opaque even to his mathematically trained mind that he was at a loss. Obviously I have no solution, but the event horizon of the small puddles of research communities barely able to communicate in the vast sea of scholarship is now upon us in some areas of biology. Our own Tower of Babel is at hand.