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k8458 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.

• Category: Science • Tags: Math 
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E. O. Wilson has a op-ed in WSJ which I find quite interesting, Great Scientist ≠ Good at Math:

For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate.

This imbalance is especially the case in biology, where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. Possibly no more than 10% have any lasting value. Only those linked solidly to knowledge of real living systems have much chance of being used.

Wilson has been on this for a bit now, to the bewilderment of some of the scientists I follow on Twitter (granted, the people I follow tend to be quantitative genomics types whose backgrounds may have been in math, physics, or statistics). Two immediate things come to mind reading this. First, a disproportionate number of the famous and successful scientists alive today are old, like E. O. Wilson. Just because you could get by with a certain level of mathematical fluency as an enfant terrible in the 1970s does not mean that that will cut it in the 2010s. Great scientists who are mathematically weak often have collaborators, post-docs, and graduate students, who do their bidding. It might be a different matter if you aren’t one of the Great Ones of the earth. From what I can tell scientists who are doing the hiring who don’t have mathematical skills prefer candidates who do have mathematical skills.

Second, a 10% success rate for formal mathematical models seems quite high to me! The vast majority of conjectures in science turn out to be garbage. If Wilson stands by the 10% figure, then that’s an argument for attaching greater value to mathematical abilities. But I suspect there is a real issue with theoretical models which haven’t been tested, or are there to simply bolster someone’s publication list (see: Journal of Theoretical Biology). In Robert Trivers’ Natural Selection and Social Theory he recounts that he was told by someone that his thinking was like that of an economist. Curiously in the same volume W. D. Hamilton advised the young Trivers to not attempt to “math up” his original ideas on reciprocal altruism so much (Trivers ignored this advice, though in hindsight he grants its wisdom). I relate this because contemporary economics does seem to have a problem where extremely powerful quantitative methods have become somewhat decoupled from the empirical questions at hand. But I don’t see that these issues are so much a problem in biology. Rather than too little formal precision, much of evolutionary biology could benefit from greater crispness.

At this point I have to offer that I’ve never talked to a geneticist (the people I know, who tend to be evolutionarily oriented) who has complained they took too much math. Rather, the opposite. Apparently when Theodosius Dobzhansky read papers by individuals such as Sewall Wright he would “hum” through the formal sections. Since Wilson admits up front that his math skills are not strong I feel comfortable in relaying what I’ve heard from several people associated with Harvard’s biology department: the controversial Nowak et. al. paper which Wilson put his name to was problematic in part because Wilson likely does not grasp the formal details of the argument that he is supporting. More concretely, E. O. Wilson has long had particular intuitions about the nature of social behavior, and he has sought out formalists who could provide him with a mathematical supporting argument. This is often how science is done, but it doesn’t seem like an optimal situation. Also, I would add that though Wilson puts the emphasis on math, perhaps just as important today is the ability to write and implement some code. Though math and programming are often connected, the rough and ready scripting which is the bread and butter of many biologists today isn’t really mathematical at all.

Of course all of this is conditional on the domain of biology one is interested in. A theoretical ecologist is going to need a lot more math than a field ecologist. Many molecular biomedical geneticists don’t have to worry about much more than standard statistical tests. And so on. But E. O. Wilson is an evolutionary biologist. Charles Darwin had great insights, and he was not a mathematical scientist. But it is striking that a disproportionate number of Darwin’s 20th century heirs had strong mathematical orientations. Fluency in math is not a necessary or sufficient condition for being a great evolutionary scientist. But it certainly increases the probability that you’ll have great insights which might forward the field.

Addednum: W. D. Hamilton was to a great extent self-taught as a population geneticist. In Nature’s Oracle Ullica Segerstrale relates that classically trained theoreticians were initially very skeptical of Hamilton’s models because they seemed rather slapdash and ad hoc. The reason Segerstrale explains is that Hamilton operated like an engineer, synthesizing his deep biological intuitions with a series of models, fine tuning the framework so that the theoretical superstructure was appropriately scaffolded upon the biological problem. This seems like an invitation to produce models which are not robust, but Nowak et. al. notwithstanding Hamilton’s achievements have stood the test of time.

• Category: Science • Tags: E. O. Wilson, Evolution, Evolutionary Genetics, Math 
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