Maths and Biology Students: My take on EO Wilson’s essay

Last week, E. O. Wilson wrote this controversial Wall Street Journal essay that has set the biology blogosphere on fire, a fire that’s mostly headed towards Wilson. I don’t want to be left out of the fun and games, so I want to add my own opinion into the cauldron. Before doing so, I will stress that while I consider Wilson one of my personal idols as one of the last remaining old-skool field naturalists, I am setting aside this bias here.

In a nutshell, the essay’s premise is that to be a great biologist, you don’t necessarily need to be good at maths. My take on the essay is that it’s split right down the middle: half of it is good and I agree with, half of it I consider invalid or at least badly argued.

In Wilson’s general defence, I read it as a semi-autobiographical take on the issue. From this point of view, I will have to disagree with the many commentaries that say he was trying to advise students in a particular direction. No. Wilson merely took his own experiences and extrapolated from them in order to give a pep talk to those students who have trouble with maths.

His experience, as described in the essay, is that you don’t necessarily need to be even an adequate mathematician in order to be a biologist, because in biology, you get new hypotheses and ideas by creative thinking, writing down notes and observations from the field, and putting these all together.

I have a lot of empathy for this. In fact, I encourage my students to do exactly this: write down all your ideas, no matter how crazy. Mull them over, talk them through with colleagues. Come up with hypotheses, and test them. It’s how the scientific method works. To me, the students that impress me the most are the ones that ask odball question, that will come to me after class and share a wacky idea they thought of, or that will run impromptu experiments out in the field because they noticed something weird. It’s also how I work as a biologist: most of my knowledge and research ideas came about as the results of thought experiments I conducted by myself and had fact-checked by professors and colleagues.

But the flipside that Wilson seems to have ignored is that instead of writing your notes in English, you can write them in maths. He considers maths as just a toolkit, when in fact it’s a language. It’s just as creative to write down a mathematical equation as it is to write down an idea in English, and putting together a mathematical model is exactly analogous to combining a series of related ideas into a general theory.

The main difference, as I see it, is your own bias. As primarily a strictly empirical field biologist, I tend to jot down ideas in a strange variant of written English only I can understand (a security measure or lazy writing? You decide). But in some cases, maths was superior: when I was wrapping my head around the concepts of genetic drift, natural selection, or group selection, maths was my thinking language of choice, because it allowed me to focus on the relevant factors and their relative importances, rather than trying to concoct an intuitive story based on wild ideas in my head. I draw my personal line at evolutionary theory and some ecology, but I know people who can break down every part of an organism into equations, and others who can’t even stand the idea of putting together a model of energy transfer from Sun to top predator (something you learn in middle school biology).

Mathematical modelling isn’t for everyone, nor should it be for everyone. This is where I agree with Wilson. But there is a very important caveat: not all biologists should have to build models, but all should be equipped to understand models. This isn’t a contradiction: my genetic and developmental labwork skills are nothing short of pathetic, but that doesn’t prevent me from successfully working on microevolutionary problems that need insights from genetics and developmental biology. Similarly, even if you can’t build a fancy Lotka-Volterra competition model from scratch, that shouldn’t prevent you from reading one in an ecology paper or even downloading the R script and playing around with it.

This is the point I feel Wilson canvassed over. He seems content to leave well enough alone. Can’t understand these differential equations because you don’t know maths? That’s okay, here’s a paragraph explaining what they mean. Such a perspective is fine if you want to popularise the science, but as a working scientist, you must be able to get down and dirty not only with results and conclusions, but with the data-generating methods, which may be mathematical models. Just like you might criticise a phylogenetic paper for not having a large enough taxon sampling, you ought to be able to take a model and criticise it. If you can’t, then you risk intellectual dishonesty that may potentially be grave: if you can’t understand how the results came to be, then you’re in no position to judge the validity of those results, and by extension, you can’t in any honesty use that data for your own research purposes.

I can’t stress this point enough. You must realise that much of the critical basics of evolution and ecology, as two of the most important fields of biology, are based on mathematical models. Fisher, Haldane, Price, Maynard Smith. Household names in evolutionary theory; their foundational work is mostly centered around mathematical models they built. If you can’t understand them and aren’t willing to make the effort to do so, then quite frankly you can just give up on truly understanding evolutionary theory. (Sidenote: I’m torn on whether it’s okay to cite papers you don’t understand completely. Ideally not, but then again we do have a trust among us, reinforced by peer review, that the conclusions are tentatively reliable. But it’s iffy, I personally wouldn’t recommend it.)

All this time, I’ve been talking about mathematical models, because I see absolutely no excuse for any biologist to not be well-versed in statistical methods. You can be forgiven for not knowing the mathematical backgrounds for them (I confess ignorance for most), but considering the myriad books available specifically for biologists, and the ubiquitous need for statistics, they’re a required part of your basic toolset.

Wilson’s solution to not knowing maths is one I mostly agree with: collaborate and cooperate (hooray consilience!). As stressed above, I don’t agree in the case of statistics, but for mathematical models, do go ahead. Wilson has done this many, many times. He comes up with the ideas, goes to a trusted mathematician colleague, and they whip up a combo mathematical model and naturalistic explanation. This was how Wilson revolutionised biogeography and community ecology. His own ideas alone were great, but what really elevated them to biological mainstay status were the accompanying models by MacArthur. The firestorm he started over kin selection is very similar: he’s had these ideas in his head, and used the help of Nowak and Tarnita to develop the mathematical models to back them up. (About that: I think there was a lot of smoke in the negative reaction towards it, as I’m pretty certain kin selection has deficiencies, which was Wilson’s point).

Finally, I need to go back to my roots and stress that I, personally, will take data gathered from observation over mathematical models anytime, because while models offer incredible precision, that precision may well be illusory. Biology is an intrinsically messy discipline that doesn’t take too well to too much reductionism. Even when I have the skill to build a model for a phenomenon, I will always prefer getting empirical, experimental, field data from the real world.

That’s all I wanted to say about this. As a teacher, I’ve often observed the same thing that Wilson did: talented students turning away from biology because suddenly they come across maths. I had the very same problem, and my mathematical abilities are very specifically self-taught (I am completely helpless with any physics maths) and are merely an extension of my intuitive biological daydreams. For the gifted students who think they’ve hit a wall, here are my two tips.

  • Befriend some mathematicians, or take some basics maths courses, or buy a “maths for dummies” book. Maths is basically a very logical language, and you just have to learn how to read it. Don’t be daunted by the apparent complexity of it (I personally find the writing of maths the most tedious aspect).
  • Find mathematical models, break them down, reconstruct them. The letters there all stand for something. Follow the thought pattern through the equation, and you will be able to piece together a paragraph explaining the meaning of every single equation you come across. I did this as a student for all the models I came across, and also tried to reconstruct the classic models of evolutionary theory. This is how I learned maths.

And whatever you do, don’t give up. If all else fails (which I understand, as even after 4 years, I still couldn’t properly calculate how fast a stupid egg will drop from an airplane), you can always collaborate, or get into a field where you need not build any mathematical models.

Basically, where I agree with Wilson is when he says that creative thinking is the most important quality of a scientist. Where I disagree with him is when he says that expressing oneself mathematically is somehow not creative.

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  1. Pingback: On Group Selection | Teaching Biology

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