“Wilson’s Principle No. 2: For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.” EO Wilson
As some might recally, this quote stems from an essay by EO Wilson entitled “Great Scientist ≠ Good at Math “ published half a year ago in the Wall Street Journal, which advocated the thesis that math skills are not essential to be a great scientist. The piece sparked a wide controversy across the blogoshere and beyond (see 1,2,3,4,5,6,7,8, 9, 10, …), with a majority of commenters disagreeing (according to my perception), but also quite a few with supportive views, often along the line that we have too much technical research and not enough intuition / creativeness etc. We could leave it there, as an academic debate, but the related question of how much math we teach in ecology has obviously some very tangible implications, both for the career opportunities of our students and for the future development of our field.
I’m therefore really happy Fred Barraquand has agreed to write a guest post about their recent online survey which demonstrates that, while EO Wilson may be correct that one can always find a discipline that doesn’t require maths, ecology might not be this discipline.
With colleagues from the INNGE-network, we performed a survey showing that early-career ecologists need and want more quantitative training (https://peerj.com/preprints/53/). Following Florian’s invitation, I elaborate on (1) the reasons why we performed the survey in the first place and (2) what was found. I add some personal thoughts on our teaching culture as compared to other disciplines. The latter is arguably a perilous exercise [for which you should not hold my coauthors responsible!], especially without reference to a particular country. I can already imagine an established professor raising his/her eyebrows: “hum, well, not really – at least not in my backyard”.
Let’s start by reassuring the imaginary professor: nobody is suggesting to throw away the traditional knowledge of biologists (e.g. physiology, cell biology, molecular genetics, evolution and taxonomy, some geology). We are also fully aware that it is difficult to design a training for ecologists specifically, because those who start in biology out of love for ecology/evolution might end up doing completely different things, and conversely molecular biologists / physicists / etc. might end up in ecology. One’s priorities and perceptions are always changing*, study choices will never be perfectly adequate for any future job. And studies are also there to broaden one’s mind – not only as a means to an end.
ecology’s teaching could be much improved when it comes to math / stats / programming.
That said, the general impression of many early-career researchers (those who battle most as first authors) is that ecology’s teaching could be much improved when it comes to math / stats / programming. Probably this is applicable to evolutionary biology as well, which in many subfields identifies with ecology. But we have not surveyed that community specifically so that is harder to say.
Most students of ecology choose that path out of a fascination for animals, plants, or life more generally. Passionate students are a good thing, but passion often leads to a romantic picture of Darwin-days exploration. One conjures images of a naturalist examining trees in the Amazonian forest, or a fish biologist on the deck of a boat, waiting to see what is in the trawler. Such moments are part of ecology for sure, yet the picture is incomplete. Add graphs of probability distributions for species abundances, computer code, scatterplots and the likes, and we would have a more faithful representation of the day-to-day life of an ecologist (and I am speaking of those who still do lots of fieldwork). The role of a good counsellor/mentor is then to replace the romantic picture of both research and applied jobs by a more down-to-earth representation, without destroying dreams altogether (a tricky task!). Because students have often no clue what they’ll do later, it is essential that study programs contain elements that the scientific community as a whole deems useful – including applied branches (which might require quantitative skills for other reasons, e.g. economics).
Essentially, there has to be some connection between what you learn and what you do >50% of your time. Many (most?) ecologists spend more time behind a computer screen than in the field – including those working predominantly on field data. Even if you spend 25% of your time covered in mud collecting samples of insects in a swamp, if you spend the remaining 75% behind a computer screen, including 40% or so working on the data you collected, you might expect that your studies will prepare you to some extent to do computer work and statistical analyses. The trouble is, they mostly don’t.
There I see the imaginary professor frowning: “Do you really think that in physics 101 they teach what physicists currently use?”. Sure, physics 101 is different from today’s physics too (well, thermodynamics/optics/electronics 101 etc.). But nobody in physics 101 tries on purpose to hide equations to avoid scaring off students as many experience in ecology 101. Ecology-related degrees then “sell” their outdoor component with charismatic fauna and flora, and mention sparingly the increasingly important statistical aspects. Biology as a whole is depicted as a mostly experimental science to be performed in the lab, remote from mathematics, and ecology is represented as the perfect getaway for those who like the outdoors (just check out webpages from ecology/environmental sciences departments, you almost never see equations – a notable counterexample being NCEAS, but that’s not a university).
“Most undergraduate students […] are simply not aware that conserving animals, reconstructing phylogenies, studying behaviour, or explaining why there are so many species on Earth involves an awful lot of statistics and programming. “
For many fellow ecologists worldwide, the first encounter with serious statistics, often at master level when reading scientific papers, is then a brutal wake-up call. Most MSc students invariably struggle with the analysis of their data. Very many times I have now heard variations of the same sentence, in several countries**: “I wish somebody had told me there would be so much statistics – I could have prepared better”. When statistics courses are available, prerequisites are often not enforced which leads to highly heterogeneous classrooms – which are both difficult to teach and inefficient for students. The imaginary professor might answer (as I’ve heard a few times): “well, that’s only partly our fault – students should take responsibility too”. Well, that’s only partly right.
Most undergraduate students choosing first biology and then ecology/environmental sciences are simply not aware that conserving animals, reconstructing phylogenies, studying behaviour, or explaining why there are so many species on Earth involves an awful lot of statistics and programming. That is hidden in scientific publications (physics textbooks offer in contrast an equation density comparable to publications). As some of our survey respondents, I feel very lucky: my biology study program included a fair deal of math and physics classes***. Some classmates who took a MSc in ecology and evolution decided to go for theory and stats like myself, others went for more experimental or empirical work, or the private sector. In any case, quantitative classes gave us the opportunity to choose our field without feeling limited or frightened by equations. Oddly enough, that’s a privilege.
Why isn’t quantitative teaching more generalised, even by small amounts? Lecturers complain that they have to explain again what are logarithms or derivatives, “for loops”, or that only a few students know how to multiply a matrix. With some students that did not receive any math course after an freshman’s introduction in the first year of university. So why the inaction? [there, the infuriated imaginary professor might want to shout that he’s been teaching statistics for biologists for 15 years and that they all learn matrix algebra and how to program – if he’s doing it, that is awesome, but definitely not the majority rule according to our survey].
… a majority is dissatisfied with both their quantitative knowledge and training. 90% want to include more mathematics courses and 95% more statistics courses overall
The initial motivation for setting up a short online survey – and why my early-career colleagues decided to jump in so eagerly – was the thought that perhaps the numbers are just missing. We know that some people are unhappy with the teaching of quantitative disciplines from corridor chats, but we do not know how many. We therefore tried to provide a more precise measure of the level of (dis)satisfaction with quantitative training. We expected respondents to be discontent, but nowhere near the measured level. The results are clear: c. 75% of early-career ecologists think they received ecological courses with too few math in it. We separated respondents by categories according to their tendency to model and math-friendly nature, and even accounting for those differences a majority is dissatisfied with both their quantitative knowledge and training. 90% want to include more mathematics courses and 95% more statistics courses overall. As surprising as this sounds, this does not depend on whether they are modellers or if they like fiddling with equations (I would bet it has a lot to do with how quantitative the subdiscipline is). There seems to be a lot of demand for good programming courses too (as those).
According to our respondents, approximately a fourth to a third of the curriculum should be constituted by quantitative courses (on average, of course, the needs vary from one subdiscipline to the next). I can think of very little universities or research institutes that do provide such training. One of the important insight of the study, something we did not really think through before, was that ecologists want more maths within ecology-related classes themselves. Given that calculus is needed before statistical courses (as highlighted by Ellison and Dennis), these mathematics driven by biology need to enter the curriculum early on. Ecology-driven calculus might be too specialized at that stage, but biology-driven calculus sounds feasible (e.g. http://www-eve.ucdavis.edu/sschreiber/reprints/MAA.pdf). Later, one could present a better integration of the mathematics and data analysis with ecological theories, which is pretty much the way physics is taught. This goes well with the recent trend for an increased fusion between statistical and theoretical ecology in the scientific literature, but obviously ecology programs should keep up****.
I hope that heads of departments might read the preprint and perhaps this post [and that the imaginary professor will still hire me afterwards!]. Of course, having more or better quantitative training will not solve all of ecology’s problems. And solutions will likely differ between countries. But recognizing the extent of the “quantitative mismatch” would go a long way to help early-career researchers. Young ecologists are very often sitting in the crazy situation where they are pressured by professors or reviewers to use complicated statistical/computational techniques, without the training to do so nor the time to learn at a reasonable pace.
* one of my motivation to do research was the putative absence of paperwork; as everyone knows this view is utterly flawed, but when I realised it I was already hooked… We all have our romantic pictures!
** only 3 countries so far, but our international team of coauthors + survey respondents had similar experiences, thus the same sound is coming from dozens of countries and several continents.
*** half the curriculum were “quantitative disciplines” but that’s country-specific (weird all-or-nothing French habits due to use of math as a selection tool). A percentage of one-fourth to one-third as in the survey would indeed be more reasonable, rather than zero in some biology programs and half in others.
**** evidence-free opinion pieces in the Wall Street Journal notwithstanding.