Simple, in theory: an empiricist’s endeavor to becoming more theoretical

Guest post by Rachel Germain, describing how her empirical lab dipped more strongly into theoretical ecology and a working group paper that followed:

Grainger, T.*, M. Barbour, K. Coblentz, J. DeLong, N. Goel, N. Jones, P-J. Ke, J. Levine, M. O’Connor, S. Otto, J. Sakarchi, A. Senthilnathan, M. Szojka, R. Germain*. An empiricist's guide to using ecological theory. In press, the American Naturalist. *corresponding authors

Have you read The Theory of Island Biogeography? Like, actually read it? If you asked me in 2013 when I (as a grad student) first cited it in a paper, I’ll admit that my answer would have been ‘no’ (it is now ‘yes’ fyi)—I’d read review papers of IBT, seen textbook summaries, and read key pages associated with certain chapters, but never actually sat down with the book; I figured I knew it sufficiently well enough. Now that I have, I realize how much I was missing out: there’s so much more to IBT than the basic graphs we’re all familiar with (a whole book’s worth, in fact).

To generalize my question, how often do many of us dig into core theory papers (classic or not) that our hypotheses are based upon? To go a step farther, how often do we endeavor to not only read and remember, but also to understand beyond a surface level? To really dig in? I suspect the answer is ‘not always or enough’.

Why? For me, for the most part*, it was the math. This is not a trivial issue—I’d “read” Chesson (2000) at least 6 times and usually give up by the 3rd page after hours of struggling. Side note: I once asked Chesson a question about his 2018 paper (specifically, about ‘scaling factors’, the world’s most mysterious concept) during his visit to UBC, who suggested that maybe I could read the paper more closely—I then pulled up the most marked up PDF you’ll ever see (Fig. 1); we all had a good chuckle. This has always been frustrating because I could see the extreme value of really knowing any theory—to go beyond the well-known big picture take-home messages (i.e., smaller or farther islands have less species) and develop an intuition that can be applied to solve new problems; to understand exceptions, nuances (e.g., “why are the lines curved as they are in IBT models?”), and to re-evaluate things we thought we knew well, by understanding the underlying mechanics.

Annotated paper
Fig. 1. Marked up page from Chesson 2018 with loads of questions (figure is deliberately unreadably small 🙂 )

In 2019 I sought to change this. I had just started a new lab at the University of British Columbia. Rather than embarking on this journey myself, I was lucky enough that my first two graduate students, Megan Szojka and Jawad Sakarchi, were keen to join me for “MacArthur Monday” (Figs. 2 and 3)—I was pleased that our meetings grew as new people joined the lab despite this meeting being optional. Our goal was simple in theory, difficult in practice: don’t skip the math! Work through an equation—figure out why it’s structured the way it is, why certain symbols or syntax are used, look up unfamiliar functions (e.g., Lyapunov functions?!) and why they are used. Try and solve equations or see how different equations are connected. We intermixed our readings of papers with readings of instructional texts (e.g., An Illustrated Guide to Theoretical Ecology by Ted Case). We occasionally hosted authors to discuss their papers with us. Funnily enough at one point we realized we hadn’t read an empirical paper in months and made an effort to add a few to our rotation.

Student on whiteboard
Fig. 2. Megan (then MSc student, now PhD student in Shoemaker lab) tearing up some theory on our smart board (Instagram: @germain_lab)

At the beginning, these meetings felt a bit like feeling around in the dark. I remember one meeting where someone pointed out that one of the terms wasn’t defined—”fancy d” (i.e., ). A student in the lab, Kelley Slimon (then an undergrad, now a PhD student in the Agrawal lab at Cornell), pointed out that this symbol represented a partial derivative and walked us through why it was used. Some papers took 5 hours to read and two meetings to discuss. Engaging in theory as a lab in this way is one of the best time investments I’ve ever made, both for myself and for my lab. I felt like we started to see things with much more clarity, our discussions became easier over time, and we began to be able to work through these papers much, much faster. At this point I feel quite comfortable with theory: in fact, 7 of the last 9 manuscripts I reviewed were entirely theoretical. I do want to point out that one’s research doesn’t need to be strongly informed by great depths of theory in order to be good, but for me, it certainly helped lead me in new directions.


Seminar Schedule
Fig. 3. Screen snip of our “Macarthur Monday” schedule (now “Volterra Vernerdi” due to move to Friday)

This experience, though invaluable, was challenging. It led me to ask: what could have helped ease this process? What advice could we give others? In 2019 I was at the ESA meeting in Louisville, KY, with my two science besties, Tess Grainger and Natalie Jones. We were on our way to lunch when we ran into Matt Barbour (who we knew) and his crew (who we met for the first time), who suggested we hit up this great sandwich place. Over the best sandwich I’ve ever had, we started chatting about what had been going down in my lab—how we, an empirical lab, had been investing huge time and effort into working through difficult theory papers, what we had learned along the way, what the challenges were, and what the benefits have been for us. While myself, Tess, and Natalie identify as more empirically-oriented, many in Matt’s group were strongly theoretical, and we all shared thoughts on the philosophy of theory and challenges to communication observed from all sides. It was then that the idea struck us: let’s assemble a group of empiricists and theoreticians to work together, to write an article to help ease this process for others. We scribbled ideas on a napkin and ended lunch with a “working group” photo (Fig. 4; the group grew post-ESA as we assembled a team to cover all bases).

Group members
Fig. 4. Primordial “working group” photo snapped at the ESA immediately following sandwiches, after having known each other for about an hour

Unfortunately Covid hit, so we never ended up being able to meet in person, but Tess organized and led a virtual meeting (Fig. 5). At this meeting, we imposed a “no judgement” policy, as our paper would only be successful if we could fully expose and get to the root of our misunderstandings. Together we decided that the paper would be structured to serve as a one-stop-shop guide, providing answers to all the burning questions someone might have when approaching theory for the first time, for example, about the more technical mathematical aspects of theory (“a toolbox for understanding equations” section - led by me) or philosophical questions about what theory is and how empiricists could use it (the first part of the paper - led by Tess). Those burning questions include: how and why is any theory created? Is theory always “right”? What’s the difference between testing and using theory? Is all theory meant to be empirically useful? How might my experiment go awry if not theoretically grounded? What terminology do I use to discuss equations? How can I better understand what an equation is describing? What symbols or functions commonly appear in theory papers, and what do they (in tangible terms) mean? How do I interpret different kinds of graphs? What other books are out there to learn more? As you can imagine, a group of 14 researchers with vastly different research programs and who range from strongly empirical to strongly theoretical had some differing opinions on the answers to these questions, which led to some great discussions and hopefully an interesting and balanced paper! A particularly fun moment for me was trying to represent the application of Hessian matrices to stability analysis in cartoon form after hours of reading and still not getting it 100% right (it was ~80% right…; Fig. 6).

Videoconferencing session
Fig. 5. Actual shot of the working group
Sally Otto
Fig. 6. Sally Otto clarifying how eigenvalues/vectors can be best represented graphically (the classic png of a stretched Mona Lisa never quite did it for me)

We were a bit uncertain of how the paper would be received by any journal (or cited by readers, for that matter, and in what context)—however, we were thrilled that AmNat, who does not normally publish “how-to” papers, saw themselves as a journal that strives to unite theoretical and empirical research, and that they would support our unconventional paper for its potential benefits to the community (thanks AmNat!). This is our hope too—that our paper will encourage those who might be theory-curious to take that first step and see how things feel, and that it may serve as a resource for, for example, new graduate students. For the theoretical ecologists reading this, the paper might also provide insight into the aspects of theory that many empiricists find most mysterious, which could be helpful for teaching or writing theory. That being said, I'll refrain from any sort of concluding sentence and instead direct you to the last paragraph of the paper itself—check it out! Out now in the American Naturalist: ­­­”An empiricist’s guide to using ecological theory” by Grainger et al.


*well, okay, IBT isn’t that mathy so in that specific case the barrier was 1. the time needed to read an entire book and 2. an (incorrect) feeling that little new could be learnt from the classics, but usually the issue was the math...


Thank you to Tess Grainger and Axel Rossberg for comments, IITE for inviting this post, and my lab for enthusiastically embarking on this journey.

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