Recently, two Oxford Mathematics postdoctoral research associates Johannes Borgqvist and Sam Palmer published an article entitled “Occam's razor gets a new edge: the use of symmetries in model selection” in the Journal of the Royal Society Interface. Both of the authors belong to the Wolfson Centre for Mathematical Biology (WCMB), an Oxford Mathematics research group, and in the article they demonstrate that so called symmetry transformations can be used as a basis for model selection in the context of mechanistic modelling, specifically applying these ideas to modelling the increase in cancer risk with age.
This work is exciting as it shows that the standard way of selecting models in mathematical biology, which is to select the model that best fits the experimental data, sometimes fails and that symmetries can in fact detect the true model describing the underlying mechanism. Also, the mathematical method involving symmetry transformations in the article is commonplace in mathematical physics and differential geometry, but it is non-standard in mathematical biology, and thus the work introduces some relatively new mathematical techniques into the field of mathematical biology.
Moreover, this work is quite special for both authors as it is the first article that both of them have published by themselves as two young, inexperienced researchers without any supervisors. And there is an interesting and instructive story behind the article which demonstrates the importance of taking risks as a researcher and collaborating with people far and wide.
Back in 2018, Johannes was in the middle of his PhD in the Department of Mathematical Sciences at the University of Gothenburg in Sweden. During this time, he was very keen to learn more mathematical techniques that could be added to the standard toolbox of mathematical biology in order to address some of the most fundamental questions in the field.
These questions were: how do we validate a mechanistic model and which model do we select if numerous candidate models fit the same experimental data equally well? During his search for answers, he stumbled upon the book “Symmetry Methods for Differential Equations: A Beginner’s Guide” by Peter E. Hydon. He began reading and calculating the tasks in the book, and was pretty quickly obsessed with the topic as he realised that this set of mathematical tools may very well play a huge role in mathematical biology.
At the same time, Associate Professor Fredrik Ohlsson at the University of Umeå moved into the same corridor as Johannes in Gothenburg, and as Fredrik had a background in using symmetry methods in theoretical physics, he thought it a very exciting prospect to introduce symmetries into mathematical biology. So out of a period of eager discussions and hard work, emerged an article in which a symmetry based methodology for model selection using simulated data was produced.
Roughly around the same time, Professor Ruth Baker at the WCMB in Oxford visited the University of Gothenburg, where she gave two presentations about her research and her research group. During a break in one of her presentations, Johannes asked Ruth if she had any postdoctoral positions in her group. From that point on, they kept in touch via e-mail, and in 2019 Johannes received two travel grants which financed two trips to Oxford. After these visits, Johannes thought it would be a dream to work as a postdoc in Ruth’s group and so they decided to apply for a scholarship financing a postdoctoral position from the Wenner-Gren Foundations in Sweden.
So as well as working on his PhD, Johannes spent a lot of time - with the guidance of Ruth as well as his previous supervisor, Professor Marija Cvijovic at the University of Gothenburg - writing his first research proposal for the Wenner-Gren scholarship about introducing symmetry methods into Mathematical Biology.
To cut a long story short, Johannes was awarded the scholarship and in December 2020 started his postdoctoral position in Oxford. During this time, he presented his previous work on how symmetries can be used in a model selection scenario based on simulated data, and after one of these presentations he was contacted by Sam Palmer who was in the audience.
Sam said that he had encountered the exact same situation that Johannes described, namely that he had two distinct mechanistic models that both described the same experimental data equally well, but in his case he had actual experimental data for the increase in cancer risk for different cancer types as function of age. So together they asked whether the symmetry based methodology for model selection could be used in order to find the correct mechanistic model of actual experimental data in the context of the increase in risk of developing cancer due to ageing. Their recent article is the result of this collaboration.
In summary all this work shows how important it is to take risks by trying out new, non-standard ideas and techniques as well as collaborating with new colleagues. And, of course, pursuing your dream.
As a homage to their research, the authors composed a song. Welcome to the Symmetry Blues.