A Study of Avian Magnetonavigation

For my applied mathematics seminar class, we were given the opportunity to explore an interesting phenomenon of our choice. An intelligent student would’ve adopted one of their two ongoing research projects for their class. Unfortunately, I was encouraged by John Bush to take a more adventerous route, suggesting animal magnetoreception. John is a fan of whales, but I’m a bigger fan of birds, and I did a project on the mechanics of avian magnetonavigation, a word that I made up.

Cool schematic of magnetoreceptive mechanisms in birds. We actually still aren’t too sure how magnetoreception works exactly, but it’s pretty likely quantum mechanics is involved, because of course it is.

Birds are actually really cool, and the mechanism of how they navigate from point A to point B is fascinating. Basically, they use the Earth’s magnetic field in a process that is somewhat still poorly understood, and using this field, they orient themselves during migration. In this project, I developed a minimal-ish model to represent this migration and tested it against actual flight trajectories of European Turtle Doves. The model is, as far as I know, novel, but I think the underpinning physical assumptions are somewhat iffy. There is, for sure, something of interest here that I may develop more in the future.

When the sensing noise increases, trajectories become less able to reach their goal.

There is also an interesting idea of a less biologically motivated problem. From a mathematical perspective, I wonder how an agent can get from point A to point B, given a known field signature at these points and knowledge of a field at its location. The crux being the agent has no knowledge of the field gradient but can use previous measurements along its trajectory. Surely there is some action minimization to optimise paths, but not knowing the local gradient is tricky. Also, things become complicated in the presence of noise. My treatment of noise in my work is somewhat naive; I think there is a more sophisticated model to be constructed for problems of this class.

The project ended up being closer to a thesis than to a class project, as I sort of started doing math, and kept on doing math for about three months straight. The full paper is here ; you know it’s good stuff when the appendices go from \(A\) to \(I\). My very long slidedeck presentation is here for anyone interested in this work.