An attempt at making a version of Evan Chen's infintely large napkin for theoretical ecology and evolutionary biology.
Evan writes:
I’ll be eating a quick lunch with some friends of mine who are still in high school. They’ll ask me what I’ve been up to the last few weeks, and I’ll tell them that I’ve been learning category theory. They’ll ask me what category theory is about. I tell them it’s about abstracting things by looking at just the structure-preserving morphisms between them, rather than the objects themselves. I’ll try to give them the standard example Gp, but then I’ll realize that they don’t know what a homomorphism is. So then I’ll start trying to explain what a homomorphism is, but then I’ll remember that they haven’t learned what a group is. So then I’ll start trying to explain what a group is, but by the time I finish writing the group axioms on my napkin, they’ve already forgotten why I was talking about groups in the first place. And then it’s 1PM, people need to go places, and I can’t help but think: "Man, if I had forty hours instead of forty minutes, I bet I could actually have explained this all."
With theoretical ecology and evolutionary biology, a very similar problem arises. For instance, one often runs into a situation like the following:
I’ll be eating a quick lunch with some mathematician/physicist/empiricist1 friends from across the campus. They’ll ask me what I’ve been up to the last few weeks, and I’ll tell them that I’ve been thinking about adaptive dynamics in social insects. They’ll ask me what adaptive dynamics is about. I tell them it’s a way of modelling the evolutionary process when ecological interactions and frequency-dependence is important. I’ll try to give them the standard example of evolutionary branching, but then I’ll realize that they don’t really understand the difference between convergence and evolutionary stability. So then I’ll start writing down the replicator equation, but then I’ll remember they're unfamiliar with matrix games. So then I’ll start trying to explain the ideas behind evolutionary game theory, but by the time I finish writing the definitin of an ESS on my napkin, they’ve already forgotten why I was talking about evolutionary games in the first place And then it’s 1PM, people need to go places, and I can’t help but think: "Man, if I had forty hours instead of forty minutes, I bet I could actually have explained this all."
1 Strangely, in the theoretical biology world, neither the pure mathematicians nor the empirical biologists typically have a clue about what we do or why we do it
This is my (currently very preliminary) attempt at writing down the big ideas behind some approaches to ecological/evolutionary theory.
The PDF is compiled using a GitHub action. The compiled PDF can be accessed here and will be auto-compiled (and thus updated) every time I push to the repo. If you are compiling manually, you should be compiling EEB_Napkin.tex using your favourite LaTeX compiler. If you wish to contribute or make suggestions, feel free to submit a pull request or email me!
Topics I would like to add at some point:
- Evolutionary graph theory
- Modern coexistence theory
- Social evolution - inclusive fitness, public goods, etc
- Life-history theory and the next generation theorem
- Evolutionary rescue?
- To add to spatial evolution: Fisher-KPP equations, pushed vs pulled waves, range expansions