How do I learn the math of cultural evolution?

Advice to students

Hi Lab,

Every so often, I get emails asking how to learn the math behind cultural evolution. Here’s one I received this week, for example:

For anyone with a similar curiosity—or who knows someone interested—here’s the roadmap I recommend.

Cultural Evolution 101

Start with Culture and the Evolutionary Process by Boyd and Richerson. This classic is the foundation of cultural evolution, and its analytical models are an excellent entry point. If you’ve taken high school calculus, you’ve got the tools to begin. Math is best learned by doing: tackle a model, and when you get stuck (and don’t despair if you do), backtrack to figure out what step you’re missing. WolframAlpha, Mathematica, SymPy, and even AI assistants like ChatGPT and Claude are your friends!

For simulation-based approaches, Paul Smaldino’s new textbook, Modeling Social Behavior: Mathematical and Agent-Based Models of Social Dynamics and Cultural Evolution, is an accessible introduction.

Once you’ve gained some footing, find a published paper with a model that aligns with your interests, replicate its steps, and then tweak it—introduce a new variable, modify an assumption, or extend its logic. See how those changes alter the predictions. You might be able to publish what you find. You could also play with this tool I use in my class: https://pb101-models.herokuapp.com

Some other useful resources are Otto and Day’s A Biologist's Guide to Mathematical Modeling in Ecology and Evolution and Hanna Kokko’s Modelling for Field Biologists and Other Interesting People. Both will give you a sense for the kinds of models that are common in the evolutionary sciences and are useful for looking things up when you get stuck.

Why Build Models?

Personally, I think all psychologists, behavioral scientists, and cultural evolutionary researchers should at least learn to read the models so that they can inform your empirical work or you can modify similar enough models for your own purposes. Ideally, we move toward general models, by building on the foundational work rather than writing down things with no link or basis to past work.

If you can’t solve something analytically, try solving it numerically, or running a simulation. You may not even end up publishing or using the model, but I promise that it will sharpen your thinking by revealing the hidden assumptions and gaps in logic that our minds hide from us as we think through a problem. It’s hard to hold more than a few interacting variables in your head, so a computer or system of equations can help you overcome those limitations. A quote from a paper I wrote with my other advisor, Mark Schaller:

Remember that the choice isn’t between modeling vs not modeling—it’s between a formal mathematical model with explicit assumptions and logic vs a fuzzy mental model with hidden assumptions and unknown leaps of logic hard to fully specify in words. Or as the OG’s Rob Boyd and Pete Richerson put it:

All scientists have mental models of the world. The part of the model that deals with their disciplinary specialty is more detailed than the parts that represent related areas of science. Many aspects of a scientist’s mental model are likely to be vague and never expressed. The real choice is between an intuitive, perhaps covert, general theory and an explicit, often mathematical one.

If other scholars have recommendations I should pass onto students, please send them my way. And please share this with young scholars who might be interested.

Best wishes,

Michael