Stochastic Dynamics in Simple Models of Evolution

Michael Desai

A variety of very simple problems in evolution display surprisingly rich behavior. This is often because the stochastic dynamics that underly these processes have unexpected subtleties. The basic issue is that beneficial mutants occur rarely but proliferate exponentially when they do. This exponential proliferation means that much of the intuition that we're used to in seemingly similar physical problems doesn't work. It also means that there are many simple and fundamentally important questions very close to the surface which are not understood.

In these lectures, I'll talk about how we can build some intuition for the stochastic dynamics of some absurdly simple models. I'll try to do this within the context of a very rough outline of the "canon" of theoretical population genetics. I'll start with a fresh perspective on some things that have been understood exactly since the 1930s. I'll try to then point the way towards some gaps in our understanding and some more open problems -- these are often only slightly less absurdly simple.

For general background, here are some notes that lay out the general framework of "canonical" population genetics:

Notes