Evolution on a Hypercube

Many biological systems evolve through the successive acquisition of discrete traits. A natural representation of such processes is as stochastic dynamics on a hypercube, where the vertices correspond to trait combinations and edges represent evolutionary transitions.

In this talk, I will present hypercube-based progression models that I have worked on during my PhD in biostatistics, including recent work on their algebraic structure through the HyperALG framework. These models raise a variety of mathematical questions concerning identifiability, model equivalence, and the geometry of families of probability distributions arising from evolutionary dynamics, providing a natural meeting point between biological applications, statistical inference, and algebraic methods.