The Jukes-Cantor Model and Phylogenetic Invariants

In this presentation, I explored the Jukes-Cantor model (JC69), a foundational model in molecular evolution that assumes equal mutation rates among all four nucleotides. Under the supervision of Prof. Matthew Macauley at Clemson University, I examine how phylogenetic invariants, polynomial relationships in DNA sequence data, can be used to assess evolutionary models. My aim is to show how these algebraic tools help reconstruct evolutionary trees and reveal the mathematical structures underlying biological processes.