Speaker: Wei-Kuo Chen (University of Minnesota)
Title: On the fitness landscape of the NK model
Abstract: The NK model, introduced by Kauffman, Levin, and Weinberger, is a random field used to describe the fitness landscape of certain species with N genetic loci, each interacting with K others. It is expected to capture rugged landscapes in some evolutionary systems and has been instrumental in studying evolutionary dynamics through adaptive walks. Earlier literature has been focused on the case K being a fixed positive integer and used tools from Ergodic and Markov theory. In this talk, I will present some new results concerning the fitness landscape in the NK model under the regime that K/N is approximately $\alpha\in (0,1]$. These include the explicit formulas for the free energy and maximum fitness, overlap gap properties, and multiple peak structure of the level set near the maximum fitness, and the existence of evolutionary paths of nearly maximum fitness. Along the way, I will discuss the implications of our results in relation to evolution dynamics and explain how spin glass theory is of great use in our study. Based on a joint work with S. Tang.