Probability Seminar

Title:  On the Fitness Landscape in 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. The model has wide applications in understanding evolutionary and natural selection as it captures the ruggedness feature of the fitness landscape. Earlier literature has been mostly focused on the case $K$ being a fixed positive integer and using tools from Ergodic and Markov theory. In this talk, I will present some new results on the fitness landscape of the NK model in the regime when $K/N\to\alpha \in(0,1]$, using spin glass methodologies. These include the explicit formulas for the free energy and maximum fitness, overlap gap properties, and multiple peak structure of the level sets, and their implications on the existence of near-fittest evolutionary paths. Based on a joint work (arXiv:2508.12464) with Wei-Kuo Chen (University of Minnesota).