MC 2035
Speaker
Matteo Smerlak | Perimeter Institute for Theoretical Physics
Title
Evolution of fitness distributions in large populations: scaling, universality and crossovers
Abstract
Selective adaptation operates on heterogeneous populations under the principle of the "survival of the fittest". Such evolutionary dynamics can be modeled as a flow in the space of fitness distributions. I will describe limit theorems which capture the dynamics of fitness distributions under this flow. These theorems identify three dynamical regimes of evolution, corresponding to directional selection, purifying selection, and innovation through mutations. Each regime is characterized by scaling laws for the evolution of the mean and variance of fitness and simple families of attracting limiting distributions for the fitness fluctuations. These results situate the famous "traveling fitness waves" within a more general catalogue of universal patterns of evolution, and predicts crossovers between these patterns. Moreover, they may provide model-independent explanations for emergent patterns recently observed in evolving microbial populations.