Statistical Physics of Evolutionary Trajectories on Fitness Landscapes

TL;DR

This paper reviews recent advances in applying statistical physics methods to analyze evolutionary trajectories on complex fitness landscapes, emphasizing path statistics, diversity, and repeatability in protein evolution.

Contribution

It introduces a systematic approach based on statistical physics to characterize evolutionary paths on arbitrary fitness landscapes, including applications to protein evolution models.

Findings

Methodology quantifies path lengths and first-passage times.

Applicable to landscapes of arbitrary complexity.

Demonstrated on a protein evolution model.

Abstract

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary theory. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current research knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean first-passage times, and other statistics of the path ensemble. This approach, based on general techniques from statistical physics, is applicable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolutionary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions.