Random walks on multidimensional landscapes are important to many areas of science and engineering. In particular, properties of adaptive first-passage trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary biology. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean times, and other statistics of the first-passage 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 folding stability while evolving new functions.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)