2013/05/06 by Michael Manhart, Alexandre V. Morozov
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #Biology #Computer science #Ecology #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Evolutionary dynamics #Fitness landscape #Machine learning #Path (computing) #Physics #Plant and animal studies #Population #Stability (learning theory) #Statistical physics #cond-mat.stat-mech #q-bio.PE
paper · pdf · doi:10.1142/9789814590297_0017
arxiv created 2013/05/06 · openalex publication_date 2014/03/20 · arxiv updated 2014/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 evolu-tionary 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 appli-cable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolution-ary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions. 1