Complexity and accessibility of random landscapes
arXiv:2502.05896 · doi:10.21468/SciPostPhysLectNotes.108
Abstract
These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer science are mentioned where appropriate. Elementary and advanced results on the structure of landscapes are described with a focus on features that are relevant to evolutionary searches, such as the number of local maxima and the existence of fitness-monotonic paths. The recent discovery of submodularity as a biologically meaningful property of fitness landscapes and its consequences for their accessibility is discussed in detail.
Lecture notes for the Les Houches summer school "Theory of Large Deviations and Applications"; 22 pages, 7 figures. The discussion of basins of attraction has been expanded and additional references have been added
References in corpus (16)
- Quantitative analyses of empirical fitness landscapes
- Evolutionary accessibility of mutational pathways
- The context-dependence of mutations: a linkage of formalisms
- From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics
- Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model
- Complex-network analysis of combinatorial spaces: The NK landscape case
- Exact Results for Amplitude Spectra of Fitness Landscapes
- Universality classes of interaction structures for NK fitness landscapes
- Genotypic complexity of Fisher's geometric model
- On the existence of accessible paths in various models of fitness landscapes
- Evolutionary accessibility in tunably rugged fitness landscapes
- Quenched complexity of equilibria for asymmetric Generalized Lotka-Volterra equations
- Geometry of fitness landscapes: Peaks, shapes and universal positive epistasis
- Accessibility Percolation on Cartesian Power Graphs
- Evolutionary accessibility of random and structured fitness landscapes
- Distribution of the number of fitness maxima in Fisher's Geometric Model