Complexity and accessibility of random landscapes

TL;DR

This paper explores the structure and properties of probabilistic high-dimensional landscape models, focusing on features like local maxima and fitness paths, with implications for evolutionary biology and related fields.

Contribution

It introduces and analyzes probabilistic landscape models, highlighting the role of submodularity in landscape accessibility and evolutionary search processes.

Findings

Number of local maxima in landscapes

Existence of fitness-monotonic paths

Impact of submodularity on landscape accessibility

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.