Evolutionary accessibility of random and structured fitness landscapes

Abstract

Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length $L$ becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotype, which can be explicitly computed for large classes of genotype graphs. The behaviour in uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.

arXiv commentAccepted contribution to the STATPHYS 28 issue of JSTAT; 30 pages, 10 figures

References in corpus (17)

• 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
• Probabilistic Analysis of the Number Partitioning Problem
• 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 of modular fitness landscapes
• The number of accessible paths in the hypercube
• Evolutionary accessibility in tunably rugged fitness landscapes
• Accessibility percolation on n-trees
• Spin glass theory and its new challenge: structured disorder
• Accessibility Percolation on Cartesian Power Graphs
• Geometry of fitness landscapes: Peaks, shapes and universal positive epistasis
• Distribution of the number of fitness maxima in Fisher's Geometric Model

Cited by in corpus (1)

• Complexity and accessibility of random landscapes