Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

  title={Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics},
  author={Atish Agarwala and Daniel S. Fisher},
The dynamics of evolution is intimately shaped by epistasis — interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past… 

Epistasis and Adaptation on Fitness Landscapes

  • C. Bank
  • Biology
    Annual Review of Ecology, Evolution, and Systematics
  • 2022
Fitness landscape theory and experiments are reviewed and their implications for the role of epistasis in adaptation are discussed and theoretical expectations in the light of empirical fitness landscapes are discussed.

Population genetics of polymorphism and divergence in rapidly evolving populations

This work shows how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one, which enables the dynamics of populations subject to a wide range of fitness effects to be described.

A model for the interplay between plastic tradeoffs and evolution in changing environments

A minimally structured effective model is presented that can help establish a null model intuition for how tradeoff evolution can be expected to depend on key parameters and serve as a baseline for comparison with experimental data.

Fitness seascapes facilitate the prediction of therapy resistance under time-varying selection

First, it is shown how modeling genotype-specific dose response curves is necessary to accurately predict evolutionary outcomes in changing environments, and an empirical fitness seascape measured in engineered E. coli is integrated into an evolutionary model with realistic pharmacological considerations.

On the sparsity of fitness functions and implications for learning

A framework to study the sparsity of fitness functions sampled from a generalization of the NK model, a widely used random field model of Fitness functions, and demonstrates that GNK models with parameters set according to structural considerations can be used to accurately approximate the number of samples required to recover two empirical protein fitness functions and an RNA fitness function.

Global Genetic Networks and the Genotype-to-Phenotype Relationship

Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories

The oriented fractal scaling component analysis (OFSCA) is developed and it is demonstrated that the numerically generated time-series of mixed fractional Gaussian noise (fGn) processes with non-orthogonal orientations and different scaling exponents is successfully decomposed into the original fGn components.

Higher-order epistasis and phenotypic prediction

A method for reconstructing sequence-to-function mappings from partially observed data that can accommodate all orders of genetic interaction and an empirical Bayes prior that in expectation matches the observed pattern of epistasis is presented.

The 2022 Feldman Prize



Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

This paper studies the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined and finds that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern.

Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.

Universality Classes of Interaction Structures for NK Fitness Landscapes

A unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L is developed, and two different universality classes of interaction structures that display different asymptotics of this quantity for large k are identified.

Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model

A simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution is proposed and compared to the known behavior in the MLM model.

The Impact of Macroscopic Epistasis on Long-Term Evolutionary Dynamics

A computational framework is developed to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time, and finds that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations.

Phase transition in random adaptive walks on correlated fitness landscapes.

The considered process is equivalent to a zero temperature Metropolis dynamics for the random energy model in an external magnetic field, thus also providing insight into the aging dynamics of spin glasses.


This study indicates that an advantage for small populations is likely whenever the fitness landscape contains local maxima, which appears at intermediate time scales, which are long enough for trapping at local fitness maxima to have occurred but too short for peak escape by the creation of multiple mutants.

On the (un)predictability of a large intragenic fitness landscape

A uniquely large multiallelic fitness landscape comprising 640 engineered mutants that represent all possible combinations of 13 amino acid-changing mutations at 6 sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity is presented.