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

@article{Nowak2015AnalysisOA,
title={Analysis of adaptive walks on NK fitness landscapes with different interaction schemes},
author={Stefan Nowak and Joachim H A Krug},
journal={Journal of Statistical Mechanics: Theory and Experiment},
year={2015},
volume={2015}
}
• Published 26 March 2015
• Mathematics
• Journal of Statistical Mechanics: Theory and Experiment
Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and…

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References

SHOWING 1-10 OF 116 REFERENCES

ESTIMATING SOME FEATURES OF NK FITNESS LANDSCAPES

• Mathematics
• 2002
Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called NK fitness landscapes. Inspired by spinglasses, these models have the attractive feature of

Evolutionary Accessibility of Modular Fitness Landscapes

• Computer Science
• 2014
The block model can be viewed as a special case of Kauffman’s NK-model, and it is shown that the number of accessible paths can be written as a product of the path numbers within the blocks, which provides a detailed analytic description of the paths statistics.

ADAPTIVE WALKS AND DISTRIBUTION OF BENEFICIAL FITNESS EFFECTS

• Biology
Evolution; international journal of organic evolution
• 2014
On taking large effect mutations into account, this work finds that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation, and can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects.

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

• Biology
• 2012
Some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2, and the relation between models for fitness landscapes and spin glasses is addressed.

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

• Biology
Genetics
• 2014
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 POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

• H. A. Orr
• Biology
Evolution; international journal of organic evolution
• 2006
It is shown that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

Exploring the Complexity of the HIV-1 Fitness Landscape

• Biology
PLoS genetics
• 2012
This study analyzes large-scale fitness landscapes based on predictive models for in vitro replicative fitness of HIV-1 and finds that these landscapes are characterized by large correlation lengths, considerable neutrality, and high ruggedness and that these properties depend only weakly on whether fitness is measured in the absence or presence of different antiretrovirals.

Predicting evolution and visualizing high-dimensional fitness landscapes

• Computer Science
• 2014
This contribution focuses on the predictability of evolution on rugged genetic fitness landscapes, and determines that peaks in such landscapes are highly clustered: high peaks are predominantly close to other high peaks, such that evolutionary trajectories towards the highest peak in the landscape can be achieved via a series of valley crossings.

Evolutionary Accessibility of Mutational Pathways

• Biology
PLoS Comput. Biol.
• 2011
Access to the globally optimal configuration should be accessible to genome wide evolution, but the repeatability of evolutionary trajectories is limited owing to the presence of a large number of alternative mutational pathways.