# Adaptive walks and extreme value theory.

@article{Neidhart2011AdaptiveWA, title={Adaptive walks and extreme value theory.}, author={Johannes Neidhart and Joachim H A Krug}, journal={Physical review letters}, year={2011}, volume={107 17}, pages={ 178102 } }

We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to genotypes, we show that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution. This result is derived analytically in a simplified setting where the…

## 31 Citations

### Number of adaptive steps to a local fitness peak

- Biology
- 2011

A population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks is considered and it is found that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean.

### Multiple Adaptive Substitutions During Evolution in Novel Environments

- BiologyGenetics
- 2011

An asexual population under strong selection–weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks is considered and the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase.

### ADAPTIVE WALKS AND DISTRIBUTION OF BENEFICIAL FITNESS EFFECTS

- BiologyEvolution; 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.

### From adaptive dynamics to adaptive walks.

- MathematicsJournal of mathematical biology
- 2019

This work considers an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event, and modelled as a measure-valued Markov process.

### Greedy adaptive walks on a correlated fitness landscape.

- MathematicsJournal of theoretical biology
- 2016

### Stochastic models for adaptive dynamics: Scaling limits and diversity

- BiologyProbabilistic Structures in Evolution
- 2019

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation…

### Properties of Random Fitness Landscapes and Their Influence on Evolutionary Dynamics. A Journey through the Hypercube

- Biology
- 2015

The individual-based Wright-Fisher model is used to study recombination of genotypes, interactions between individuals and the influence of the underlying fitness landscape on these mechanisms.

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

- Mathematics
- 2015

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.

### Adaptive walks on correlated fitness landscapes with heterogeneous connectivities

- Mathematics
- 2012

We propose a model for studying the statistical properties of adaptive walks on correlated fitness landscapes which are established in genotype spaces of complex structure. The fitness distribution…

### Accessibility percolation in random fitness landscapes

- Biology
- 2019

This chapter reviews studies of accessibility percolation that use probabilistic fitness landscape models to explore the emergence of paths as a function of the initial fitness, the parameters of the landscape or the structure of the genotype graph and discusses their implications for the predictability of evolutionary processes.

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