# On the existence of accessible paths in various models of fitness landscapes

@article{Hegarty2014OnTE, title={On the existence of accessible paths in various models of fitness landscapes}, author={Peter V. Hegarty and Anders Martinsson}, journal={Annals of Applied Probability}, year={2014}, volume={24}, pages={1375-1395} }

We present rigorous mathematical analyses of a number of well-known mathematical models for genetic mutations. In these models, the genome is represented by a vertex of the n-dimensional binary hypercube, for some n, a mutation involves the flipping of a single bit, and each vertex is assigned a real number, called its fitness, according to some rules. Our main concernis with the issue of existence of (selectively) accessible paths; that is, monotonic paths in the hypercube along which fitness…

## 41 Citations

### 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.

### Accessibility Percolation on Cartesian Power Graphs

- Mathematics
- 2019

This work derives a lower bound on $\beta^\ast$ for general $A$ and conjecture that this bound is tight for a large class of allele graphs, and compares favorably to published numerical results for multiallelic Hamming graphs.

### 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.

### Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

- BiologybioRxiv
- 2016

Accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences, suggesting that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

### Universality Classes of Interaction Structures for NK Fitness Landscapes

- Biology
- 2017

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.

### Evolutionary constraints in fitness landscapes

- Computer ScienceHeredity
- 2018

This paper presents some measures of evolutionary constraints based on the similarity between accessible paths and the abundance and characteristics of “chains” of obligatory mutations, that are paths going through genotypes with a single fitter neighbor, and shows how they shed light on evolutionary constraints and predictability in experimentally resolved landscapes.

### Accessibility percolation with backsteps

- Mathematics
- 2014

It is shown that, in the large $L$ limit, the probability that an accessible path exists from an arbitrary starting point to the (random) fittest site is no more than 1-\frac12\sinh^{-1}(2) =0.27818\ldots and conjecture that this probability does converge to $x^*_{1/2}$.

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

- BiologyGenetics
- 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.

### Fitness Landscapes, Adaptation and Sex on the Hypercube

- Biology
- 2014

In this thesis, several models of fitness landscapes are analyzed with different analytical and numerical methods to identify characteristics in order to compare the model landscapes to experimental measurements.

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

- MathematicsJournal of theoretical biology
- 2016

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