• Corpus ID: 249240084

RMF accessibility percolation on oriented graphs

  title={RMF accessibility percolation on oriented graphs},
  author={Frank Duque and Daniel Ramirez-Gomez and Alejandro Rold'an-Correa and Leon A. Valencia},
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology: a random number, called its fitness, is assigned to each vertex of a graph, then a path in the graph is accessible if fitnesses are strictly increasing through it. In the Rough Mount Fuji (RMF) model the fitness function is defined on the graph as ω ( v ) = η ( v )+ θ · d ( v ) , where θ is a positive number called the drift, d is the distance to the source of the graph and η ( v ) are i.i.d. random… 

Figures from this paper



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

The main results resolve open questions about three well-known mathematical models for genetic mutations, which in the biophysics literature are known as house of cards (HoC), constrained house of card (CHoC) and rough Mount Fuji (RMF).

Random Walks and Percolation on Trees

There is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree. It equals the exponential of the Hausdorff dimension of the boundary in an appropriate

A simple model for the balance between selection and mutation

  • J. Kingman
  • Biology
    Journal of Applied Probability
  • 1978
A model for the variation in time of the fitness distribution in a large haploid population is shown to have simple limiting properties which can be elucidated in fairly explicit terms. The novel

Accessibility percolation in random fitness landscapes

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.


The theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.

Fitness Landscapes, Adaptation and Sex on the Hypercube

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.

Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin.

This model may provide a good approximation of real sections of local landscapes for current biopolymers phenomenologically and theoretically explained discrepancies between the fitnesses of multiple mutants and those predicted based on strict additivity of the component mutations by using a model of the rough Mt Fuji-type landscape.

Low-density series expansions for directed percolation on square and triangular lattices

Greatly extended series have been derived for moments of the pair-connectedness for bond and site percolation on the directed square and triangular lattices. The length of the various series has been

Phase Transition for Accessibility Percolation on Hypercubes

In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0, 1] random variables on vertices of a hypercube, and study whether there is a path connecting two