# 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}
}
• Published 17 October 2012
• Mathematics
• Annals of Applied Probability
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…

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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

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