Accessibility percolation in random fitness landscapes

Krug, Joachim

doi:10.48550/arxiv.1903.11913

Cited by 1 publication

(1 citation statement)

References 56 publications

(118 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From previous work, it is known that for the case of two alleles, V = {0, 1}, and a linear distance d ab ∼ αL, there is a critical value β * depending on α for the fitness difference β = F b − F a , such that for fixed β > β * , the likelihood of b being accessible from a converges to 1 in L, while for β < β * , the likelihood converges to 0 [8,3,13,2,12]. The transition occurring at β = β * has been referred to as accessibility percolation [15,11]. Apart from a computational study [20], so far accessibility percolation has been studied only for the biallelic case where the genotype space is the L-dimensional hypercube.…”

Section: Introductionmentioning

confidence: 99%

Accessibility Percolation on Cartesian Power Graphs

Schmiegelt¹,

Krug²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

A fitness landscape is a mapping from the space of genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes connected by single mutational steps. Such a path is said to be accessible if the fitness values of the genotypes encountered along the path increase monotonically. We study accessible paths on random fitness landscapes of the House-of-Cards type, which implies that the fitness values are independent, identically and continuously distributed random variables. The genotype space is taken to be a Cartesian power graph A L , where L is the number of genetic loci and the allele graph A encodes the possible allelic states and mutational transitions on one locus. The probability of existence of accessible paths between two genotypes at a distance linear in L displays a sharp transition from 0 to 1 at a threshold value β * of the fitness difference between the initial and final genotype. We derive a lower bound on β * for general A and conjecture that this bound is tight for a large class of allele graphs. Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs. A key tool of our analysis is the concept of quasi-accessibility, which eliminates the need to account for the self-avoidance of accessible paths.

show abstract