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Accessibility percolation on Cartesian power graphs.

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Accessible paths on random fitness landscapes exist above a critical fitness difference threshold. This study derives a tight lower bound for this threshold, generalizing prior accessibility percolation research.

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Area of Science:

  • Evolutionary Biology
  • Theoretical Biology
  • Computational Biology

Background:

  • Fitness landscapes map genotypes to fitness values, guiding evolutionary trajectories.
  • Accessible paths represent evolutionary routes with monotonically increasing fitness.
  • Understanding path accessibility is crucial for predicting evolutionary dynamics.

Purpose of the Study:

  • To investigate accessible paths on random House-of-Cards fitness landscapes.
  • To determine the conditions for the existence of accessible paths between genotypes.
  • To derive and validate bounds for the fitness difference threshold.

Main Methods:

  • Modeling genotype space as Cartesian power graphs with specified allele graphs.
  • Analyzing the probability of accessible path existence as a function of genotype distance and fitness difference.
  • Deriving a lower bound for the critical fitness difference threshold.

Main Results:

  • A sharp transition in accessible path probability from 0 to positive values was observed at a critical fitness difference.
  • A general lower bound for this critical fitness difference was derived.
  • The derived bound was shown to be tight for various allele graph classes.

Conclusions:

  • The study provides a theoretical framework for understanding evolutionary accessibility on complex fitness landscapes.
  • Results generalize and align with existing findings in accessibility percolation and numerical simulations.
  • The derived bounds offer predictive power for evolutionary pathfinding in silico and in nature.