Accessibility percolation on Cartesian power graphs

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.