Vanishing punctuated dynamics on high-dimensional fitness landscapes: a deep-basin condition

Monte Carlo simulation of evolutionary dynamics on NK fitness landscapes with two tunable Gaussian basins, spanning dimensions d=10–300 with over 10¹1 total steps across approximately 23, 000 runs. Three dynamical regimes are discovered: diffusive, punctuated, and frozen. The punctuated regime occupies a narrow band that shrinks and vanishes as dimensionality increases, closing at d≈20. This vanishing is driven by concentration of measure on the binary hypercube and is independent of the epistasis parameter K (tested for K=0–16). The results establish a deep-basin condition: basin depth must scale with genetic dimensionality to sustain punctuated dynamics, a condition that in biological systems would require mechanisms such as stabilizing selection or developmental constraints.