Evolution on degenerate fitness landscapes is not random: Curvature drives directional drift

Degeneracy-the multiplicity of phenotypes with equal fitness-is a prevalent feature of biological systems. Such degeneracy is often associated with neutral evolution, under the assumption that adaptive dynamics on degenerate fitness manifolds is random and lacks direction. Here we show that this is not generally the case. Using a minimal model of evolutionary dynamics on smooth degenerate fitness landscapes, we demonstrate that stochastic mutation-selection dynamics induce a directional drift on manifolds of optimal fitness toward regions of reduced curvature. This drift arises from an interaction between population variability and landscape curvature: Curvature shapes phenotypic variation, which in turn biases evolutionary exploration even when fitness gradients vanish. As a result evolution exhibits an implicit bias, preferentially selecting flat and robust regions of the degenerate fitness manifolds, without explicit optimization for these properties. Interestingly, similar flatness-seeking implicit biases have been discovered in other stochastic optimization algorithms; here we reveal their different underlying mechanisms despite similar outcome, demonstrating the unique properties of evolutionary dynamics. Our results highlight a general mechanism by which degeneracy shapes long-term evolutionary outcomes, affecting our interpretation of phenotypic variability, robustness, and neutrality in high-dimensional biological systems.