Self-propelled evolution on regenerating landscapes

Abstract: Evolving populations both respond to and reshape their environments, making fitness landscapes dynamic rather than static. We present a minimal eco-evolutionary model that couples replicator dynamics for a population density with a regenerating resource-driven landscape through a single environmental sensitivity parameter. This allows evolving populations to generate and ride self-induced selection gradients, enabling directed motion in trait space even on initially flat landscapes. Our analysis reveals sustained oscillations, chaotic dynamics, and evolutionary branching. To explain these, we derive reduced dynamical equation that extend Fisher's fundamental theorem to deformable landscapes by incorporating curvature-driven variance dynamics and environmental feedback. Together, these results show how populations actively reshape and self-propel themselves on regenerating landscapes.