Simple biological controllers drive the evolution of soft modes.

Biological systems, with many interacting components, face high-dimensional environmental fluctuations, ranging from diverse nutrient deprivations to toxins, drugs, and physical stresses. Yet, many biological control mechanisms are 'simple' - they restore homeostasis through low-dimensional representations of the system's high-dimensional state. How do low-dimensional controllers maintain homeostasis in high-dimensional systems? We develop an analytically tractable model of integral feedback for complex systems in fluctuating environments. We find that selection for homeostasis leads to the emergence of a soft mode that provides the dimensionality reduction required for the functioning of simple controllers. Our theory predicts that simple controllers that buffer environmental perturbations (e.g., stress response pathways) will also buffer mutational perturbation, an equivalence we test using experimental data across 5000 strains in the yeast knockout collection. We also predict, counterintuitively, that knocking out a simple controller will