Temporal Structure of Environmental Noise Controls the Localization and Tracking of Populations of Chemotactic Microorganisms

The ability of chemotactic populations to localize and track targets in fluctuating environments depends critically on the temporal structure of environmental signals. Using a minimal agent-based framework of non-interacting run-and-tumble cells implementing an E. coli-inspired temporal sensing strategy, populations are exposed to static and moving chemoattractant fields perturbed by noise with controlled temporal structure, spanning white, pink (1/f), and correlated Ornstein-Uhlenbeck processes. Chemotactic populations are found to act as temporal filters, robustly suppressing fast fluctuations while remaining highly sensitive to slowly varying perturbations. As a consequence, chemotactic performance is governed not by noise amplitude, but by its temporal correlations. By continuously varying the noise correlation time, a critical regime emerges at{tau} c [~]{tau} run, where aggregates lose stability, tracking errors increase sharply, and spatial dispersion rises. Power spectral analysis further shows that the low-frequency power fraction of the signal provides a strong predictor of failure, outperforming total signal variance and establishing a direct link between environmental noise spectra and collective behavior. Introducing external flow reveals that advective transport amplifies noise-induced destabilization when it overlaps the chemotactic capture region, defining a combined spatiotemporal constraint on robustness. Together, these results identify temporal correlations and spectral structure as fundamental control parameters for chemotactic organization and provide a quantitative framework for predicting and designing collective behavior in fluctuating environments.