Pollution-Driven Spatial Dynamics in a Personality Based Prey-Taxis Model

Abstract. Industrial pollution poses serious threats to ecosystems and is often distributed heterogeneously. Studies have shown that animals with different personality traits (bold versus shy) may experience distinct exposure risks; however, the resulting spatial dynamics remain poorly understood. Relevance to Life Sciences. We examine how spatially heterogeneous pollutants influence bold and shy individuals and the resulting effects on spatial distribution and movement patterns. Under weak predation pressure, bold individuals dominate low-pollution areas, whereas shy individuals dominate more polluted regions. Animals follow pollution gradients and may exhibit quasi-periodic movement in highly polluted environments. These spatial patterns may serve as biomarkers for environmental pollution detection. Mathematical Content. We propose a personality-based prey-taxis model in which predation and taxis coefficients depend explicitly on the spatial distribution of pollution to investigate population dynamics in polluted environments. We establish the global existence of classical solutions by progressively improving solution regularity through heat kernel estimates and a bootstrap argument. We perform local stability analysis to study long-term dynamics in weak and strong predation regimes.