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<p>In this paper, we investigate a reaction-diffusion-advection predator-prey model in spatially heterogeneous environments, where predators adopt a movement strategy combining random diffusion with advection along prey resource gradients. We systematically analyze how predator advection strength, mortality rates, and diffusion rates of both species jointly shape system dynamics and invasion outcomes. Our results reveal that the principal eigenvalue, governing the stability of the prey-only equilibrium, varies monotonically with predator diffusion but exhibits non-monotonic behavior with respect to prey diffusion. This gives rise to multiple critical thresholds that distinguish successful from failed predator invasions under different mortality regimes. Notably, under strong directed movement, lower prey diffusion rates enhance predator invasion, while higher rates tend to inhibit it. These insights enhance our understanding of how resource-driven movement influences predator-prey interactions and provide a refined modeling framework for exploring spatial ecological systems.</p>

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Resource-Driven Movement and Invasion Dynamics in Spatially Heterogeneous Predator-Prey Systems

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Lei Li,
  • Qian Qin,
  • Hua Nie

摘要

In this paper, we investigate a reaction-diffusion-advection predator-prey model in spatially heterogeneous environments, where predators adopt a movement strategy combining random diffusion with advection along prey resource gradients. We systematically analyze how predator advection strength, mortality rates, and diffusion rates of both species jointly shape system dynamics and invasion outcomes. Our results reveal that the principal eigenvalue, governing the stability of the prey-only equilibrium, varies monotonically with predator diffusion but exhibits non-monotonic behavior with respect to prey diffusion. This gives rise to multiple critical thresholds that distinguish successful from failed predator invasions under different mortality regimes. Notably, under strong directed movement, lower prey diffusion rates enhance predator invasion, while higher rates tend to inhibit it. These insights enhance our understanding of how resource-driven movement influences predator-prey interactions and provide a refined modeling framework for exploring spatial ecological systems.