Modeling the impact of Allee effect, herd behavior and harvesting on kelp beds: A cross-diffusion-ODE dynamical approach

The density fluctuation of sea urchin may trigger the transition of kelp beds into barrens with low structural complexity under the dual pressure from human disturbances and environmental changes. A cross-diffusion-ODE model, consisting of kelp and sea urchins as well as urchin predators, is formulated to explore the intricate interplay of the Allee effect, herd behavior, and harvesting on the urchin density and the restoration of kelp beds. The existence and stability of possible equilibria are deliberately investigated, an optimal harvesting strategy is delineated, a spectrum of dynamic behaviors such as cyclic phenomena and bistability are identified, and criteria for Turing instability and pattern formation are established. The key findings highlight that moderate harvesting and low-intensity Allee effect can promote the coexistence of kelp, sea urchins, and predators, and herd behavior promotes the survival of sea urchins and is not beneficial to the survival of kelp. Furthermore, the variations in cross-diffusion, harvesting, and Allee effect can induce spatiotemporal patterns and phase transitions, which are essential for implementing strategies for the successful conservation or restoration of kelp beds and provide a theoretical basis for taking appropriate management measures to protect benthic ecosystems.