Dynamics of Coral-Algae Phase Shifts via Ecological Stoichiometric Approach

Abstract

Coral reefs have evolved over hundreds of millions of years and are now considered one of the most critical yet vulnerable ecosystem on earth. Environmental changes, including variations in light availability, nutrient levels, and fishing pres- sure, can significantly impact the health of coral reefs, potentially leading to ecosys- tem degradation. A coral-macroalgae-herbivorous fish model is developed based on ecological stoichiometry to investigate the dynamics of coral-algae phase shifts. The positivity, invariance, and dissipativity of the model are carefully established, the exis- tence and stability of equilibria are rigorously demonstrated, and rich dynamics such as bistability and various types of periodic oscillations are numerically explored. Fur- thermore, the effects of environmental factors (e.g., light intensity, nutrient levels, and fishing pressure) on the system’s dynamics are investigated. The main findings high- light that environmental variations are key drivers of ecological phase transitions in coral reef ecosystems, providing more insights into the mechanisms underlying coral- algae dynamics and offering implications for the sustainable management of coral reefs.

Keywords

Dynamic model / coral reef degradation / phase shifts / stability analysis / asymmetric dispersal