Abstract
We consider a computer simulation, which was found to be faithful to time series data for Caribbean coral reefs, and an analytical model to help understand the dynamics of the simulation. The analytical model is a system of ordinary differential equations (ODE), and the authors claim this model demonstrates the existence of alternative stable states. The existence of an alternative stable state should consider a sudden shift in coral and macroalgae populations, while the grazing rate remains constant. The results of such shifts, however, are often confounded by changes in grazing rate. Although the ODE suggest alternative stable states, the ODE need modification to explicitly account for shifts or discrete events such as hurricanes. The goal of this paper will be to study the simulation dynamics through a simplified analytical representation. We proceed by modifying the original analytical model through incorporating discrete changes into the ODE. We then analyze the resulting dynamics and their bifurcations with respect to changes in grazing rate and hurricane frequency. In particular, a "kick" enabling the ODE to consider impulse events is added. Beyond adding a "kick" we employ the grazing function that is suggested by the simulation. The extended model was fit to the simulation data to support its use and predicts the existence cycles depending nonlinearly on grazing rates and hurricane frequency. These cycles may bring new insights into consideration for reef health, restoration and dynamics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.