Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Macroalgal allelopathy in the emergence of coral diseases

Pages: 741 - 762, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017036

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Joydeb Bhattacharyya - Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, Texas 77840, United States (email)
Samares Pal - Department of Mathematics, University of Kalyani, Kalyani-741235, India (email)

Abstract: Microbial disease in corals associated with the proliferation of benthic macroalgae are the major contributors to the decline of coral reefs over the past few decades. Several benthic macroalgae species produce allelopathic chemical compounds that negatively affect corals. The emergence of microbial diseases in corals occurs simultaneously with the elevated abundance of benthic macroalgae. The release of allelochemicals by toxic-macroalgae enhances microbial activity on coral surfaces via the release of dissolved compounds. Proliferation of benthic macroalgae in coral reefs results in increased physical contacts between corals and macroalgae, triggering the susceptibility of coral disease. The abundance of macroalgae changes the community structure towards macroalgae dominated reef ecosystem. We investigate coral-macroalgal phase shift in presence of macroalgal allelopathy and microbial infection on corals by means of an eco-epidemiological model under the assumption that the transmission of infection is mediated by the pathogens shed by infectious corals and under the influence of macroalgae in the environment. We perform equilibrium and stability analysis on our non-linear ODE model and found that the system is capable of exhibiting the existence of two stable configurations of the community under the same environmental conditions by allowing saddle-node bifurcations that involves in creation and destruction of fixed points and associated hysteresis effect. It is shown that the system undergoes a sudden change of transition when the transmission rate of the infection crosses some certain critical thresholds. Computer simulations have been carried out to illustrate different analytical results.

Keywords:  Coral disease, phase shifts, transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation.
Mathematics Subject Classification:  Primary: 92B05, 92D25; Secondary: 92D40.

Received: November 2015;      Revised: April 2016;      Available Online: January 2017.