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Resilience and Dynamics of Coral Reefs Impacted by Chemically Rich Seaweeds and Unsustainable Fishing

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Mathematical Modelling, Optimization, Analytic and Numerical Solutions

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

Coral reefs are globally threatened by numerous natural and anthropogenic impacts. The proliferation of seaweeds in coral reefs is one of the most common and significant reasons for the decline of healthy corals. Some seaweeds release chemicals that are harmful to corals. The chemicals released by toxic seaweeds damage corals in areas of direct contact. While herbivorous reef fish play an important role in preventing the overgrowth of seaweeds on corals, unsustainable fishing of herbivores disrupts the ecological balance in coral reefs. This induces changes in the community structure from the dominant reef-building corals to one by seaweeds. We have considered a mathematical model of interactions between coral, toxic seaweeds, and herbivores to investigate the phase shifts from coral- to seaweed-dominated states. We investigate how seaweed toxicity and overfishing trigger negative effects on the ecological resilience of coral reefs through trophic cascades. It is observed that in the presence of seaweed toxicity and unsustainable fishing, the system can exhibit an irreversible dynamics through hysteresis cycles. Further, we employ Mawhin’s coincidence degree theory to investigate the existence of a unique positive almost periodic solution of the nonautonomous version of our model by incorporating synchronous or asynchronous seasonal variations in different parameters. The results from computer simulations have potential applications to control the overgrowth of seaweeds in coral reefs as well as to prevent coral bleaching.

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Acknowledgements

SP is supported by the grants from Science & Technology and Biotechnology Department, Govt. of West Bengal, India (No. ST/P/S&T/16G-22/2018). JB acknowledges financial support in the form of research grants from Science & Technology and Biotechnology Department, Govt. of West Bengal, India (No. ST/P/S&T/16G-06/2018).

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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Nadia, 741235, WB, India

    Samares Pal

  2. Department of Mathematics, Karimpur Pannadevi College, Nadia, 741152, WB, India

    Joydeb Bhattacharyya

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  1. Samares Pal
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Correspondence to Samares Pal .

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Editors and Affiliations

  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India

    Pammy Manchanda

  2. Laboratory Math, J.A. Dieudonné, University Côte d’Azur, Nice, France

    René Pierre Lozi

  3. School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

    Abul Hasan Siddiqi

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Pal, S., Bhattacharyya, J. (2020). Resilience and Dynamics of Coral Reefs Impacted by Chemically Rich Seaweeds and Unsustainable Fishing. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Mathematical Modelling, Optimization, Analytic and Numerical Solutions. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-0928-5_12

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