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An ecological perspective on marine reserves in prey–predator dynamics

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Abstract

This paper describes a prey–predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.

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Acknowledgement

The first author also gratefully acknowledges Director, INCOIS for his encouragement and unconditional help. We are also thankful to Mr. Nimit Dilip Joshi for helping us in proof reading of the manuscript. This is INCOIS contribution number 150.

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Authors and Affiliations

  1. Information Services and Ocean Sciences Group, Indian National Centre for Ocean Information Services, Hyderabad, Ocean Valley, Pragathi Nagar (BO), Nizampet (SO), Hyderabad, 500090, India

    Kunal Chakraborty

  2. Department of Mathematics, Sashinara High School, Sashinara, Memari, Burdwan, 713146, India

    Kunal Das

  3. Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103, India

    T. K. Kar

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  1. Kunal Chakraborty
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  2. Kunal Das
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  3. T. K. Kar
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Correspondence to Kunal Chakraborty.

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Chakraborty, K., Das, K. & Kar, T.K. An ecological perspective on marine reserves in prey–predator dynamics. J Biol Phys 39, 749–776 (2013). https://doi.org/10.1007/s10867-013-9329-5

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  • DOI: https://doi.org/10.1007/s10867-013-9329-5

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