Title: Marine reserve and its consequences in a predator-prey system for ecotourism and fishing

Authors: Debabrata Das; Tapan Kumar Kar

Addresses: Department of Mathematics, B.P. Poddar Institute of Management and Technology, Kolkata-700052, West Bengal, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India

Abstract: With a marine reserve implementation, this article investigates the effects of introducing density regulation over a fishery. We discuss the inter-relationship between fishing effort and marine reserve with fish biomass, catches, and total rent. It outlines the impacts of exploitation both over maximum sustainable yield and maximum economic yield. We also illustrate some economic consequences of introducing marine reserves on fishery and ecotourism, including the effect of density regulation. Reserve areas can prevent extinction due to over-exploitation, but for a predator-prey interaction, the benefit of the reserve may be diminished. With the increase of density regulation, fish biomass increases, though the absence of reserve catches vanishes as effort exceeds a certain level, irrespective of given importance to density regulation. Finally, we observe that the optimal reserve size corresponding to fisheries management is less than the reserve size when both the fishery rent and ecotourism rent are jointly considered.

Keywords: predator-prey; theta logistic; marine reserve; maximum sustainable yield; MSY; ecotourism.

DOI: 10.1504/IJMMNO.2021.111720

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.1, pp.20 - 36

Received: 12 Nov 2019
Accepted: 08 Mar 2020

Published online: 11 Dec 2020 *

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