A spatial food chain model for the Black Sea Anchovy, and its optimal fishery

Demir, Mahir; Lenhart, Suzanne

doi:10.3934/dcdsb.2020373

Cited by 9 publications

(11 citation statements)

References 32 publications

(54 reference statements)

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“…The optimality system consists of the state system (1) with its initials, the adjoint system (4)- (5), and the characterization of the optimal controls (6). Since the adjoint system is linear in λ 1 and λ 2 with bounded coefficients, the solutions are bounded for all t ∈ [0, T ].…”

Section: Optimal Control For Harvesting Strategiesmentioning

confidence: 99%

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Optimizing Predator-Prey Relation of Atlantic Bonito and Anchovy, and their Sustainable Fishery in the Black Sea

Demir

2023

Preprint

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There is no consistent harvesting strategy for the fisheries of the Atlantic bonito (Sarda sarda) and the Black Sea anchovy (Engraulis encrasicolus) on the southern part of the Black Sea. To address this problem, the predator-prey relation of the Atlantic bonito and the Black Sea anchovy is optimized and stabilized as both species are facing harvesting on the southern part of the Black Sea. A fishery model was built and a stability analysis was applied to the fishery model to obtain stable predator-prey dynamics. After that, it was coupled with Optimal Control Theory (OCT) to optimize the stable predator-prey dynamics of these species, and to obtain an optimal and sustainable landing. This study not only provides optimal and stable predator-prey dynamics for these species but also provides more landings and profits for the commercial fishery of these species as compared with the predicted current harvesting strategy obtained in this study. It also provides optimal and sustainable yields to be considered as fishing quotes for these fisheries. MSC Classification: 92B05 , 92B99 , 34H15 , 93D99

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Section: Optimal Control For Harvesting Strategiesmentioning

confidence: 99%

“…But, solely using mathematical models is not enough to understand the dynamics of species and avoid overfishing. Therefore, it is also important to implement a stability analysis to understand the dynamics of species and avoid overfishing ( [17]; [14]; [1]; [4]; [5]; [11]).…”

Section: Introductionmentioning

confidence: 99%

Optimizing Predator-Prey Relation of Atlantic Bonito and Anchovy, and their Sustainable Fishery in the Black Sea

Demir

2023

Preprint

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“…But, solely using mathematical models is not enough to understand the dynamics of species and avoid overfishing. Therefore, it is also important to make stability analyses to understand the dynamics of key species in food webs and avoid overfishing (see the studies: Panja and Mondal 2015;Bentounsi et al, 2017;Agmour et al, 2018;Demir, 2019;Demir and Lenhart, 2019;Demir and Lenhart, 2021). Since fish populations depend on primary producers that are at the bottom of the food chain and consist of phytoplankton and zooplankton, it is essential to include them as key species in the investigation of food webs.…”

Section: Introductionmentioning

confidence: 99%

Importance of Stability Analysis for Sustainable Fisheries in the Absence of Important Data

Demir

2023

Acta Aquatica Turcica

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In this study, predator-prey relations of a food web are investigated when two species face harvesting in the food web. A food chain model built on ordinary differential equations is used to investigate such a food web. After ensuring the existence of a solution for the food chain model, all the possible equilibrium points are found and investigated. Then, the stability analysis of important equilibrium points is numerically made. After capturing important values of harvest rates for a sustainable fishery, the predator-prey system is investigated under different levels of harvesting. This investigation shows us how important stability analysis is to control fish stocks and capture sustainable fisheries.

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“…The logistic growth model is the workhorse of economics, ecology, and theoretical biology for describing the growth processes of renewable natural resources; recent examples are Demir and Lenhart (2021), Grass et al (2019), Hening et al (2019), Pichika and Zawka (2018), Tan et al (2019), and Upmann and Behringer (2020). In particular, logistic growth is frequently assumed in harvesting and fishing models where, following the catch–effort specification of Schaefer (1954), the yield from harvesting (or fishing) is assumed to be linear, while the associated cost is either linear or quadratic in the harvesting effort 1.…”

Section: Introductionmentioning

confidence: 99%

The structure of optimal solutions for harvesting a renewable resource

Upmann

Gromov

2022

Natural Resource Modeling

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We consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy. Recommendations for Resource Managers: We have rigorously explored a standard optimal harvesting model and its steady states. We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution). With some modifications, similar results hold for a finite planning horizon. Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

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A spatial food chain model for the Black Sea Anchovy, and its optimal fishery

Cited by 9 publications

References 32 publications

Optimizing Predator-Prey Relation of Atlantic Bonito and Anchovy, and their Sustainable Fishery in the Black Sea

Optimizing Predator-Prey Relation of Atlantic Bonito and Anchovy, and their Sustainable Fishery in the Black Sea

Importance of Stability Analysis for Sustainable Fisheries in the Absence of Important Data

The structure of optimal solutions for harvesting a renewable resource

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