Optimizing shellfish aquaculture in nitrogen and fisheries management

Year 2025, Volume: 5 Issue: 1, 18 - 37, 31.03.2025

Worku T. Bitew , Temesgen B. Getahun , Tsegaye G. Ayele , Simon D. Zawka

https://doi.org/10.53391/mmnsa.1525113

Abstract

Water quality and the invasion of weeds due to nutrient eutrophication have been a concern in major lakes and coastal areas. Scholars have advocated the cultivation of some species of shellfish as a new potential to facilitate the bioremediation of the polluted environment due to excessive nutrients. In this paper, our objective is to determine the optimal area that must be dedicated to shellfish aquaculture relative to the level of nitrogen pollution, other fisheries activities, and the performance of wild catch. The optimal size also depends on the effort outside the water body to control pollution from the point source. We set up transition equations that describe the system’s state based on pollution reduction efforts, nitrogen concentration level, and the size of shellfish cultivation. We show that the impact of the nitrogen concentration level in the habitat can be minimized by allocating optimal management efforts to reduce nitrogen waste from the source and setting aside an area for shellfish cultivation. We found the optimal steady-state solutions and analyzed the optimal solutions based on biological and economic parameters.

Keywords

Nitrogen pollution, shellfish aquaculture, space allocation, fisheries management, optimal effort

References

• [1] Rose, J.M., Gosnell, J.S., Bricker, S., Brush, M.J., Colden, A., Harris, L. et al. Opportunities and challenges for including oyster-mediated denitrification in nitrogen management plans. Estuaries and Coasts, 44, 2041-2055, (2021).
• [2] Wang, D., Gan, X., Wang, Z., Jiang, S., Zheng, X., Zhao, M. et al. Research status on remediation of eutrophic water by submerged macrophytes: A review. Process Safety and Environmental Protection, 169, 671-684, (2023).
• [3] Boopathy, R. Factors limiting bioremediation technologies. Bioresource Technology, 74(1), 63-67, (2000).
• [4] Fetahi, T. Eutrophication of Ethiopian water bodies: a serious threat to water quality, biodiversity and public health. African Journal of Aquatic Science, 44(4), 303-312, (2019).
• [5] Liu, C., Zhang, F., Ge, X., Zhang, X., Chan, N.W. and Qi, Y. Measurement of total nitrogen concentration in surface water using hyperspectral band observation method. Water, 12(7), 1842, (2020).
• [6] United Nations Environment Programme: Mediterranean Action Plan. Approaches for Eutrophication assessment of Mediterranean coastal waters. UNEP(DEPI)/MED WG.321/Inf.6, (2007).
• [7] Caspers, H. OECD: Eutrophication of Waters. Monitoring, Assessment and Control.—154 pp. Paris: Organisation for Economic Co-Operation and Development 1982. (Publié en français sous le titre» Eutrophication des Eaux. Méthodes de Surveillance, d’Evaluation et de Lutte «). nternationale Revue der gesamten Hydrobiologie und Hydrographie, 69(2), 200, (1984).
• [8] Xuan, B.B. and Armstrong, C.W. Marine reserve creation and interactions between fisheries and capture-based aquaculture: A bioeconomic model analysis. Natural Resource Modeling, 30, 1–16, (2016).
• [9] US Environmental Protection Agency (EPA), National Recommended Water Quality Criteria, (2002). https://www.epa.gov/sites/default/files/2018-12/documents/ national-recommended-hh-criteria-2002.pdf
• [10] Smith, V.H. Cultural eutrophication of inland, estuarine, and coastal waters. In Successes, Limitations, and Frontiers in Ecosystem Science (pp. 7-49). New York, NY: Springer New York, (1998).
• [11] Humphries, A.T., Ayvazian, S.G., Carey, J.C., Hancock, B.T., Grabbert, S., Cobb, D. et al. Directly measured denitrification reveals oyster aquaculture and restored oyster reefs remove nitrogen at comparable high rates. Frontiers in Marine Science, 3, 74, (2016).
• [12] Ray, N.E., Hancock, B., Brush, M.J., Colden, A., Cornwell, J., Labrie, M.S. et al. A review of how we assess denitrification in oyster habitats and proposed guidelines for future studies. Limnology and Oceanography: Methods, 19(10), 714-731, (2021).
• [13] Petersen, J.K., Saurel, C., Nielsen, P. and Timmermann, K. The use of shellfish for eutrophication control. Aquaculture International, 24, 857-878, (2016).
• [14] Mykoniatis, N. and Ready, R. The potential contribution of oyster management to water quality goals in the Chesapeake Bay. Water Resources and Economics, 32, 100167, (2020).
• [15] Turner, J.S., Kellogg, M.L., Massey, G.M. and Friedrichs, C.T. Minimal effects of oyster aquaculture on local water quality: Examples from southern Chesapeake Bay. PLoS One, 14(11), e0224768, (2019).
• [16] Mykoniatis, N. and Ready, R. Spatial harvest regimes for a sedentary fishery. Environmental and Resource Economics, 65, 357-387, (2016).
• [17] Ngatia, L., Grace III, J.M. and Moriasi, D. Nitrogen and phosphorus eutrophication in marine. In Monitoring of Marine Pollution (pp. 77-93). IntechOpen: London, (2019).
• [18] Foley, N.S., Armstrong, C.W., Kahui, V., Mikkelsen, E. and Reithe, S. A review of bioeconomic modelling of habitat-fisheries interactions. International Journal of Ecology, 2012(1), 861635, (2012).
• [19] Pichika, S.D.N. and Zawka, S.D. Optimal harvesting of a renewable resource in a polluted environment: An allocation problem of the sole owner. Natural Resource Modeling, 32(2), e12206, (2019).
• [20] Tahvonen, O. On the dynamics of renewable resource harvesting and pollution control. Environmental and Resource Economics, 1, 97-117, (1991).
• [21] Akpalu, W. and Bitew, W.T. Externalities and foreign capital in aquaculture production in developing countries. Environment and Development Economics, 23(2), 198-215, (2018).
• [22] Chatterjee, A. and Pal, S. A predator-prey model for the optimal control of fish harvesting through the imposition of a tax. An International Journal of Optimization and Control: Theories & Applications, 13(1), 68-80, (2023).
• [23] Allen, L.J.S. An Introduction to Mathematical Biology. Pearson Prentice Hall: Italy, (2007).
• [24] Smith, V.H., Tilman, G.D. and Nekola, J.C. Eutrophication: impacts of excess nutrient inputs on freshwater, marine, and terrestrial ecosystems. Environmental Pollution, 100(1-3), 179-196, (1999).
• [25] Hailu, F.F., Bitew, W.T., Ayele, T.G. and Zawka, S.D. Marine protected areas for resilience and economic development. Aquatic Living Resources, 36, 22, (2023). [CrossRef]
• [26] Wirkus, S.A., Swift, R.J. and Szypowski, R. A Course in Differential Equations with Boundary Value Problems. Chapman and Hall/CRC: New York, (2017).
• [27] Soulaimani, S., Kaddar, A. and Rihan, F.A. Stochastic stability and global dynamics of a mathematical model for drug use: Statistical sensitivity analysis via PRCC. Partial Differential Equations in Applied Mathematics, 12, 100964, (2024).
• [28] Getahun, T.B., Bitew, W.T., Ayele, T.G. and Zawka, S.D. Optimal effort, fish farming, and marine reserve in fisheries management. Aquaculture and Fisheries, 9(6), 975-980, (2024).
• [29] Nepf, M., Dvarskas, A. and Walsh, P.J. Economic valuation for coastal water infrastructure planning: Analysis of the housing market and nutrient pollution in Suffolk County, NY. Marine Resource Economics, 37(4), 369-386, (2022).
• [30] Hackbusch, W. A numerical method for solving parabolic equations with opposite orientations. Computing, 20(3), 229-240, (1978).