Modeling of Marine Ecosystems: Experience, Modern Approaches, Directions of Development (Review). Part 2. Population and Trophodynamic Models
S. V. Berdnikov1, ✉, V. V. Selyutin1, F. A. Surkov2, Yu. V. Tyutyunov1
1 Federal Research Center the Southern Scientific Center of the Russian Academy of Sciences (SSC RAS), Rostov-on-Don, Russian Federation
2 Southern Federal University (SFedU), Rostov-on-Don, Russian Federation
✉ e-mail: berdnikovsv@yandex.ru
Abstract
Purpose. The paper presents the second part of the review of the publications devoted to the problems of marine ecosystem modeling. In this part, major attention is paid to modern approaches to the management of marine biological resources which implement the ecosystem principles of modeling and monitoring the spatiotemporal dynamics of water objects.
Methods and Results. The review consists of three sections. The first one deals with the models for forecasting dynamics of the exploited populations and for optimizing fishery. The second section considers the trophodynamic models used to study the structure, productivity, and functional role of marine biota interacting with other species and environment at various trophic levels. The trophodynamic models are often applied both for assessing the impact of fishery on marine ecosystems, and for analyzing the influence of the factors directly or indirectly related to climatic variability and anthropogenic activity (eutrophication, salinity, environmental changes). The third section of the review is devoted to a relatively recent direction in marine ecosystem modeling which is based on the geo-information systems. The onrush of the geo-information technologies permitting to connect the data both of the field observations and simulations with their geolocation had an impact on the achievements in the field of ecological modeling.
Conclusions. In the coming years, the role of mathematical modeling in study and management of marine ecosystems will grow. The most important areas of research seem to be as follows: perfection of a model description of primary links in the marine ecosystem food webs (NPZD-models); the flows of matter and energy in the marine food chains; eutrophication and oxygen regime in the sea bays; distribution and transformations of pollutants, and their impact on ecosystems; functioning of marine reserves; the means of taking into account climatic factors in the ecosystem models; and application of satellite monitoring data for identifying and verifying the ecosystem individual components (chlorophyll, oil slicks, suspensions).
Keywords
marine ecosystems, trophodynamic models, fishery models, information technologies, geo-information systems
Acknowledgements
The work was carried out within the framework of the state assignment of SSC RAS for 2022 on the themes No. 122013100131-9 and No. 122020100349-6.
Original russian text
Original Russian Text © The Authors, 2022, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 38, Iss. 2, pp. 196-217 (2022)
For citation
Berdnikov, S.V., Selyutin, V.V., Surkov, F.A. and Tyutyunov, Yu.V., 2022. Modeling of Marine Ecosystems: Experience, Modern Approaches, Directions of Development (Review). Part 2. Population and Trophodynamic Models. Physical Oceanography, 29(2), pp. 182-203. doi:10.22449/1573-160X-2022-2-182-203
DOI
10.22449/1573-160X-2022-2-182-203
References
- Tyutyunov, Yu.V., Titova, L.I., Senina, I.N. and Dashkevich, L.V., 2020. Quasi- Extinction Risk Assessment Practices for Harvested Fish Species Based on a Long- Term Forecast Modelling of Population Dynamics. Studies of the Southern Scientific Centre of the Russian Academy of Science, 8, pp. 181-198. doi:10.23885/1993-6621- 2020-8-181-198 (in Russian).
- Dombrovsky, Yu.А., Obushchenko, N.I. and Tyutyunov, Yu.V., 1991. [Fish Populations in a Stochastic Environment: Management and Survival Models]. Rostov-on-Don: Rostov University Publ., 155 p. (in Russian).
- Tyutyunov, Yu., Arditi, R., Büttiker, B., Dombrovsky, Yu. and Staub, E., 1993. Modelling Fluctuation and Optimal Harvesting in Perch Population. Ecological Modelling, 69(1–2), pp. 19-42. https://doi.org/10.1016/0304-3800(93)90046-U
- Beverton, R.J.H. and Holt, S.J., 1957. On the Dynamics of Exploited Fish Populations. London: Her Majesty's Stationery Office, 552 p.
- Clark, C.W., 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. New York: Wiley, 352 p.
- Senina, I., Tyutyunov, Yu. and Arditi, R., 1999. Extinction Risk Assessment and Optimal Harvesting of Anchovy and Sprat in the Azov Sea. Journal of Applied Ecology, 36(2), pp. 297-306. https://doi.org/10.1046/j.1365-2664.1999.00399.x
- Abakumov, A. and Izrailsky, Yu., 2022. Optimal Harvest Problem for Fish Population – Structural Stabilization. Mathematics, 10(6), 986. https://doi.org/10.3390/math10060986
- Tyutyunov, Yu.V., Senina, I.N., Surkov, F.А. and Arditi, R.R., 2001. [Models for Assessing the Risk of Reducing the Number of Commercial Fish Populations]. In: G. G. Matishov, ed., 2001. Environment, Biota, Modeling of Ecological Processes in the Sea of Azov. Apatity: Kola Science Centre of RAS, pp. 380-396 (in Russian).
- Tyutyunov, Yu., Senina, I., Jost, C. and Arditi, R., 2002. Risk Assessment of the Harvested Pike-Perch Population of the Azov Sea. Ecological Modelling, 149(3), pp. 297-311. https://doi.org/10.1016/S0304-3800(01)00478-1
- Vorovich, I.I., Dombrovskii, Yu.A., Obushchenko, N.I. and Surkov, F.A., 1989. Problems of Optimal Management of a Fishery with Competing Fish Populations in the Azov Sea. Doklady Mathematics, 34(4), pp. 294-296.
- Berdnikov, S.V., Selyutin, V.V., Vasilchenko, V.V. and Caddy, J.F., 1999. Trophodynamic Model of the Black and Azov Sea Pelagic Ecosystem: Consequences of the Comb Jelly, Mnemiopsis leydei, Invasion. Fisheries Research, 42(3), pp. 261-289. https://doi.org/10.1016/S0165-7836(99)00049-1
- Matishov, G.G., Gargopa, Yu.M., Berdnikov, S.V. and Dzhenyuk, S.L., 2006. [Patterns of Ecosystem Processes in the Sea of Azov]. Moscow: Nauka, 304 p. (in Russian).
- Luts, G.I., 2009. Habitat Conditions, Specificities of Stock Formation and Fishery of the Azov Tyulka. Rostov-on-Don: FSUE “AzNIIRKH”, 118 p. Available at: http://dspace.vniro.ru/handle/123456789/1655 [Accessed: 26 February 2022] (in Russian).
- Drozdov, V.V., 2010. Features of Long-Term Dynamics of an Ecosystem of Sea of Azov under the Influence of Climatic and Anthropogenous Factors. In: RSHU, 2010. Proceedings of the Russian State Hydrometeorological University. Saint Petersburg: RSHU. Iss. 15, pp. 155-176 (in Russian).
- Vorovich, I.I., Gorelov, A.S., Gorstko, A.B., Dombrovsky, Yu.А., Zhdanov, Yu.A., Surkov, F.A. and Epshteyn, L.V., 1981. [Rational Use of Water Resources in the Sea of Azov Basin: Mathematical Models]. Moscow: Nauka, 360 p. (in Russian).
- Ricker, W.E., 1954. Stock and Recruitment. Journal of the Fisheries Research Board of Canada, 11(5), pp. 559-623. https://doi.org/10.1139/f54-039
- May, R.M., 1975. Biological Populations Obeying Difference Equations: Stable Points, Stable Cycles, and Chaos. Journal of Theoretical Biology, 51(2), pp. 511- 524. https://doi.org/10.1016/0022-5193(75)90078-8
- Frisman, E.Y., Neverova, G.P. and Revutskaya, O.L., 2011. Complex Dynamics of the Population with a Simple Age Structure. Ecological Modelling, 222(12), pp. 1943-1950. https://doi.org/10.1016/j.ecolmodel.2011.03.043
- Gorstko, A.B., Dombrovsky, Yu.А. and Surkov, F.A., 1984. [Ecological and Economic Systems Management Models]. Moscow: Nauka, 119 p. (in Russian).
- Ilichev, V.G., 2009. [Resilience, Adaptation and Management in Ecological Systems]. Moscow: Fizmatlit, 230 p. (in Russian).
- Frisman, E.Ya., Zhdanova, O.L., Kulakov, M.P., Neverova, G.P. and Revutskaya, O.L., 2021. Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I. Biology Bulletin, 48(1), pp. 1-15. https://doi.org/10.1134/S1062359021010064
- Neverova, G.P., Abakumov, A.I. and Frisman, E.Ya., 2017. Dynamic Modes of Limited Structured Population under Age Specific Harvest. Mathematical Biology and Bioinformatics, 12(2), pp. 327-342. doi:10.17537/2017.12.327 (in Russian).
- Vorovich, I.I., Gorstko, A.B., Dombrovskii, Yu.A., Zhdanov, Yu.A. and Surkov, F.A., 1981. The Use of a Mathematical Model of the Sea-of-Azov Ecosystem for the Investigation of the Functioning Regularities and System Structure. Doklady Akademii Nauk SSSR, 259(2), pp. 302-306 (in Russian).
- Beddington, J.R. and Taylor, D.B., 1973. 356. Note: Optimum Age Specific Harvesting of a Population. Biometrics, 29(4), pp. 801-809. https://doi.org/10.2307/2529145
- Dombrovskii, Yu.A., 1979. [Optimal Harvesting in a Population Model with Intermittent Generations]. Voprosy Kibernetiki, 52, pp. 48-59 (in Russian).
- Menshutkin, V.V., 1971. [Mathematical Modeling of Populations and Communities of Aquatic Animals]. Leningrad: Nauka, 196 p. (in Russian).
- Getz, W.M. and Haight, R.G., 1989. Population Harvesting: Demographic Models of Fish, Forest, and Animal Resources. Princeton: Princeton University Press, 391 p.
- Arditi, R. and Dacorogna, B., 1992. Maximum Sustainable Yield of Populations with Continuous Age-Structure. Mathematical Biosciences, 110(2), pp. 253-270. https://doi.org/10.1016/0025-5564(92)90040-4
- Dacorogna, B., Weissbaum, F. and Arditi, R., 1994. Maximum Sustainable Yield with Continuous Age Structure and Density-Dependent Recruitment. Mathematical Biosciences, 120(1), pp. 99-126. https://doi.org/10.1016/0025-5564(94)90039-6
- Frisman, E.Ya., Last, E.V. and Skaletskaya, E.I., 2006. Population Dynamics of Harvested Species with Complex Age Structure (for Pacific Salmons Fish Stocks as an Example). Ecological Modelling, 198(3–4), pp. 463-472. https://doi.org/10.1016/j.ecolmodel.2006.05.019
- Egorova, A.V. and Rodina, L.I., 2019. On Optimal Harvesting of Renewable Resource from the Structured Population. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki, 29(4), pp. 501-517. https://doi.org/10.20537/vm190403 (in Russian).
- Frisman, E.Ya., Kulakov, M.P., Revutskaya, O.L., Zhdanova, O.L. and Neverova, G.P., 2019. The Key Approaches and Review of Current Researches on Dynamics of Structured and Interacting Populations. Computer Research and Modeling, 11(1), pp. 119-151. doi:10.20537/2076-7633-2019-11-1-119-151 (in Russian).
- Abakumov, A.I., 1993. [Control and Optimization in Models of Exploited Populations]. Vladivostok: Dalnauka, 129 p. (in Russian).
- Abakumov, A.I. and Izrailsky, Y.G., 2017. The Stabilizing Role of Fish Population Structure under the Influence of Fishery and Random Environment Variations. Computer Research and Modeling, 9(4), pp. 609-620. doi:10.20537/2076-7633- 2017-9-4-609-620 (in Russian).
- Derendjaeva, T.M., 2016. Probabilistic Models in the Theory Prediction of Commercial Fish Stocks. Teorija i Praktika Sovremennoj Nauki, (12), pp. 345-348 (in Russian).
- Tyutyunov, Y.V., Senina, I.N., Titova, L.I. and Dashkevich, L.V., 2020. Long- Range Prediction of the Risk of Extinction Faced by the Pikeperch in the Azov Sea: Was the Prediction Correct? Biophysics, 65(2), pp. 338-348. https://doi.org/10.1134/S0006350920020256
- Tyutyunov, Yu.V., Dombrovsky, Yu.A. and Obushchenko, N.I., 1996. [Optimal Management of the Exploited Population while Minimizing the Risk of Its Extinction in a Stochastic Habitat]. OP&PM Surveys on Applied and Industrial Mathematics, 3(3), pp. 412-433 (in Russian).
- Senina, I.N., 2015. [Mathematical Modeling of Migrations of Fish Populations in Application to Fishery Optimization and Forecasting of Tuna Stocks]. In: F. A. Surkov and V. V. Selyutin, eds., 2015. Systems Analysis and Mathematical Modeling of Complex Ecological and Economic Systems. Theoretical Foundations and Applications. Rostov-on-Don: SFU. Chapter 3, pp. 57-80 (in Russian).
- Baranov, F.I., 1971. Selected Works. Vol. 3. Moscow: Pishhevaja Promyshlennost', 304 p. (in Russian).
- Shibaev, S.V., 2015. Formal Theory of Fishes Life by F.I. Baranov and Its Importance for Development of Fishery Science. Trudy VNIRO, 157, pp. 127-142 (in Russian).
- Abakumov, A.I., Il’in, O.I. and Ivanko, N.S., 2016. Game Problems of Harvesting in a Biological Community. Automation and Remote Control, 77(4), pp. 697-707. https://doi.org/10.1134/S0005117916040135
- Lindstrøm, U., Smout, S., Howell, D. and Bogstad, B., 2009. Modelling Multi- Species Interactions in the Barents Sea Ecosystem with Special Emphasis on Minke Whales and Their Interactions with Cod, Herring and Capelin. Deep Sea Research Part II: Topical Studies in Oceanography, 56(21–22), pp. 2068-2079. https://doi.org/10.1016/j.dsr2.2008.11.017
- Pérez-Rodríguez, A., Howell, D., Casas, M., Saborido-Rey, F. and Ávila-de Melo, A., 2017. Dynamic of the Flemish Cap Commercial Stocks: Use of a Gadget Multispecies Model to Determine the Relevance and Synergies among Predation, Recruitment, and Fishing. Canadian Journal of Fisheries and Aquatic Sciences, 74(4), pp. 582-597. https://doi.org/10.1139/cjfas-2016-0111
- Howell, D., Filin, A.A., Bogstad, B. and Stiansen, J.E., 2013. Unquantifiable Uncertainty in Projecting Stock Response to Climate Change: Example from North East Arctic Cod. Marine Biology Research, 9(9), pp. 920-931. https://doi.org/10.1080/17451000.2013.775452
- Howell, D. and Filin, A.A., 2014. Modelling the Likely Impacts of Climate-Driven Changes in Cod-Capelin Overlap in the Barents Sea. ICES Journal of Marine Science, 71(1), pp. 72-80. doi:10.1093/icesjms/fst172
- Fournier, D.A., Hampton, J. and Sibert, J.R., 1998. MULTIFAN-CL: A Length- Based, Age-Structured Model for Fisheries Stock Assessment, with Application to South Pacific Albacore, Thunnus Alalunga. Canadian Journal of Fisheries and Aquatic Sciences, 55(9), pp. 2105-2116. https://doi.org/10.1139/f98-100
- Lehodey, P., Senina, I. and Murtugudde, R., 2008. A Spatial Ecosystem and Populations Dynamics Model (SEAPODYM) – Modeling of Tuna and Tuna-Like Populations. Progress in Oceanography, 78(4), pp. 304-318. https://doi.org/10.1016/j.pocean.2008.06.004
- Lehodey, P., Senina, I., Calmettes, B., Hampton, J. and Nicol, S., 2013. Modelling the Impact of Climate Change on Pacific Skipjack Tuna Population and Fisheries. Climatic Change, 119(1), pp. 95-109. https://doi.org/10.1007/s10584-012-0595-1
- Lehodey, P., Conchon, A., Senina, I., Domokos, R., Calmettes, B., Jouanno, J., Hernandez, O. and Kloser, R., 2015. Optimization of a Micronekton Model with Acoustic Data. ICES Journal of Marine Science, 72(5), pp. 1399-1412. https://doi.org/10.1093/icesjms/fsu233
- Senina, I., Lehodey, P., Sibert, J. and Hampton, J., 2020. Integrating Tagging and Fisheries Data into a Spatial Population Dynamics Model to Improve Its Predictive Skills. Canadian Journal of Fisheries and Aquatic Sciences, 77(3), pp. 576-593. https://doi.org/10.1139/cjfas-2018-0470
- Senina, I., Lehodey, P., Hampton, J. and Sibert, J., 2020. Quantitative Modelling of the Spatial Dynamics of South Pacific and Atlantic Albacore Tuna Populations. Deep Sea Research Part II: Topical Studies in Oceanography, 175, 104667. https://doi.org/10.1016/j.dsr2.2019.104667
- Senina, I., Borderies, M. and Lehodey, P., 2015. A Spatio-Temporal Model of Tuna Population Dynamics and Its Sensitivity to the Environmental Forcing Data. Applied Discrete Mathematics and Heuristic Algorithms, 1(3), pp. 5-20. Available at: https://disk.yandex.ru/i/rhmtyzcjGdz2nw [Accessed: 20 April 2022].
- Svendsen, E., Skogen, M., Budgell, P., Huse, G., Stiansen, J.E., Ådlandsvik, B., Vikebø, F., Asplin, L. and Sundby, S., 2007. An Ecosystem Modeling Approach to Predicting Cod Recruitment. Deep Sea Research Part II: Topical Studies in Oceanography, 54(23–26), pp. 2810-2821. doi:10.1016/j.dsr2.2007.07.033
- Skogen, M.D., Olsen, A., Børsheim, K.Y., Sandø, A.B. and Skjelvan, I., 2014. Modelling Ocean Acidification in the Nordic and Barents Seas in Present and Future Climate. Journal of Marine Systems, 131, pp. 10-20. https://doi.org/10.1016/j.jmarsys.2013.10.005
- Chai, F., Dugdale, R.C., Peng, T.-H., Wilkerson, F.P. and Barber, R.T., 2002. One- Dimensional Ecosystem Model of the Equatorial Pacific Upwelling System. Part I: Model Development and Silicon and Nitrogen Cycle. Deep Sea Research Part II: Topical Studies in Oceanography, 49(13–14), pp. 2713-2745. https://doi.org/10.1016/S0967-0645(02)00055-3
- Chai, F., Jiang, M.S., Barber, R.T., Dugdale, R.C. and Chao, Y., 2003. Interdecadal Variation of the Transition Zone Chlorophyll Front: A Physical-Biological Model Simulation between 1960 and 1990. Journal of Oceanography, 59(4), pp. 461-475. https://doi.org/10.1023/A:1025540632491
- Aumont, O., Ethé, C., Tagliabue, A., Bopp, L. and Gehlen, M., 2015. PISCES-v2: An Ocean Biogeochemical Model for Carbon and Ecosystem Studies. Geoscientific Model Development, 8(8), pp. 2465-2513. doi:10.5194/gmd-8-2465-2015
- McAllister, M.K. and Kirkwood, G.P., 1998. Bayesian Stock Assessment: a Review and Example Application Using the Logistic Model. ICES Journal of Marine Science, 55(6), pp. 1031-1060. https://doi.org/10.1006/jmsc.1998.0425
- McAllister, M.K., 2013. Using Bayes Factors to Evaluate the Credibility of Stock- Recruitment Relationships for Western Atlantic Bluefin Tuna. ICCAT Collective Volume of Scientific Papers, 69(2), pp. 913-937. Available at: https://iccat.int/Documents/CVSP/CV069_2013/n_2/CV069020913.pdf [Accessed: 20 April 2022].
- Lee, H.-H., Maunder, M.N., Piner, K.R. and Methot, R.D., 2011. Estimating Natural Mortality within a Fisheries Stock Assessment Model: An Evaluation Using Simulation Analysis Based on Twelve Stock Assessments. Fisheries Research, 109(1), pp. 89-94. https://doi.org/10.1016/j.fishres.2011.01.021
- Lee, H.-H., Maunder, M.N., Piner, K.R. and Methot, R.D., 2012. Can Steepness of the Stock–Recruitment Relationship Be Estimated in Fishery Stock Assessment Models? Fisheries Research, 125-126, pp. 254-261. https://doi.org/10.1016/j.fishres.2012.03.001
- Lee, H.-H., Piner, K.R., Maunder, M.N. and Methot Jr., R.D., 2015. Simulation of Methods of Dealing with Age-Based Movement in PBF Stock Assessment. Working Paper. In: WCPFC, 2015. ISC 16 Report (Annex 4) of the Pacific Bluefin Tuna Working Group Intersessional Workshop. Kaohsiung, Chinese Taipei, pp. 13, ISC/15/PBFWG-2/12. Available at: https://meetings.wcpfc.int/file/5091/download [Accessed: 20 April 2022].
- Lisunova, N.S. and Berdnikov, S.V., 2011. Sharefish 2.0 Mathematical Model Use for the Analysis of Factors, Influencing on North-East Arctic Cod Stock. In: G. G. Matishov, ed., 2011. [Study and Development of Marine and Terrestrial Ecosystems in the Arctic and Arid Climate: Proceedings of the International Scientific Conference]. Rostov-on-Don: SCC RAS, pp. 414-417 (in Russian).
- Bulatov, O.A., 2015. On the Question of the Methodology of Stock Assessment Forecasting and Pollock Fishery Strategy. Trudy VNIRO, 157, pp. 45-70. Available at: http://vniro.ru/files/trydi_vniro/archive/tv_2015_t_157_article_4.pdf [Accessed: 20 April 2022] (in Russian).
- Bulatov, O.A., Kotenyov, B.N., Moiseyenko, G.S. and Borisov, V.M., 2007. Present-Day State of the Barents Sea Cod Stock and TAC prognosis for 2008. Rybnoe Hozyajstvo, (5), pp. 61-65. Available at: http://dspace.vniro.ru/bitstream/handle/123456789/4806/17.Булатов.pdf?sequence= 19 [Accessed: 20 April 2022] (in Russian).
- Vasilyev, D.A. and Bulgakova, T.I., 2007. Alternative Assessment of Barents Sea Cod Stock by the TISVPA Model. Rybnoe Hozyajstvo, (5), pp. 54-60 (in Russian).
- Vasilyev, D.A. and Bulatov, O.A. 2015. North-East Arctic Cod and Haddock Stock Assessment by means of TISVPA Model. Problems of Fisheries, 16(4), pp. 497-505. Available at: http://www.vniro.ru/files/voprosy_rybolovstva/archive/vr_2015_t16_4_article_11.p df [Accessed: 20 April 2022] (in Russian).
- Bulgakova, T.I., 2009. The Scenario Model for Testing Some Trade Control Rules (TCR): the North-East Arctic Cod. Rybnoe Hozyajstvo, (4), pp. 77-80 (in Russian).
- Borisov, V.M., Kotenyov, B.N. and Borisov, A.I., 2006. Russian Overfishing of Cod in the Sea and in Norwegian Reports. Rybnoe Hozyajstvo, (5), pp. 6-9 (in Russian).
- Zhichkin, A.P., 2014. Spatial and Temporal Variability of Commercial Significance of Different Fishery Areas in the Barents Sea. Vestnik of MSTU, 17(3), pp. 465-473. Available at: http://vestnik.mstu.edu.ru/v17_3_n58/465_473_zhich.pdf [Accessed: 20 April 2022] (in Russian).
- Kotenyov, B.N., Bulatov, O.A., Vasilyev, D.A., Borisov, V.M. and Moiseyenko, G.S., 2007. The Assessment of the Barents Sea Cod Stock. Fisheries, (5), pp. 51-53 (in Russian).
- Shuntov, V.P. and Temnykh, O.S., 2013. Illusions and Realities of Ecosistem Approach to Study and Management of Marine and Oceanic Biological Resources. Izvestiya TINRO, 173, pp. 3-29 (in Russian).
- Borovkov, V.A., Karsakov, A.L., Yaragina, N.A., Antsiferov, M.Yu. and Ivshin, V.A., 2014. [Effects of Modern Climate Change in the Distribution of Commercial Aggregations of Northeastern Arctic Cod during the Feeding Period]. Voprosy Promyslovoj Okeanologii, (11), pp. 61-75 (in Russian).
- Berdnikov, S.V., Dashkevich, L.V. and Selyutin, V.V., 2002. [Marine Protected Areas as a Method of Protecting Exploited Populations (on the Example of the Photen-Barents Cod (Gadus morhua morhua)]. Izvestiya Vuzov. Severo-Kavkazskii Region. Natural Science, (4), pp. 68-73 (in Russian).
- Zhichkin, A.P., 2009. [Atlas of the Russian Cod Fishery in the Barents Sea (1977– 2006)]. Murmansk: Raditsa, 212 p. (in Russian).
- Berdnikov, S.V., Dashkevich, L.V., Lisunova, N.S., Kalenchenko, M.M. and Selyutin, V.V., 2010. Environmental Design on basis of Mathematical Modeling Approach and Legal Aspects of Implementation of Marine Environment In Situ Conservation Measures (on Example of Atlantic Cod Gadus Morhua Morhua L.). Rybnoe Hozyajstvo, (6), pp. 58-66 (in Russian).
- Berdnikov, S.V., Kulygin, V.V., Sorokina, V.V., Dashkevich, L.V. and Sheverdyaev, I.V., 2019. An Integrated Mathematical Model of the Large Marine Ecosystem of the Barents Sea and the White Sea as a Tool for Assessing Natural Risks and Efficient Use of Biological Resources. Doklady Earth Sciences, 487(2), pp. 963-968. https://doi.org/10.1134/S1028334X19080117
- Tittensor, D.P., Eddy, T.D., Lotze, H.K., Galbraith, E.D., Cheung, W., Barange, M., Blanchard, J.L., Bopp, L., Bryndum-Buchholz, A. [et al.], 2018. A Protocol for the Intercomparison of Marine Fishery and Ecosystem Models: Fish-MIP v1.0. Geoscientific Model Development, 11(4), pp. 1421-1442. https://doi.org/10.5194/gmd-11-1421-2018
- Fulton, E.A. and Link, J.S., 2014. Modeling Approaches for Marine Ecosystem- Based Management. In: M. J. Fogarty and J. J. McCarthy, eds., 2014. Marine Ecosystem-Based Management. Harvard: Harvard University Press, 568 p.
- Peck, M.A., Arvanitidis, C., Butenschön, M., Canu, D.M., Chatzinikolaou, E., Cucco, A., Domenici, P., Fernandes, J.A., Gasche, L. [et al.], 2018. Projecting Changes in the Distribution and Productivity of Living Marine Resources: A Critical Review of the Suite of Modelling Approaches Used in the Large European Project VECTORS. Estuarine, Coastal and Shelf Science, 201, pp. 40-55. https://doi.org/10.1016/j.ecss.2016.05.019
- Nielsen, J.R., Thunberg, E., Holland, D.S., Schmidt, J.O., Fulton, E.A., Bastardie, F., Punt, A.E., Allen, I., Bartelings, H. [et al.], 2017. Integrated Ecological- Economic Fisheries Models – Evaluation, Review and Challenges for Implementation. Fish and Fisheries, 19(1), pp. 1-29. https://doi.org/10.1111/faf.12232
- Christensen, V. and Walters, C.J., 2004. Ecopath with Ecosim: Methods, Capabilities and Limitations. Ecological Modelling, 172(2–4), pp. 109-139. https://doi.org/10.1016/j.ecolmodel.2003.09.003
- Polovina, J.J., 1984. Model of a Coral Reef Ecosystem. 1. The ECOPATH Model and Its Application to French Frigate Shoals. Coral Reefs, 3(1), pp. 1-11. https://doi.org/10.1007/BF00306135
- Pauly, D., Christensen, V. and Walters, C., 2000. Ecopath, Ecosim, and Ecospace as Tools for Evaluating Ecosystem Impact of Fisheries. ICES Journal of Marine Science, 57(3), pp. 697-706. https://doi.org/10.1006/jmsc.2000.0726
- Christensen, V., Coll, M., Buszowski, J., Cheung, W.W.L., Frölicher, T., Steenbeek, J., Stock, C.A., Watson, R.A. and Walters, C.J., 2015. The Global Ocean is an Ecosystem: Simulating Marine Life and Fisheries. Global Ecology and Biogeography, 24(5), pp. 507-517. https://doi.org/10.1111/geb.12281
- Niiranen, S., Yletyinen, J., Tomczak, M.T., Blenckner, T., Hjerne, O., Mackenzie, B.R., Müller-Karulis, B., Neumann, T. and Meier, H.E.M., 2013. Combined Effects of Global Climate Change and Regional Ecosystem Drivers on an Exploited Marine Food Web. Global Change Biology, 19(11), pp. 3327-3342. https://doi.org/10.1111/gcb.12309
- Vasslides, J.M., de Mutsert, K., Christensen, V. and Townsend, H., 2017. Using the Ecopath with Ecosim Modeling Approach to Understand the Effects of Watershed- Based Management Actions in Coastal Ecosystems. Coastal Management, 45(1), pp. 44-55. http://dx.doi.org/10.1080/08920753.2017.1237241
- Christensen, V., Walters, C.J., Ahrens, R., Alder, J., Buszowskj, J., Christensen, L.B., Cheung, W.W.L., Dunne, J., Froese, R. [et al.], 2009. Database-Driven Models of the World’s Large Marine Ecosystems. Ecological Modelling, 220(17), pp. 1984- 1996. https://doi.org/10.1016/j.ecolmodel.2009.04.041
- Christensen, V., Coll, M., Steenbeek, J., Buszowski, J., Chagaris, D. and Walters, C.J., 2014. Representing Variable Habitat Quality in a Spatial Food Web Model. Ecosystems, 17(8), pp. 1397-1412. https://doi.org/10.1007/s10021-014-9803-3
- Colleter, M., Valls, A., Guitton, J., Gascuel, D., Pauly, D. and Christensen, V., 2015. Global Overview of the Applications of the Ecopath with Ecosim Modeling Approach Using the EcoBase Models Repository. Ecological Modelling, 302, pp. 42-53. https://doi.org/10.1016/j.ecolmodel.2015.01.025
- Heymans, J.J., Coll, M., Link, J.S., Mackinson, S., Steenbeek, J., Walters, C. and Christensen, V., 2016. Best Practice in Ecopath with Ecosim Food-Web Models for Ecosystem-Based Management. Ecological Modelling, 331, pp. 173-184. https://doi.org/10.1016/j.ecolmodel.2015.12.007
- Walters, C., Pauly, D. and Christensen, V., 1999. Ecospace: Prediction of Mesoscale Spatial Patterns in Trophic Relationships of Exploited Ecosystems, with Emphasis on the Impacts of Marine Protected Areas. Ecosystems, 2(6), pp. 539-554. https://doi.org/10.1007/s100219900101
- Walters, C., Christensen, V., Walters, W. and Rose, K., 2010. Representation of Multistanza Life Histories in Ecospace Models for Spatial Organization of Ecosystem Trophic Interaction Patterns. Bulletin of Marine Science, 86(2), pp. 439-459. Available at: https://www.ingentaconnect.com/contentone/umrsmas/bullmar/2010/00000086/00000002/art00017 [Accessed: 20 April 2022].
- Vasslides, J.M., de Mutsert, K., Christensen, V. and Townsend, H., 2017. Using the Ecopath with Ecosim Modeling Approach to Understand the Effects of Watershed- Based Management Actions in Coastal Ecosystems. Coastal Management, 45(1), pp. 44-55. https://doi.org/10.1080/08920753.2017.1237241
- Steenbeek, J., Coll, M., Gurney, L., Mélin, F., Hoepffner, N., Buszowski, J. and Christensen, V., 2013. Bridging the Gap between Ecosystem Modeling Tools and Geographic Information Systems: Driving a Food Web Model with External Spatial–Temporal Data. Ecological Modelling, 263, pp. 139-151. https://doi.org/10.1016/j.ecolmodel.2013.04.027
- Whitehouse, G.A. and Aydin, K.Y., 2020. Assessing the Sensitivity of Three Alaska Marine Food Webs to Perturbations: an Example of Ecosim Simulations Using Rpath. Ecological Modelling, 429, 109074. https://doi.org/10.1016/j.ecolmodel.2020.109074
- Berdnikov, S.V. and Sorokina, V.V., 2012. [Results of Applying the EwE Approach to Assess the Acceptable Fishing Impact on Fish Populations in the Barents, Okhotsk, Bering, Kara and Black Seas]. In: SFU, 2012. Ecology. Economy. Informatics. XL Сonference on Mathematical Modeling for the Problems of Rational Nature Management: Proceedings of the International Scientific Conference. Abrau-Durso, September 3-8, 2012. Rostov-on-Don: Publishing House of the Southern Federal University, pp. 35-39 (in Russian).
- Radchenko, V.I., 2015. Characterization of the Sea of Okhotsk Ecosystem Based on Ecosystem Modelling. Trudy VNIRO, 155, pp. 79-111. Available at: http://vniro.ru/files/trydi_vniro/archive/tv_2015_t_155_article_7.pdf [Accessed: 20 April 2022] (in Russian).
- Zavolokin, A.V., Radchenko, V.I. and Kulik, V.V., 2014. Dynamics of Trophic Structure for the Epipelagic Community in the Western Bering Sea. Izvestiya TINRO, 179, pp. 204-219. https://doi.org/10.26428/1606-9919-2014-179-204-219 (in Russian).
- Shin, Y.-J. and Cury, P., 2001. Exploring Fish Community Dynamics through Size- Dependent Trophic Interactions Using a Spatialized Individual-Based Model. Aquatic Living Resources, 14(2), pp. 65-80. https://doi.org/10.1016/S0990-7440(01)01106-8
- Travers, M., Shin, Y.-J., Jennings, S., Machu, E., Huggett, J.A., Field, J.G. and Cury, P.M., 2009. Two-Way Coupling Versus One-Way Forcing of Plankton and Fish Models to Predict Ecosystem Changes in the Benguela. Ecological Modelling, 220(21), pp. 3089-3099. https://doi.org/10.1016/j.ecolmodel.2009.08.016
- Yemane, D., Shin, Y.-J. and Field, J., 2009. Exploring the Effect of Marine Protected Areas on the Dynamics of Fish Communities in the Southern Benguela: an Individual-Based Modelling Approach. ICES Journal of Marine Science, 66(2), pp. 378-387. https://doi.org/10.1093/icesjms/fsn171
- Hyder, K., Rossberg, A.G., Allen, J.I., Austen, M.C., Barciela, R.M., Bannister, H.J., Blackwell, P.G., Blanchard, J.L., Burrows, M.T. [et al.], 2015. Making Modelling Count – Increasing the Contribution of Shelf-Seas Community and Ecosystem Models to Policy Development and Management. Marine Policy, 61, pp. 291-302. https://doi.org/10.1016/j.marpol.2015.07.015
- Berdnikov, S.V., Selyutin, V.V., Vasilchenko, V.V. and Caddy, J.F., 1999. Trophodynamic Model of the Black and Azov Sea Pelagic Ecosystem: Consequences of the Comb Jelly, Mnemiopsis Leydei, Invasion. Fisheries Research, 42(3), pp. 261-289. https://doi.org/10.1016/S0165-7836(99)00049-1
- Dashkevich, L.V., Berdnikov, S.V. and Golubev, V.A., 2007. [Application of the Trophodynamic Model of the Barents Sea to Analyze the Commercial Population Dynamics and Assess the Permissible Load on the Ecosystem]. In: G. G. Matishov, ed., 2007. Complex Investigations of Processes, Сharacteristics and Resources of Russian Seas of North European Basin. Apatity: KSC RAS. Iss. 2, pp. 64-103 (in Russian).
- Matishov, G. and Levitus, S., eds., 2006. Climatic Atlas of the Azov Sea. NOAA Atlas NESDIS 59. Washington D.C.: U.S. Government Printing Office, 148 p. CD-ROM.
- Levitus, S., 2013. NODC Standard Product: International Ocean Atlas Volume 11 – Climatic Atlas of the Sea of Azov 2008 (1 disc set) (NCEI Accession 0098574). NOAA National Centers for Environmental Information. Dataset. Available at: https://www.ncei.noaa.gov/archive/accession/0098574 [Accessed: 26 February 2022].
- Matishov, G.G., Sherman, K. and Levitus, S., eds., 2014. Atlas of Climatic Changes in Nine Large Marine Ecosystems of the Northern Hemisphere (1827-2013). NOAA Atlas NESDIS 78. Washington D.C., 131 p. doi:10.7289/V5Q52MK5
- Ch. Sheppard, ed., 2019. World Seas: An Environmental Evaluation. Volume I Europe. The Americas and West Africa. 2nd Edition. Academic Press, 912 p. https://doi.org/10.1016/C2015-0-04330-1
- Ch. Sheppard, ed., 2019. World Seas: An Environmental Evaluation. Volume II: the Indian Ocean to the Pacific. 2nd Edition. Academic Press, 932 p. https://doi.org/10.1016/C2015-0-04332-5
- Ch. Sheppard, ed., 2019. World Seas: an Environmental Evaluation. Volume III: Ecological Issues and Environmental Impacts. 2nd Edition. Academic Press, 666 p. https://doi.org/10.1016/C2015-0-04336-2
- Wright, D.J., Haymon, R.M., Macdonald, K.C. and Goodchild, M., 1994. The Power of Geographic Information Systems (GIS) for Oceanography: Implications for Spatio-Temporal Modelling of Mid-Ocean Ridge Evolution. Conference Paper. In: Oceanograhy Society, 1994. Proceedings of The Oceanography Society Pacific Basin Meeting. Honolulu, Hawaii, pp. 66.
- Ouellette, W. and Getine, W., 2016. Remote Sensing for Marine Spatial Planning and Integrated Coastal Areas Management: Achievements, Challenges, Opportunities and Future Prospects. Remote Sensing Applications: Society and Environment, 4, pp. 138-157. https://doi.org/10.1016/j.rsase.2016.07.003
- Fingas, M., 2019. Remote Sensing for Marine Management. In: Ch. Sheppard, ed., 2019. World Seas: an Environmental Evaluation. Volume III: Ecological Issues and Environmental Impacts. 2nd Edition. Academic Press, pp. 103-119. https://doi.org/10.1016/B978-0-12-805052-1.00005-X
- Anderson, T.R., 2010. Progress in Marine Ecosystem Modelling and the “Unreasonable Effectiveness of Mathematics”. Journal of Marine Systems, 81(1–2), pp. 4-11. https://doi.org/10.1016/j.jmarsys.2009.12.015
- Robson, B.J., 2014. When Do Aquatic Systems Models Provide Useful Predictions, What is Changing, and What is Next? Environmental Modelling & Software, 61, pp. 287-296. https://doi.org/10.1016/j.envsoft.2014.01.009
- Tyutyunov, Y.V. and Titova, L.I., 2020. From Lotka–Volterra to Arditi–Ginzburg: 90 Years of Evolving Trophic Functions. Biology Bulletin Reviews, 10(3), pp. 167- 185. https://doi.org/10.1134/S207908642003007X
- Prieß, M., Koziel, S. and Slawig, T., 2013. Marine Ecosystem Model Calibration with Real Data Using Enhanced Surrogate-Based Optimization. Journal of Computational Science, 4(5), pp. 423-437. https://doi.org/10.1016/j.jocs.2013.04.001