Mathematical Modelling of the Bioproductivity of a Shallow Water Body under Sudden Depression Caused by Scyphozoan Jellyfish

Introduction. The relevance of this study is determined by the need for a quantitative assessment of the negative impact of mass outbreaks of scyphozoan jellyfish (Aurelia aurita and Rhizostomeae) on the bioresources of the Azov Sea, which is subjected to a complex combination of anthropogenic pressures. The theoretical framework of the research is based on the concept of trophic interactions and biological invasions in marine ecosystems. The aim of this study is to develop a mathematical model of the dynamics of the fish community in the Azov Sea that accounts for both competitive and predatory pressure exerted by jellyfish, in order to identify critical biomass thresholds leading to the depression of commercial fish stocks.
Materials and Methods. To investigate the influence of scyphozoan jellyfish on the bioresources of the Azov Sea, a mathematical model of biological kinetics was employed as the primary research tool. The model describes the dynamics of three key ecosystem components (zooplankton, fish, and jellyfish), incorporating mechanisms of competition and predation. The research material consists of a system of theoretical equations with appropriate interaction parameters and initial and boundary conditions.
Results. Numerical simulations demonstrated that under environmental conditions typical of the summer period in the Azov Sea (elevated water temperature and eutrophication), an increase in scyphozoan jellyfish biomass by more than threefold during July–August leads to an abrupt shift of the ecosystem to an alternative stable state dominated by jellyfish. This transition is driven by the combined effects of intense competition for zooplankton and direct predation by jellyfish on the early life stages of fish, and is accompanied by a critical reduction in food availability, which suppresses the recovery of commercial fish populations.
Discussion. The results confirm the high ecological significance of mass aggregations of scyphozoan jellyfish and provide a quantitative justification for the risk of a regime shift in the Azov Sea ecosystem toward an alternative, less productive state dominated by jellyfish. From a theoretical perspective, the study contributes to the development of trophic interaction models that incorporate multiple impact mechanisms of invasive species.
Conclusion. The practical significance of this work lies in the fact that the proposed model serves as a tool for predictive assessment of bioresource status and for substantiating management decisions aimed at mitigating the consequences of eutrophication and biological invasions. Future research will focus on further refinement of the model, including the incorporation of seasonal and climatic factors to improve the accuracy of long-term forecasts.

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