A nonlinear multispecies fisheries model for Namibian coastal waters: Implications for food security and marine ecosystem resilience
DOI:
https://doi.org/10.58524/td7hp091Keywords:
Benguela Current Ecosystem, Ecosystem-based Fisheries Management, Harvesting Dynamics, Multispecies Fisheries Model, Stability AnalysisAbstract
Background: The Benguela Current Large Marine Ecosystem supports major fisheries that are essential to Namibia's food security and economy. The dynamics of Cape hake, horse mackerel, and sardine are strongly influenced by ecological interactions and harvesting, highlighting the need for mathematically rigorous multispecies fisheries models.
Aims: This study aims to develop an analytically tractable nonlinear multispecies fisheries model that describes the ecological interactions among Cape hake, horse mackerel, and sardine under harvesting pressure, while providing a rigorous mathematical framework for evaluating ecosystem stability and sustainable fisheries management.
Method: The proposed model integrates logistic growth, predator–prey interactions, interspecific competition, and species-specific harvesting mortality. Qualitative analysis is performed using nonlinear dynamical systems theory to establish existence and uniqueness, positivity, boundedness, equilibrium conditions, and local and global stability. Local stability is analyzed using linearization and the Routh–Hurwitz criterion, whereas global stability is established through a Volterra-type Lyapunov function and LaSalle’s Invariance Principle. In addition, a harvesting-rate estimation framework based on fisheries catch, effort, and biomass data is formulated to facilitate future model calibration.
Result: The mathematical analysis establishes the well-posedness of the proposed model and derives analytical conditions for biologically feasible coexistence and system stability. Numerical simulations validate the theoretical results by demonstrating convergence toward a stable coexistence equilibrium under biologically realistic parameter values. The simulations further show that increasing harvesting intensity reduces equilibrium biomass and ecosystem resilience, while excessive exploitation of sardine populations indirectly destabilizes higher trophic levels by reducing prey availability for predator species.
Conclusion: The proposed model provides a mathematically rigorous framework for analyzing multispecies fisheries dynamics and offers quantitative insights into the ecological consequences of harvesting. The results support ecosystem-based fisheries management by providing a scientific basis for evaluating sustainable harvesting strategies, establishing science-based catch quotas, identifying precautionary harvesting thresholds, and informing evidence-based policies to strengthen the long-term resilience and sustainability of Namibia's marine fisheries.
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