Akademik Veri Yönetim Sistemi
BULLETIN OF BIOMATHEMATICS, cilt.4, sa.1, ss.131-159, 2026 (TRDizin)
In this study, a four-species predator–prey model representing a mesopredator-driven trophic structure in the Black Sea ecosystem, including the harvesting process, is developed and analyzed. The model involves anchovy (A), horse mackerel (H), bluefish (B), and Atlantic bonito (P). The model incorporates intraguild predation, logistic prey regulation, predator-dependent persistence, and proportional harvesting at all trophic levels within a seasonal time window. Subsequent to non-dimensionalization, positivity, forward invariance, and uniform boundedness of solutions are established. The explicit derivation of all biologically feasible boundary and interior equilibria is a key highlight of the study. Local stability conditions are obtained via Jacobian spectral analysis and Routh–Hurwitz criteria, and a Volterra-type logarithmic Lyapunov function is constructed to establish asymptotic stability of the coexistence equilibrium within a positively invariant ordering region. In order to establish a connection between theoretical concepts and practical applications, annual harvesting data are converted into dimensionless pressure indices, and a constrained numerical calibration is performed. The calibrated regime is characterized by a strictly positive and locally asymptotically stable coexistence equilibrium. Continuation analysis with respect to harvesting intensities reveals asymmetric trophic sensitivity: while the anchovy–horse mackerel axis remains structurally robust, bluefish and bonito exhibit significantly larger long-run variability under harvest perturbations. The results establish explicit stability thresholds for multi-species fisheries under harvesting and show that selective exploitation can drive trophic redistribution without destabilizing coexistence. The framework provides a rigorous, management-relevant approach to modeling harvested marine ecosystems.