We investigate a fishery population model subject to periodic harvesting and interspecific predation, where harvesting alternates between open and closed seasons and predation follows a Holling type II response. When formulated as a switching dynamical system, the model admits a critical closed-season threshold \(\bar{T}^{*}\) that governs the long-term persistence or extinction of the population. If the closed season exceeds \(\bar{T}^{*}\) , the population recovers and persists; in contrast, when the closed season is insufficient and a critical parameter condition is satisfied ( \(r\ge \tfrac{Kmb}{a^{2}}\) ) the population is driven to extinction due to overharvesting. Numerical simulations support the theoretical findings and further reveal complex dynamical behaviors in the complementary parameter regime \(r< \tfrac{Kmb}{a^{2}}\) , where analytical characterization remains challenging. Moreover, neglecting predator effects leads to an underestimation of both habitat-size and closed-season thresholds, potentially resulting in incorrect assessments of the conditions required for population persistence. These results provide a theoretical basis for sustainable fishery management and highlight the importance of choosing appropriate closed-season durations to balance conservation and harvesting.
