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Effective management of invasive species requires robust projections of how alternative management strategies influence long-term invasion outcomes, required effort, and associated trade-offs. We used a spatially explicit population model, linked with empirical data on aerial culling efficiency, to project (from 2023 to 2060) alternative management scenarios for limiting the spread and establishment of an invasive fallow deer ( Dama dama ) population in a high-value conservation area, the Walls of Jerusalem National Park (WJNP), Tasmania, Australia. We compared six feasible aerial culling scenarios that varied in the frequency (annual, biennial, or five-yearly) and spatial extent (broad versus concentrated management zones) of control, relative to a baseline scenario with no future management. Scenarios were evaluated in terms of their ability to limit deer occupancy and abundance within the WJNP, the cumulative presence of deer over time, the amount of management effort required, and population-level animal welfare outcomes. All management scenarios reduced deer invasion into the WJNP relative to no management, but strategies that applied culling across a broad spatial extent were consistently more effective than those targeting only high-density source areas. More frequent culling further improved outcomes, although gains were modest relative to changes in spatial extent. Strategies that combined broad-scale culling with annual or biennial frequency achieved the best balance between reducing invasion pressure and limiting management effort, while also resulting in fewer deer being culled overall. Complete exclusion of deer from the WJNP was achievable only under a more intensive strategy involving annual culling across a substantially expanded area, but this required a nearly four-fold increase in effort compared to the scenarios aimed at minimising, rather than eliminating, invasion. Our results highlight trade-offs between management effectiveness, effort, and welfare outcomes, and demonstrate how spatial population models coupled with operational data can support practical, evidence-based decisions for managing invasive species.