Projecting future damage costs of non-native species using combined dynamical and cost-density equations.

Biological invasions threaten biodiversity, economic stability, and public health, exacerbated by intensive global trade and transport. The economic costs of these invasions have exceeded US$2 trillion globally and continue to increase. Although past invasion costs have been described across various contexts, there are few robust projections of future costs, limiting effective management planning. We developed a mathematical framework to project future economic damage caused by biological invasions, combining cost-density relationships with a density-time function based on logistic population growth. We tested the model on five well-documented non-native mammal species in Japan, a country with long-term, high-resolution invasion cost records and a well-characterized history of mammal introductions: Pallas' squirrel Callosciurus erythraeus, small Indian mongoose Herpestes javanicus, nutria Myocastor coypus, masked palm civet Paguma larvata, and raccoon Procyon lotor. Species-level cost-density relationships were characterized by two distinct forms: a high-density curve for M. coypus and P. lotor, where costs increase progressively with density but the rate of escalation slows at higher densities, and a high-threshold curve for C. erythraeus, H. javanicus, and P. larvata, where costs remain minimal until populations exceed a density threshold, after which they rise steeply. Our model projected accumulated costs to 2050 varying over several orders of magnitude, from US$0.43 million (H. javanicus) to US$88 million (P. larvata), with proportional increases ranging from ~15% (M. coypus) to ~78% (H. javanicus). Under business-as-usual management, we explicitly model damage-only costs, assuming a historically observed management trend. These projections should therefore be interpreted as maximum estimates. Our approach identifies thresholds beyond which damages escalate rapidly-costs begin to surge 40-80 years after the first record, with 90% of expected long-term damages incurred typically within 10-20 years. For managers, these results highlight the importance of timely interventions, underscoring the need for tailored management strategies considering species-specific dynamics, socioeconomic contexts, and the speed of cost escalation. Early-stage cost dynamics can project future trajectories of existing and emerging invasions, helping guide proactive management prioritization. Our projections equip policymakers and resource managers with improved foresight to anticipate and mitigate future economic burdens of non-native species across spatial scales and for different taxa.