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Nonnative insects and pathogens pose major threats to forest ecosystems worldwide, greatly diminishing the ecosystem services trees provide. Given the high global diversity of arthropod and microbial species, their often unknown biological features or even identities, and their ease of accidental transport, there is an urgent need to better forecast the most likely species to cause damage. Several risk assessment approaches have been proposed or implemented to guide preventative measures. However, the underlying assumptions of each approach have rarely been explicitly identified or critically evaluated. We propose that evaluating the implicit assumptions, optimal usages, and advantages and limitations of each approach could help improve their combined utility. We consider four general categories: using prior pest status in native and previously invaded regions; evaluating statistical patterns of traits and gene sequences associated with a high impact; sentinel and other plantings to expose trees to insects and pathogens in native, nonnative, or experimental settings; and laboratory assays using detached plant parts or seedlings under controlled conditions. We evaluate how and under what conditions the assumptions of each approach are best met and propose methods for integrating multiple approaches to improve our forecasting ability and prevent losses from invasive pests. [ABSTRACT FROM AUTHOR]