Modelling the invasion and emergence of forest pests and pathogens (PnPs) is necessary to quantify the risk levels for forest health and provide key information for policy makers. Here, we make a short review of the models used to quantify the invasion risk of exotic species and the emergence risk of native species. Regarding the invasion process, models tackle each invasion phase, e.g. pathway models to describe the risk of entry, species distribution models to describe potential establishment, and dispersal models to describe (human-assisted) spread. Concerning the emergence process, models tackle each process: spread or outbreak. Only a few spread models describe jointly dispersal, growth, and establishment capabilities of native species while some mechanistic models describe the population temporal dynamics and inference models describe the probability of outbreak. We also discuss the ways to quantify uncertainty and the role of machine learning. Overall, promising directions are to increase the models’ genericity by parameterization based on meta-analysis techniques to combine the effect of species traits and various environmental drivers. Further perspectives consist in considering the models’ interconnection, including the assessment of the economic impact and risk mitigation options, as well as the possibility of having multi-risks and the reduction in uncertainty by collecting larger fit-for-purpose datasets.

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