Abstract1. Many alien taxa are known to cause socio-economic impacts by affecting the different constituents of human well-being (security; material and non-material assets; health; social, spiritual and cultural relations; freedom of choice and action).

Some alien species cause substantial impacts, yet most are innocuous. Given limited resources, forecasting risks from alien species will help prioritise management. Given that risk assessment (RA) approaches vary widely, a synthesis is timely to highlight best practices. We reviewed quantitative and scoring RAs, integrating > 300 publications into arguably the most rigorous quantitative RA framework currently existing, and mapping each study onto our framework, which combines Transport, Establishment, Abundance, Spread and Impact (TEASI). Quantitative models generally measured single risk components (78% of studies), often focusing on Establishment alone (79%). Although dominant in academia, quantitative RAs are underused in policy, and should be made more accessible. Accommodating heterogeneous limited data, combining across risk components, and developing generalised RAs across species, space and time without requiring new models for each species may increase attractiveness for policy applications. Comparatively, scoring approaches covered more risk components (50% examined > 3 components), with Impact being the most common component (87%), and have been widely applied in policy (> 57%), but primarily employed expert opinion. Our framework provides guidance for questions asked, combining scores and other improvements. Our risk framework need not be completely parameterised to be informative, but instead identifies opportunities for improvement in alien species RA.

The number of invasive alien species is increasing and so are the impacts these species cause to the environment and economies. Nevertheless, resources for management are limited, which makes prioritization unavoidable. We present a prioritization framework which can be useful for decision makers as it includes both a scientific impact assessment and the evaluation of impact importance by affected stakeholders. The framework is divided into five steps, namely 1) stakeholder selection and weighting of stakeholder importance by the decision maker, 2) factual description and scoring of changes by scientists, 3) evaluation of the importance of impact categories by stakeholders, 4) calculation of weighted impact categories and 5) calculation of final impact score and decision making. The framework could be used at different scales and by different authorities. Furthermore, it would make the decision making process transparent and retraceable for all stakeholders and the general public.

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