Assessing species establishment risk is an important task used for informing biosecurity activities aimed at preventing biological invasions. Propagule pressure is a major contributor to the probability of invading species establishment; however, direct assessment of numbers of individuals arriving is virtually never possible. Inspections conducted at borders by biosecurity officials record counts of species (or higher-level taxa) intercepted during inspections, which can be used as proxies for arrival rates. Such data may therefore be useful for predicting species establishments, though some species may establish despite never being intercepted. We present a stochastic process-based model of the arrival-interception-establishment process to predict species establishment risk from interception count data. The model can be used to estimate the probability of establishment, both for species that were intercepted and species that had no interceptions during a given observation period. We fit the stochastic model to data on two insect families, Cerambycidae and Aphididae, that were intercepted and/or established in the United States or New Zealand. We also explore the effects of variation in model parameters and the inclusion of an Allee effect in the establishment probability. Although interception data sets contain much noise due to variation in inspection policy, interception effort and among-species differences in detectability, our study shows that it is possible to use such data for predicting establishments and distinguishing differences in establishment risk profile between taxonomic groups. Our model provides a method for predicting the number of species that have breached border biosecurity, including both species detected during inspections but also "unseen arrivals" that have never been intercepted, but have not yet established a viable population. These estimates could inform prioritization of different taxonomic groups, pathways or identification effort in biosecurity programs.

Faculty of Forestry and Wood Sciences Czech University of Life Sciences Prague 165 00 Praha 6 Suchdol Czech Republic

School of Forestry University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand

School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand

Scion Christchurch 8440 P O Box 29237 New Zealand

Swiss Federal Research Institute WSL Zürcherstrasse 111 8903 Birmensdorf Switzerland

Te Pūnaha Matatini The University of Auckland Private Bag 92019 Auckland 1142 New Zealand

USDA Forest Service Northern Research Station Morgantown West Virginia 26505 USA

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