The risk of being relative about invasions

Waiting time formulations of invasive species risk assessment provide a useful tool for predicting where and when a species is likely to invade.  Estimating the invasion waiting time for a species at a single location requires knowing the individual probability of survival and the number of arriving individuals.  However, many risk assessment approaches are able to capture only one of these two inputs.  For example, models of invasion susceptibility are well documented for the mountain pine beetle system, but the dispersal mechanisms are les known.  With such limited information, the invasion waiting time cannot be directly estimated. We show how relative waiting times can be estimated and highlight the assumptions. For waiting time risk assessments, these assumptions are similarity in survival probabilities in the locations that are being compared and a low probability of invasion.  We apply relative waiting time formulations to the invasion of Chinese mitten crab into five US ports and show why the assumptions for this potential invader appear to be reasonable.  In contrast, we use a study of the invader scentless chamomile to show the limitations to predicting successful invasions from relative measures.  Additionally we show how waiting time invasion risk models may be validated.  Although having estimates of both the individual probability of survival and number of arriving individuals is more useful for managing invasions, it is sometimes necessary to apply relative measures. We believe this formulation will be useful to many studies where complete information is unavailable and the assumptions are met.