Propagule pressure in the presence of uncertainty: extending the utility of proxy variables with hierarchical models

Summary Species invasions depend on the abundance and rate at which organisms are introduced to new localities, known as propagule pressure. Due to the challenges of measuring propagule pressure, proxy variables are often used; however, untested proxy variables may obscure the role of propagule pressure vs. ecological factors that facilitate invasion, leading to uncertainty about the invasion process and confounding management response. To generate absolute estimates of propagule pressure and facilitate meaningful comparison among pathways of species introduction, we extend proxy variables by combining ecological and global trade data with hierarchical statistical models. We derive absolute propagule pressure with probability distribution functions (propagule size: the probability of introducing n propagules per event; and overall propagule pressure: the probability of introducing n propagules per year) and, based on these projections, evaluate the performance of ballast water volume (m 3 ) as a common proxy variable. Hindcast accuracy of ballast water volume was low but strongly scale‐dependent, exhibiting poor accuracy ( R 2  = 0·058) at small scales and only marginal accuracy at large scales (overall R 2  = 0·169). As a result, conclusions about propagule pressure are likely to be biased based on the ballast volume proxy, as may be conclusions about species invasion when ballast water volume has been used. Irrespective of geographic pathway, estimated propagule sizes demonstrated extreme leptokurtosis and long right tails, with maximum values between 131‐fold and 2966‐fold greater than median values. These characteristics signify a subset of introduction events involving extreme propagule abundance that may provide opportunity to overcome Allee thresholds or marginal environmental conditions. Developing meaningful propagule supply functions is critical to resolve the role of propagule pressure within the invasion process and test hypotheses about species colonization at landscape scales. By joining absolute propagule pressure with existing theory about species extinction, the expected ecological outcome of environmental policy to manage propagule pressure can be estimated within a statistical framework.