Evaluation of stochastic gravity model selection for use in estimating non-indigenous species dispersal and establishment

Predicting dispersal of nonindigenous species (NIS) is an essential component of risk analysis and management, as preventative measures are most readily applied at this stage of the invasion sequence. Gravity models provide one of the most useful techniques available to model dispersal of nonindigenous invasive species (NIS) across heterogeneous landscapes, as these models are able to capture transport patterns of recreational boaters who are dominant vectors responsible for aquatic NIS dispersal. Despite the widespread use of gravity models in forecasting biological invasions, different classes of gravity models have not been evaluated regarding their comparative ability to capture recreational transport patterns and subsequent use in predicting NIS establishment. Here we evaluate model selection between unconstrained, total-flowconstrained, production-constrained and doubly-constrained stochastic gravity models to assess dispersal of the spiny waterflea Bythotrephes between Ontario lakes. Differences between the models relate to the amount of data required and constraints under which calculations of source/destination interactions are made. For each class of gravity model, we then estimated the probability of a lake having established Bythotrephes populations by modeling the relationship between empirical presence/absence data and inbound recreational traffic (i.e. propagule pressure) via boosted regression. The unconstrained gravity model provided the best fit to observed traffic patterns of recreational boaters. However, when output from the gravity models was used to predict Bythotrephes establishment, the doubly-constrained gravity model provided the strongest relationship between inbound recreational traffic and observed Bythotrephes presence/absence, followed by the production-constrained model. Our results indicate production-constrained gravity models offer an acceptable balance between modeling recreational boater traffic and their utility to estimate establishment probabilities.