In this talk I will outline a recent interdisciplinary effort to model and understand the spread of invasive copepods across lake networks in North America. This 5-year project, developed through the Canadian Aquatic Invasive Species Network (CAISN), tracked the invasion status of approximately 500 interconnected lakes in the Canadian shield. Here the invader, spiny waterflea, is spread by recreational boaters moving between the lakes. The water flea modifies the trophic structure of lake it encounters and has a major ecological impact. To understand spread we used a stochastic gravity model, parameterized by boater survey data. In this model, the number of trips linking lakes is a random variable whose magnitude is a nonlinear function of empirically measured quantities such as lake size and distance between lakes. In our work, the gravity model was used to infer the total propagule pressure experienced by each lake. This propagule pressure was then linked to an establishment model. The establishment model estimates the probability that a propagule will establish at a given lake, depending upon local physical and chemical conditions. Fitting our hybrid model to large datasets has been an interesting challenge. As I will show, our hybrid gravity/establishement modelling approach has proved to be very effective at determining which lakes become invaded as the invasion spreads across the complex network. This work is collaborative with Subhash Lele, Jim Muirhead, Alex Potapov and Norm Yan.