The characteristics of spread for an invasive species should influence how environmental authorities or government agencies respond to an initial incursion. High-resolution predictions of how, where, and the speed at which a newly established invasive population will spread across the surrounding heterogeneous landscape can greatly assist appropriate and timely risk assessments and control decisions. The Argentine ant (Linepithema humile) is a worldwide invasive species that was inadvertently introduced to New Zealand in 1990. In this study, a spatially explicit stochastic simulation model of species dispersal, integrated with a geographic information system, was used to recreate the historical spread of L. humile in New Zealand. High-resolution probabilistic maps simulating local and human-assisted spread across large geographic regions were used to predict dispersal rates and pinpoint at-risk areas. The spatially explicit simulation model was compared with a uniform radial spread model with respect to predicting the observed spread of the Argentine ant. The uniform spread model was more effective predicting the observed populations early in the invasion process, but the simulation model was more successful later in the simulation. Comparison between the models highlighted that different search strategies may be needed at different stages in an invasion to optimize detection and indicates the influence that landscape suitability can have on the long-term spread of an invasive species. The modeling and predictive mapping methodology used can improve efforts to predict and evaluate species spread, not only in invasion biology, but also in conservation biology, diversity studies, and climate change studies.