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Fruit flies are a major pest worldwide for fruit producing industries. Incursions into fly free areas usually occurs via infested fruit; however, little is reported about the size of a propagule to start a new establishment. Propagule pressure is an important predictor of the probability that an invasive species will establish a breeding population. Recently, individual-based model (IBM) became a valuable modelling tool for exploring invasive species. Here, we developed a spatially-explicit individual-based model (IBM) specifically parameterized for the Queensland fruit fly (Qfly) (Bactrocera tryoni Froggatt), a major horticultural pest species in Australia and a major quarantine concern worldwide. Usually, new establishments or incursions originate from the introduction of infested fruit and larvae must progress through several stages to become sexually mature adults. For a Qfly incursion to establish a breeding population, flies must avoid predators and survive long enough to become reproductively mature, find a mate, and find ripening fruit. Additionally, their offspring must survive and successfully reproduce. The IBM model simulated release of a fixed number of flies into a heterogeneous environment of varying suitability. We conducted simulations to delineate the contributions of demographic stochasticity and Allee effects (finding a mate in a spatial environment) on establishment probability. Our model delineated several key influential factors, especially tree density, extrinsic mortality and mating range. We performed sensitivity analyses to identity which biological and ecological mechanisms strongly affect establishment probability. Integrating the model's findings with information on transport of infested fruit helps explain why Qfly incursions are common, but yet most fail to establish. Our model predicted that circa 16 and 50 flies were required for a 50% and 99% chance of establishment respectively. Additionally, our model predicted the mating distance for Qfly was 16.1 m. The mean daily dispersal distance was 30 m. We discuss how this knowledge might be used to better manage Qfly by alterations in surveillance and male annihilation technique. • We used a spatially-explicit individual-based model (IBM) specifically parameterized for the Queensland fruit fly (Qfly). • Our model predicted that circa 16 and 50 flies were required for a 50% and 99% chance of establishment respectively. • Our model predicted the mating distance for Qfly was 16.1 m. • We predicted that the mean daily dispersal distance was 30 m. • Growers can modify their landscapes and control measures to prevent the establishment of Qfly breeding populations. [ABSTRACT FROM AUTHOR]