Predicting how increasing rates of global trade will result in new establishments of potentially damaging invasive species is a question of critical importance to the development of national and international policies aimed at minimizing future invasions. Centuries of historical movement and establishment of invading species may have depleted the supply of species available for future invasions, and it has been suggested that the problem of invasions will diminish as a result of this. However, the extent to which source pool depletion affects future invasions remains unclear. Here we describe a mechanistic model that captures the simultaneous effects of depletion of source species pools along with increases in pathway rates (e.g. imports) to predict future numbers of new invasions. We assume that the distribution of species abundance within invasion pathways is positively skewed, which is modelled using a log-normal distribution. Given their high propagule pressure, the most abundant species are likely to invade first, while the many rare species are likely to invade only under high pathway volumes. We apply this model to the case study of bark beetle, Scolytinae, invasions in the USA. Source species pools in Europe and Asia (225 and 655 species of Scolytinae, respectively) are much larger than numbers that have historically established (16 and 32). Parameterization of the model indicates a highly skewed species abundance distribution in the pathway and this is confirmed by species frequencies in port inspection records, thus explaining why only a small fraction of species has historically invaded. Forecasts from the model indicate that with increasing rates of imports, more species from these regions are likely to invade in the future despite the depletion of the most abundant species from source species pools. Previous statistical models tend to underestimate future establishments in the presence of increasing import rates due to their failure to account for key underlying mechanisms. Policy implications. The mechanistic model developed here is widely applicable for predicting future invasions of all taxa and provides insights into how increases in rates of imports counteract the species pool depletion effect, resulting in the continued establishment of new species.