No members of the genus Copitarsia are known to occur within the United States, but these taxa often arrive from Mexico and South America. A pathway analysis from Peru, for example, demonstrates that more than 17 mating pairs may escape into the wild of the United States at approximately the same time each year. Demographic and environmental stochasticity at the point of arrival lowers the probability of these individuals successfully founding a new population. We used the software @Risk to prepare a probabilistic projection matrix that characterizes variation and uncertainty in insect survivorship, development, and reproduction. This matrix was then used to forecast the minimum number of individuals needed for establishment to occur. Even under ideal temperature conditions, establishment is possible, but unlikely, if an inadequate number of mating pairs is introduced. The probability of successful establishment increases as the number of mating pairs increases. These models advance our understanding of the mechanics of species invasions and emphasize the uncertain outcome from the early stages of invasion.