A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. But many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbor on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that with increasing variability, the Allee effect increasingly promotes genetic diversity in successful populations. Successful Allee-effect populations with highly variable population dynamics escape rapidly from the region of small population sizes and do not linger around the critical population size. Therefore, they are exposed to relatively little genetic drift. It is also conceivable, however, that an Allee effect itself leads to an increase in offspringnumber variation. In this case, successful populations with an Allee effect can exhibit less genetic diversity despite growing faster at small population sizes. Unlike in many classical population genetics models, the role of offspring-number variation for the population genetic consequences of the Allee effect cannot be accounted for by an effective-population-size correction. Thus, our results highlight the importance of detailed biological knowledge, in this case on the probability distribution of family sizes, when predicting the evolutionary potential of newly founded populations or when using genetic data to reconstruct their demographic history.T HE demographic Allee effect, a reduction in per-capita population growth rate at small population sizes (Stephens et al. 1999), is of key importance for the fate of both endangered and newly introduced populations and has inspired an immense amount of empirical and theoretical research in ecology (Courchamp et al. 2008). By shaping the population dynamics of small populations, the Allee effect should also strongly influence the strength of genetic drift they are exposed to and hence their levels of genetic diversity and evolutionary potential. In contrast to the well-established ecological research on the Allee effect, however, research on its population genetic and evolutionary consequences is only just beginning (Kramer and Sarnelle 2008;Hallatschek and Nelson 2008;Roques et al. 2012). In this study, we focus on the case in which the average population growth rate is negative below a certain critical population size. This phenomenon is called a strong demographic Allee effect (Taylor and Hastings 2005). Our goal is to quantify levels of genetic diversity in introduced populations that have successfully overcome such a strong demographic Allee effect. Of course, the population genetic consequences of the Allee effect could depend on a variety of factors, some of which we investigated in a companion article ). Here we f...