The detrimental effects of the introduced ship rat on bird species on the Lavezzi Mediterranean archipelago has led to the decision to eradicate the rodent from the main island, Lavezzu (73 ha), as well as from several neighbouring islets. A genetic study using eight microsatellite markers has revealed some of the dynamics of this rat population. First, it has been shown that the rat population was genetically stable (no departure from Hardy-Weinberg equilibrium and no linkage disequilibrium) and as suggested by paleontological data, established for a long time. This information is encouraging in term of viability of the eradication campaign in the long term, even if rare immigration events cannot be excluded. Second, this study shows that rats are likely to swim between the main island and the islets quite regularly since no clear genetic differentiation has been detected between them. This result is quite surprising since the ship rat is not known for its swimming abilities. Third, a cryptic genetic structure has been detected on the main island, with the north peninsula differentiated from the rest. This result correlates the observation of particular predation behaviours only observed in this part of the island. Finally, evolutionary hypotheses (e.g., dispersal limitation, emergence of family groups, local adaptation) are discussed to explain the genetic patterns observed and the population functioning inferred. These results should be of particular interest to wildlife managers concerned with rat eradications, and also provide clear insights into the study of other biological invasions.