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Invasive species usually go through a period of reduced genetic variability due to a bottleneck. The genetic constitution of an invading population should therefore reflect the time since invasion and the number of introduction events. We studied genetic population structure of three rat species occurring sympatrically on the island of Futuna (46 km2), where they were introduced recently ( R attus rattus), 80-170 years ago ( R . norvegicus) and about 3000 years ago ( R . exulans). From 2007 to 2012, we trapped 3900 rats during a rodent regulation programme over 20 000 trap nights and took 565 rat tissue samples for genetic analyses. By examining genetic variation and spatial distribution of genetic resemblance, we evaluated the consequences of the time after introduction for genetic population structure. Observed heterozygosity, expected heterozygosity, number of alleles and allelic richness generally increased with increasing length of time a species was introduced to the island. The species with longer invasion history had also higher spatial admixture. However, in R . norvegicus, the observed heterozygosity was lower and inbreeding higher than expected by the invasion history. We relate this with the assumption that this species was introduced once or a few times and in low numbers, while R . exulans was intentionally introduced many times by Polynesian navigators and R . rattus had a high chance of being introduced on multiple occasions in recent times. [ABSTRACT FROM AUTHOR]