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Introduced and geographically expanding populations experience similar eco‐evolutionary challenges, including founder events, genetic bottlenecks, and novel environments. Theory predicts that reduced genetic diversity resulting from such phenomena limits the success of introduced populations. Using 1900 SNPs obtained from restriction‐site‐associated DNA sequencing, we evaluated hypotheses related to the invasion history and connectivity of an invasive population of Tench (Tinca tinca), a Eurasian freshwater fish that has been expanding geographically in eastern North America for three decades. Consistent with the reported history of a single introduction event, our findings suggest that multiple introductions from distinct genetic sources are unlikely as Tench had a small effective population size (~114 [95% CI = 106–123] individuals), no strong population subdivision across time and space, and evidence of a recent genetic bottleneck. The large genetic neighbourhood size (220 km) and weak within‐population genetic substructure suggested high connectivity across the invaded range, despite the relatively large area occupied. There was some evidence for a small decay in genetic diversity as the species expanded northward, but not southward, into new habitats. As eradicating the species within a ~112 km radius would be necessary to prevent recolonization, eradicating Tench is likely not feasible at watershed—and possibly local—scales. Management should instead focus on reducing abundance in priority conservation areas to mitigate adverse impacts. Our study indicates that introduced populations can thrive and exhibit relatively high levels of genetic diversity despite severe bottlenecks (<1.5% of the ancestral effective population size) and suggests that landscape heterogeneity and population demographics can generate variability in spatial patterns of genetic diversity within a single range expansion. [ABSTRACT FROM AUTHOR]