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Although the impact of Pleistocene glacial cycles on the diversification of the tropical biota was once dismissed, increasing evidence suggests that Pleistocene climatic fluctuations greatly affected the distribution and population divergence of tropical organisms. Landscape genomic analyses coupled with paleoclimatic distribution models provide a powerful way to understand the consequences of past climate changes on the present-day tropical biota. Using genome-wide SNP data and mitochondrial DNA, combined with projections of the species distribution across the late Quaternary until the present, we evaluate the effect of paleoclimatic shifts on the genetic structure and population differentiation of Hypsiboas lundii, a treefrog endemic to the South American Cerrado savanna. Our results show a recent and strong genetic divergence in H. lundii across the Cerrado landscape, yielding four genetic clusters that do not seem congruent with any current physical barrier to gene flow. Isolation by distance (IBD) explains some of the population differentiation, but we also find strong support for past climate changes promoting range shifts and structuring populations even in the presence of IBD. Post-Pleistocene population persistence in four main areas of historical stable climate in the Cerrado seems to have played a major role establishing the present genetic structure of this treefrog. This pattern is consistent with a model of reduced gene flow in areas with high climatic instability promoting isolation of populations, defined here as " isolation by instability," highlighting the effects of Pleistocene climatic fluctuations structuring populations in tropical savannas.