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Detecting loci under selection is an important task in evolutionary biology. In conservation genetics detecting selection is key to investigating adaptation to the spread of infectious disease. Loci under selection can be detected on a spatial scale, accounting for differences in demographic history among populations, or on a temporal scale, tracing changes in allele frequencies over time. Here we use these two approaches to investigate selective responses to the spread of an infectious cancer--devil facial tumor disease (DFTD)--that since 1996 has ravaged the Tasmanian devil (Sarcophilus harrisii). Using time-series 'restriction site associated DNA' (RAD) markers from populations pre- and post DFTD arrival, and DFTD free populations, we infer loci under selection due to DFTD and investigate signatures of selection that are incongruent among methods, populations, and times. The lack of congruence among populations influenced by DFTD with respect to inferred loci under selection, and the direction of that selection, fail to implicate a consistent selective role for DFTD. Instead genetic drift is more likely driving the observed allele frequency changes over time. Our study illustrates the importance of applying methods with different performance optima e.g. accounting for population structure and background selection, and assessing congruence of the results.