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In some species, meiotic recombination is concentrated in small genomic regions. These “recombination hotspots” leave signatures in fine-scale patterns of linkage disequilibrium, raising the prospect that the genomic landscape of hotspots can be characterized from sequence variation. This approach has led to the inference that hotspots evolve rapidly in some species, but are conserved in others. Historic demographic events, such as population bottlenecks, are known to affect patterns of linkage disequilibrium across the genome, violating population genetic assumptions of this approach. Although such events are prevalent, demographic history is generally ignored when making inferences about the evolution of recombination hotspots. To determine the effect of demography on the detection of recombination hotspots, we use the coalescent to simulate haplotypes with a known recombination landscape. We measure the ability of popular linkage disequilibrium-based programs to detect hotspots across a range of demographic histories, including population bottlenecks, hidden population structure, population expansions, and population contractions. We find that demographic events have the potential to greatly reduce the power and increase the false positive rate of hotspot discovery. Neither the power nor the false positive rate of hotspot detection can be predicted without also knowing the demographic history of the sample. Our results suggest that ignoring demographic history likely overestimates the power to detect hotspots and therefore underestimates the degree of hotspot sharing between species. We suggest strategies for incorporating demographic history into population genetic inferences about recombination hotspots.