MFDM (Maximum Frequency of Derived Mutations) is designed to reliably detect recent positive selection in a varying size population, even if you only have polymorphism data from a single locus (i.e. a very short piece of DNA).
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A new test for detecting recent positive selection that is free from the confounding impacts of demography.
Mol Biol Evol. 2011 Jan;28(1):365-75. doi: 10.1093/molbev/msq211.