Development of statistical tests to detect selection (strictly speaking, departures from the neutral equilibrium model) has been an active area of research in population genetics over the last 15 years. With the advent of dense genome sequencing of many domesticated crops, some of this machinery (which heretofore has been largely restricted to human genetics and evolutionary biology) is starting to be applied in the search for genes under recent selection in crop species. We review the population genetics of signatures of selection and formal tests of selection, with discussions as to how these apply in the search for domestication and improvement genes in crops and for adaptation genes in their wild relatives. Plant domestication has specific features, such as complex demography, selfing, and selection of alleles starting at intermediate frequencies, that compromise many of the standard tests, and hence the full power of tests for selection has yet to be realized.
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