Time series data of allele frequencies are a powerful resource for detecting and classifying natural and artificial selection. Ancient DNA now allows us to observe these trajectories in natural populations of long-lived species such as humans. Here, we develop a hidden Markov model to infer selection coefficients that vary over time. We show through simulations that our approach can accurately estimate both selection coefficients and the timing of changes in selection. Finally, we analyze some of the strongest signals of selection in the human genome using ancient DNA. We show that the European lactase persistence mutation was selected over the past 5,000 years with a selection coefficient of 2-2.5% in Britain, Central Europe and Iberia, but not Italy. In northern East Asia, selection at the ADH1B locus associated with alcohol metabolism intensified around 4,000 years ago, approximately coinciding with the introduction of rice-based agriculture. Finally, a derived allele at the FADS locus was selected in parallel in both Europe and East Asia, as previously hypothesized. Our approach is broadly applicable to both natural and experimental evolution data and shows how time series data can be used to resolve fine-scale details of selection. ### Competing Interest Statement The authors have declared no competing interest.
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