  We construct a reliable estimation of evolutionary parameters within the
Wright-Fisher model, which describes changes in allele frequencies due to
selection and genetic drift, from time-series data. Such data exists for
biological populations, for example via artificial evolution experiments, and
for the cultural evolution of behavior, such as linguistic corpora that
document historical usage of different words with similar meanings. Our method
of analysis builds on a Beta-with-Spikes approximation to the distribution of
allele frequencies predicted by the Wright-Fisher model. We introduce a
self-contained scheme for estimating the parameters in the approximation, and
demonstrate its robustness with synthetic data, especially in the
strong-selection and near-extinction regimes where previous approaches fail. We
further apply to allele frequency data for baker's yeast (Saccharomyces
cerevisiae), finding a significant signal of selection in cases where
independent evidence supports such a conclusion. We further demonstrate the
possibility of detecting time-points at which evolutionary parameters change in
the context of a historical spelling reform in the Spanish language.
