When selection is acting on a large genetically diverse population, beneficial alleles increase in frequency. This fact can be used to map quantitative trait loci by sequencing the pooled DNA from the population at consecutive time points and observing allele frequency changes. Here, we present a population genetic method to analyze time series data of allele frequencies from such an experiment. Beginning with a range of proposed evolutionary scenarios, the method measures the consistency of each with the observed frequency changes. Evolutionary theory is utilized to formulate equations of motion for the allele frequencies, following which likelihoods for having observed the sequencing data under each scenario are derived. Comparison of these likelihoods gives an insight into the prevailing dynamics of the system under study. We illustrate the method by quantifying selective effects from an experiment, in which two phenotypically different yeast strains were first crossed and then propagated under heat stress (Parts L, Cubillos FA, Warringer J, et al. [14 co-authors]. 2011. Revealing the genetic structure of a trait by sequencing a population under selection. Genome Res). From these data, we discover that about 6% of polymorphic sites evolve nonneutrally under heat stress conditions, either because of their linkage to beneficial (driver) alleles or because they are drivers themselves. We further identify 44 genomic regions containing one or more candidate driver alleles, quantify their apparent selective advantage, obtain estimates of recombination rates within the regions, and show that the dynamics of the drivers display a strong signature of selection going beyond additive models. Our approach is applicable to study adaptation in a range of systems under different evolutionary pressures.