Natural selection has almost certainly shaped many evolutionary trajectories documented in fossil lineages, but it has proven difficult to demonstrate this claim by analyzing sequences of evolutionary changes. In a recently published and particularly promising test case, an evolutionary time series of populations displaying armor reduction in a fossil stickleback lineage could not be consistently distinguished from a null model of neutral drift, despite excellent temporal resolution and an abundance of indirect evidence implicating natural selection. Here, we revisit this case study, applying analyses that differ from standard approaches in that: (1) we do not treat genetic drift as a null model, and instead assess neutral and adaptive explanations on equal footing using the Akaike Information Criterion; and (2) rather than constant directional selection, the adaptive scenario we consider is that of a population ascending a peak on the adaptive landscape, modeled as an Orstein–Uhlenbeck process. For all three skeletal features measured in the stickleback lineage, the adaptive model decisively outperforms neutral evolution, supporting a role for natural selection in the evolution of these traits. These results demonstrate that, at least under favorable circumstances, it is possible to infer in fossil lineages the relationship between evolutionary change and features of the adaptive landscape.