Natural decision-making often involves extended decision sequences in response to variable stimuli with complex structure. As an example, many animals follow odor plumes to locate food sources or mates, but turbulence breaks up the advected odor signal into intermittent filaments and puffs. This scenario provides an opportunity to ask how animals use sparse, instantaneous, and stochastic signal encounters to generate goal-oriented behavioral sequences. Here we examined the trajectories of flying fruit flies (Drosophila melanogaster) and mosquitoes (Aedes aegypti) navigating in controlled plumes of attractive odorants. While it is known that mean odor-triggered flight responses are dominated by upwind turns, individual responses are highly variable. We asked whether deviations from mean responses depended on specific features of odor encounters, and found that odor-triggered turns were slightly but significantly modulated by two features of odor encounters. First, encounters with higher concentrations triggered stronger upwind turns. Second, encounters occurring later in a sequence triggered weaker upwind turns. To contextualize the latter history dependence theoretically, we examined trajectories simulated from three normative tracking strategies. We found that neither a purely reactive strategy nor a strategy in which the tracker learned the plume centerline over time captured the observed history dependence. In contrast, infotaxis, in which flight decisions maximized expected information gain about source location, exhibited a history dependence aligned in sign with the data, though much larger in magnitude. These findings suggest that while true plume tracking is dominated by a reactive odor response it might also involve a history-dependent modulation of responses consistent with the accumulation of information about a source over multi-encounter timescales. This suggests that short-term memory processes modulating decision sequences may play a role in natural plume tracking.