  Many chemotactic bacteria inhabit environments in which chemicals appear as
localized pulses and evolve by processes such as diffusion and mixing. We show
that, in such environments, physical limits on the accuracy of temporal
gradient sensing govern when and where bacteria can accurately measure the cues
they use to navigate. Chemical pulses are surrounded by a predictable dynamic
region, outside which bacterial cells cannot resolve gradients above noise. The
outer boundary of this region initially expands in proportion to $\sqrt{t}$,
before rapidly contracting. Our analysis also reveals how chemokinesis - the
increase in swimming speed many bacteria exhibit when absolute chemical
concentration exceeds a threshold - may serve to enhance chemotactic accuracy
and sensitivity when the chemical landscape is dynamic. More generally, our
framework provides a rigorous method for partitioning bacteria into populations
that are "near" and "far" from chemical hotspots in complex, rapidly evolving
environments such as those that dominate aquatic ecosystems.
