Bacteria communicate using external chemical signals called autoinducers (AI) in a process known as quorum sensing (QS). QS efficiency is reduced by both limitations of AI diffusion and potential interference from neighboring strains. There is thus a need for predictive theories of how spatial community structure shapes information processing in complex microbial ecosystems. As a step in this direction, we apply a reaction-diffusion model to study autoinducer signaling dynamics in a single-species community as a function of the spatial distribution of colonies in the system. We predict a dynamical transition between a local quorum sensing (LQS) regime, with the AI signaling dynamics primarily controlled by the local population densities of individual colonies, and a global quorum sensing (GQS) regime, with the dynamics being dependent on collective intercolony diffusive interactions. The crossover between LQS to GQS is intimately connected to a trade-off between the signaling network's latency, or speed of activation, and its throughput, or the total spatial range over which all the components of the system communicate.