Many ecosystems suffer systemwide outbreaks of damaging species propagating from primary outbreak sites. Connectivity patterns can identify parts of the ecosystem that help turn local outbreaks into a systemwide contagion through a series of transmission events. Here, we show that patterns of larval connectivity among reefs can help explain periodic crown-of-thorns starfish (COTS) epidemics across the Great Barrier Reef (GBR). We simulated potential dispersal of COTS larvae to obtain a connectivity network of coral reefs across the entire GBR. Network analysis revealed areas of high local connectivity where any outbreaks could be amplified locally, as well as those areas with potential to cause large-scale epidemics with ecosystem-wide impacts. We find that the regions where COTS epidemics are known to originate are predictable from their high local and systemwide connectivity. Extensive larval exchanges among reef clusters in these regions can start a chain reaction of COTS population build-up. The same regions also have high potential to reach and affect other parts of the GBR, thereby maximizing the likelihood that any outbreaks would eventually propagate throughout the ecosystem. Hydrodynamic properties and geography of the GBR make it vulnerable to COTS epidemics. Using network analysis to identify regions with high-risk high-impact sources could help control these devastating events in future. Synthesis and applications. The observed centre of origin for COTS epidemics (the Cooktown–Cairns region) can be predicted from its elevated short- and long-range levels of larval connectivity. Connectivity analysis of per-reef risks provides spatially explicit targets to guide surveillance and control measures that might help curtail COTS epidemics through prioritization of highly connected reefs. The analytical approach developed here for COTS connectivity can also be applied to identify well-connected patches and regions in other interconnected ecological systems.