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Islands are global hotspots of both biodiversity and extinction. Invasive species are a primary threat, and the majority of islands have been invaded by more than one. Multispecies eradications are essential for conserving the biodiversity of these islands, but experience has shown that eradicating species at the wrong time can be disastrous for endemic species., Managers not only have to decide how to eradicate each invasive species, they need to determine when to target each species, and how to control multiple species with a limited budget. We use dynamic control theory to show that, when resources are limited, species should be eradicated in a particular order (an eradication schedule). We focus on a common invaded island ecosystem motif, where one invasive predator consumes two prey species (one endemic, one invasive), and managers wish to eradicate both invasives while ensuring the persistence of the endemic species. We identify the optimal eradication schedule for this entire class of problem. To illustrate the application of our solution, we also analyse a particular case study from California's Channel Islands., For any island ecosystem that shares this motif, managers should begin by allocating all of their resources towards invasive predator control. Only later should resources be shifted towards controlling the invasive prey. This shift should ideally be gradual, but an abrupt shift is very close to optimal. The Channel Islands case study confirms these findings. Targeting both species simultaneously is substantially suboptimal., We reach the robust conclusion that the same eradication schedule should be applied to any island with this ecosystem motif, even if the ecosystem contains different species to the Channel Islands case study., Synthesis and applications. Although very numerous, the world's invaded island ecosystems could be described by a limited range of invaded ecosystem motifs. By calculating robust optimal eradication schedules for each motif, the approach defined in this study could offer rapid decision-support for a large number of future conservation projects where specific data are scarce. [ABSTRACT FROM AUTHOR]