The degree and direction of morphological change in invasive species with a long history of introduction are insufficiently known for a larger scale than the archipelago or island group. Here, I analyse data for 105 island populations of Polynesian rats, Rattus exulans, covering the entirety of Oceania and Wallacea to test whether body size differs in insular populations and, if so, what biotic and abiotic features are correlated with it. All insular populations of this rat, except one, exhibit body sizes up to twice the size of their mainland conspecifics. Body size of insular populations is positively correlated with latitude, consistent with thermoregulatory predictions based on Bergmann's rule. Body size is negatively correlated with number of co-occurring mammalian species, confirming an ecological hypothesis of the island rule. The largest rats are found in the temperate zone of New Zealand, as well as on mammalian species-poor islands of Polynesia and the Solomon Islands. Carnivory in the form of predation on nesting seabird colonies seems to promote 1.4- to 1.9-fold body size increases.