Variation in skull size was investigated for three species of rats (kiore –Rattus exulans Peale; ship rat –R. rattus L.; Norway rat –R. norvegicus Berkenhout) which were introduced by humans to various islands in New Zealand and other Pacific islands. Data from seventy-one islands and 882 specimens are examined for evidence of the effects of latitude, island size and interspecific competition among rats and the house mouse (Mus musculus L.) on skull size, using multiple regressions. For R. exulans, skull size increases with latitude as predicted by Bergmann's rule, but no such effect occurs for the other two rats. There was a positive relationship between island size and the number of species inhabiting it, and some species combinations were more likely to occur than others. For example, R. exulans and R. norvegicus were more likely to occur together, while R. rattus and R. exulans were rarely sympatric. R. exulans and R. rattus skull size was negatively correlated with the number of other rodents on the same island. R. exulans skull size increased on smaller islands in some island groups, perhaps because increased density and consequent increased intraspecific competition on smaller islands favours increased body size. This effect is more pronounced in tropical islands (Solomon islands), than in subtropical ones (Hawaiian islands) and less so in temperate New Zealand. Collectively the data demonstrate that rapid evolution of body size in predictable directions can follow within 150 years of the introduction of species to new receiving communities.