1. The evolutionary advantages that have driven the evolution of sex are still very much debated, and a number of benefits of parthenogenesis over sexual reproduction have been proposed. In particular, parthenogenetic individuals are thought to exhibit higher probabilities of establishment following arrival in new, isolated habitats such as islands. 2. One notable example of parthenogenesis occurring in islands is the damselfly Ischnura hastata, an American species that has colonised the Azores archipelago, where the populations consist only of females. This is the only known example of parthenogenesis within the insect order Odonata. 3. Here, two island populations of I. hastata were studied, one in the Galapagos and one in Cuba, to test whether island colonisation is consistently associated with parthenogenesis in this species. Field capture–mark–recapture studies and laboratory rearing of field-collected eggs were undertaken in both areas. 4. Sex ratios in the field were found to be heavily female-biased among mature individuals; however, fertility rates of field-collected eggs were high, and the sex ratios in the laboratory did not differ from 1 : 1. Data from laboratory rearing showed that shorter larval development times and shorter adult life spans in males result in protandry, which might explain the skewed sex ratios in the field. 5. These findings are consistent with sex differences in key demographic parameters which could predispose I. hastata to parthenogenesis. However, the Azores population of I. hastata remains the only documented case of asexual reproduction in this insect group.