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Personality variation, defined as among‐individual differences in behaviour that are repeatable across time and context, is widely reported across animal taxa. From an evolutionary perspective, characterising the amount and structure of this variation is useful since differences among individuals are the raw material for adaptive behavioural evolution. However, behavioural variation among individuals also has implications for more applied areas of evolution and ecology—from invasion biology to ecotoxicology and selective breeding in captive systems. Here, we investigate the structure of personality variation in the red cherry shrimp, Neocaridina heteropoda, a popular ornamental species that is readily kept and bred under laboratory conditions and is emerging as a decapod crustacean model across these fields, but for which basic biological, ecological and behavioural data are limited. Using two assays and a repeated measures approach, we quantify behaviours putatively indicative of shy–bold variation and test for sexual dimorphism and/or size‐dependent behaviours (as predicted by some state‐dependent models of personality). We find moderate‐to‐high behavioural repeatabilities in most traits. Although strong individual‐level correlations across behaviours are consistent with a major personality axis underlying these observed traits, the multivariate structure of personality variation does not fully match a priori expectations of a shy–bold axis. This may reflect our ecological naivety with respect to what really constitutes bolder, more risk‐prone, behaviour in this species. We find no evidence for sexual dimorphism and only weak support for size‐dependent behaviour. Our study contributes to the growing literature describing behavioural variation in aquatic invertebrates. Furthermore, it lays a foundation for further studies harnessing the potential of this emerging model system. In particular, this existing behavioural variation could be functionally linked to life‐history traits and invasive success and serve as a target of artificial selection or bioassays. It thus holds significant promise in applied research across ecotoxicology, aquaculture and invasion biology. [ABSTRACT FROM AUTHOR]