Invasive species may reduce biodiversity in the long term by displacing resident species. Previous studies of geckos have suggested that invasive species can displace residents by monopolizing limited resources, and this competitive advantage may be exacerbated in structurally simple human-altered habitats. Lepidodactylus lugubris is a parthenogenetic gecko that comprises four major clones. On many Pacific islands A-clones have recently become numerically dominant over several other clones. We tested the general hypothesis that A-clones displace B-clones in structurally simple habitats owing to behavioural differences that influence foraging and aggression. Based on previous studies and the pattern of invasion, we predicted that A-clones would consume more insects and show higher levels of aggression and social dominance than would B-clones. We also tested the hypothesis that increasing topographic structure would affect clone behaviour asymmetrically and reduce the advantages of invading A-clones. We found that A-clones consumed more insects and initiated foraging faster compared to B-clones. However, A-clones were not consistently socially dominant over B-clones. Habitat structure affected foraging tactics, reduced aggression and decreased activity, but clones were affected equally and A-clones remained superior foragers in the structurally complex habitat. Although B-clones were more active, they were also more shy. They occupied and defended shelter more, which may partially explain their persistence in forested habitat. We conclude that part of the advantage A-clones have in structurally simple human landscapes stems from their innate boldness, which increases their ability to exploit limited food resources.