Box 1: Invasion outcomes driving local diversity change. Integration: Invader integrates and coexists with resident species (Moyle & Light 1996), leading to increased diversity. Occupancy: Invader occupies a niche vacated by a species lost from the resident community prior to the invasion event (Herbold & Moyle 1986), leading to increased diversity. Rescue: Invader fails to persist in the system but facilitates the persistence of a resident species that would otherwise go extinct (Brown & Kodric-Brown 1977), leading to increased diversity. Substitution: Invader replaces its resident competitor (Bøhn et al. 2008), leaving the diversity unchanged. Resistance: Invader disappears without affecting the resident community. This includes both environmental and biotic resistance to invasion (Moyle & Light 1996) and leaves the diversity unchanged. Vulnerability: Invading species permanently or temporarily destabilizes the resident system and triggers diversity loss through extinctions (Downing et al. 2012; Macdougall et al. 2013).