1. The establishment of new botanic gardens in tropical regions highlights a need for weed risk assessment tools suitable for tropical ecosystems. The relevance of plant traits for invasion into tropical rainforests has not been well studied.2. Working in and around four botanic gardens in Indonesia where 590 alien species have been planted, we estimated the effect of four plant traits, plus time since species introduction, on: (a) the naturalization probability and (b) abundance (density) of naturalized species in adjacent native tropical rainforests; and (c) the distance that naturalized alien plants have spread from the botanic gardens.3. We found that specific leaf area (SLA) strongly differentiated 23 naturalized from 78 non-naturalized alien species (randomly selected from 577 non-naturalized species) in our study. These trends may indicate that aliens with high SLA, which had a higher probability of naturalization, benefit from at least two factors when establishing in tropical forests: high growth rates and occupation of forest gaps. Naturalized aliens had high SLA and tended to be short. However, plant height was not significantly related to species' naturalization probability when considered alongside other traits.4. Alien species that were present in the gardens for over 30 years and those with small seeds also had higher probabilities of becoming naturalized, indicating that garden plants can invade the understorey of closed canopy tropical rainforests, especially when invading species are shade tolerant and have sufficient time to establish.5. On average, alien species that were animal dispersed spread 78 m further into the forests and were more likely to naturalize than animal-dispersed species. We did not detect relationships between the measured traits and estimated density of naturalized aliens in the adjacent forests.6. : Traits were able to differentiate alien species from botanic gardens that naturalized in native forest from those that did not; this is promising for developing trait-based risk assessment in the tropics. To limit the risk of invasion and spread into adjacent native forests, we suggest tropical botanic gardens avoid planting alien species with fast carbon capture strategies and those that are shade tolerant.