Intact tropical rainforests on continents and continental islands are considered to be relatively resistant to invasions by introduced plant species, but fragmentation and degradation may render them susceptible, especially to species from predominantly shade-tolerant families with centres of diversity in the tropics, such as palms. We investigated the seedling establishment patterns of the most common exotic palm species in Singapore's secondary forest patches, the Macarthur palm (Ptychosperma macarthurii), in relation to landscape-level planting intensity, abiotic conditions, and recipient community composition. We first used conditional inference forests to narrow down the set of possible explanatory variables, followed by fitting generalised linear models with the forest patch and individual plots as random intercepts, to account for the nesting of plots within patches and overdispersion, respectively. The number of cultivated adults in the vicinity was not an important variable. Instead, leaf litter was the most important predictor of seedling density. Thick leaf litter in the disturbed and younger secondary forest matrix that surrounds old growth forest patches may therefore serve as a buffer against invasions, especially by small-seeded exotics. However, if adults of exotic species are allowed to establish unchecked, for example along forest trails that lead into the interior of the forested landscape, the seed rain may eventually reach old growth forest where leaf litter is typically thin. Further studies are required to determine if second-generation adults within invaded habitats contribute disproportionately more to propagule pressure than first-generation cultivated plants outside the invaded habitat.