Siamweed is an asteraceous shrub native to the Neotropics that ranks among the world's most widespread and troublesome invasive species. It was introduced in several regions of Africa, Southeast Asia, and the Pacific Islands, where it severely infests natural habitats and plantation crops. Although extensive data document the weed's abundance and distribution throughout the invaded continents, the details of its current range are not fully known, especially within its native region. In this study, we used point-occurrence data and digital maps summarizing relevant environmental parameters to generate predictions for the species' geographic distributional potential—specifically, we modeled the native range of siamweed in the Neotropics using the genetic algorithm for rule-set prediction, an evolutionary computing approach. The native range occurrence data set contained 239 published and herbarium records. Models were trained on a random subset of half the points and tested using the other half. The rule sets of the native-range models were projected onto the invaded continents to predict the weed's potential for invasion, blind to its known occurrences in such regions. Native-range models predicted a wide potential distribution of siamweed throughout tropical America, from southern United States to northern Argentina and southern Brazil. The weed's occurrence has been confirmed on the northern Pacific coast, in southeast Brazil, and in other South American areas, where it was supposed to be absent. Independent model projections to Africa, Asia, and Oceania are supported by known occurrence records. Four regions are predicted to be susceptible to siamweed spread: (1) Central Africa, currently being invaded from Western Africa; (2) Infestations spreading northward from South Africa, which have already reached Swaziland and Mozambique and may extend to East Africa and Madagascar; and (3) northern New Zealand and (4) Australia, which are at risk from uncontrolled infestations on several western Pacific islands.