We used a simulation approach to test whether species composition on oceanic islands follows deterministic assembly rules based on probabilities of successful dispersal and establishment. The study was performed with two island biota in the eastern Pacific: the Galápagos, dominated by dry vegetation and montane humid forest, and Cocos Island, covered by wet tropical forest. We used leaf-dwelling (foliicolous) lichens as the study group and compiled occurrence data from previous studies on both island biota and new collections from the Galápagos. Species composition was simulated using randomization from a continental species pool, without and with filtering through ecogeographic parameters. Parameters for filtering were continental distribution range, commonness, and microsite exposure for successful dispersal, and preferences regarding vegetation type, seasonality, elevation, and microhabitat for successful establishment. Whereas neutral random selection predicted insular species composition imprecisely, ecogeographic parameter filtering resulted in rather accurate prediction. Commonness was the parameter that most contributed to the determination of species assembly. Empirical comparison with sites in continental Ecuador and Costa Rica suggests a closer affinity of the Galápagos with Ecuador, indicating that distance plays some role in species assembly as well. Based on our results we conclude that insular species assembly in this group of organisms is largely deterministic, rejecting a purely neutral approach. Highlights • Composition of randomized assemblies from a known species pool occurring on the American continent supports the hypothesis that island colonization largely follows deterministic assembly rules. • Stochastic components included a small number of unpredictable species and missing species as a result of disharmonic assembly. • Commonness was the most important parameter in shaping assembly. • Empirical comparison with sites in continental Ecuador and Costa Rica suggests a closer affinity of the Galápagos with Ecuador. • This study appears to be the first to test species assembly in island biota through simulation based on predictions from continental source metacommunities. Keywords: Cocos Island, foliicolous lichens, Galápagos Islands, Guajalito, Jatun Sacha, Las Cruces, La Selva, lichens, ordination, species assembly.