Founder-event speciation, where a rare jump dispersal event founds a new genetically isolated lineage, has long been considered crucial by many historical biogeographers, but its importance is disputed within the vicariance school. Probabilistic modeling of geographic range evolution creates the potential to test different biogeographical models against data using standard statistical model choice procedures, as long as multiple models are available. I re-implement the Dispersal-Extinction-Cladogenesis (DEC) model of LAGRANGE in the R package BioGeoBEARS, and modify it to create a new model, DEC + J, which adds founder-event speciation, the importance of which is governed by a new free parameter, [Formula: see text]. The identifiability of DEC and DEC + J is tested on data sets simulated under a wide range of macroevolutionary models where geography evolves jointly with lineage birth/death events. The results confirm that DEC and DEC + J are identifiable even though these models ignore the fact that molecular phylogenies are missing many cladogenesis and extinction events. The simulations also indicate that DEC will have substantially increased errors in ancestral range estimation and parameter inference when the true model includes + J. DEC and DEC + J are compared on 13 empirical data sets drawn from studies of island clades. Likelihood-ratio tests indicate that all clades reject DEC, and AICc model weights show large to overwhelming support for DEC + J, for the first time verifying the importance of founder-event speciation in island clades via statistical model choice. Under DEC + J, ancestral nodes are usually estimated to have ranges occupying only one island, rather than the widespread ancestors often favored by DEC. These results indicate that the assumptions of historical biogeography models can have large impacts on inference and require testing and comparison with statistical methods. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: firstname.lastname@example.org.