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Molecular phylogenies have been constructed and calibrated against time for several plant lineages in the Hawaiian Islands, and had an enormous impact on our understanding of speciation, adaptive radiation, and historical biogeography. Yet none published to date have had the kind of rigorous analysis – involving DNA sequences of hundreds of single-copy nuclear loci and entire plastomes – needed to infer relationships among very closely related taxa and disentangle patterns of hybridization and other forms of reticulate evolution in rigorous fashion. Here we present the first such study, focusing on the native Hawaiian lobeliads, the largest Hawaiian plant lineage, including five endemic genera and two endemic sections of cosmopolitan Lobelia. We elucidate phylogenetic relationships within this group using whole plastomes and 389 nuclear loci for 95 of 107 extant species, screen for reticulate evolution, and then conduct time-dependent analyses of historical biogeography. Our results suggest a new but poorly supported backbone topology: ((Lobelia § Revolutella, (Lobelia § Galeatella, Tremato¬lobelia)), ((Brighamia, Delissea), (Polynesian Sclerotheca, (Cyanea, Clermontia)))), implying a single gain of axillary inflorescences from ancestral terminal inflorescences, and either a single gain and two losses of fleshy fruits, or two independent gains of such fruits. We estimate relationships and inter-island dispersal events within each of these genera and sections, and find that (1) each of these groups is monophyletic, except that Clermontia is sister to the purple-fruited clade of Cyanea, with the orange-fruited clade of Cyanea sister to them both; (2) there is no evidence of reticulate evolution among the nine major clades, but hybridization appears to have occurred seven times within four such clades (Clermontia, orange- and purple-fruited Cyanea, and Lobelia § Revolutella); (3) relationships within Cyanea appear to parallel in several respects the six subclades recognized in an earlier restriction-site study; (4) 26 of 27 inter-island dispersal events from Kauaʻi or younger islands follow the progression rule from one island to the next younger island (or island group) in the chain, with only one dispersal event skipping over Oʻahu from Kauaʻi directly to Maui Nui; and (5) four very rapid radiations appear to have happened very recently, including species of the former Rollandia on Oʻahu, species of orange-fruited Cyanea on Kauaʻi, species of purple-fruited Cyanea on Kauaʻi, and species of Clermontia on the Big Island. Nearly 63% of cladogenetic events within the Hawaiian lobeliads appear to have occurred within islands rather than between islands. At least eight inter-island dispersal events occurred from older, now submerged tall islands to Kauaʻi, carrying forward single representatives of each native genus or section of Lobelia; and at least one long-distance dispersal event occurred from an older island to French Polynesia or the Cook Islands to found Sclerotheca.