SUPPLEMENTARY DATA - Expanded phylogeny elucidates <i>Deinosuchus </i>relationships, crocodylian osmoregulation and body-size evolution

Transmarine distribution and gigantism in the Late Cretaceous North American crocodyliform <i>Deinosuchus</i> has been difficult to reconcile with consistently inferred phylogenetic relationships to alligatorids, an otherwise freshwater and smaller-bodied group. We present an expanded phylogeny with increased spatiotemporally coherence that reinterprets species of <i>Deinosuchus</i> as stem-group crocodylians, together with further putative alligatoroids, <i>Leidyosuchus canadensis</i> and the European<i> </i><i>Diplocynodon</i> spp. (closely related to North American <i>Borealosuchus</i>). The novel topology elucidates the evolution of osmoregulation in Crocodylia and its close relatives by inferring plesiomorphic saltwater tolerance for <i>Deinosuchus</i> and the crown-group and secondary loss already in stem-group alligatorids. Divergence of Alligatoroidea coincided with extreme mid-Cretaceous sea level highs and the distribution of <i>Deinosuchus</i> across the Western Interior Seaway can be best explained by marine dispersal. Phylogenetic body-length analysis using a head-width proxy reveals phyletic dwarfism early in alligatoroid evolution and a reasonable total length estimate for the most complete specimen of <i>Deinosuchus riograndensis</i>. We find that gigantism in crocodyliforms is correlated with high-productive extensive aquatic ecosystems in the present and the past.