The rare tooth-billed pigeon
or manumea, (Didunculus strigirostris, Figs. 1, 2) is considered by Wikipedia “a large pigeon found only in Samoa. It has a large, curved, and hooked bright red bill with tooth-like projections on the lower mandible. The genus name means ‘little dodo.'” The parrot-like beak arose by convergence with parrots.
Figure 1. Skull of Didunculus compared to tracing of photo and adjusted to match.
Shapiro et al. 2002
used DNA to nest the solitaire (Pezophaps) with the dodo (Raphus) with outgroups including the Nicobar pigeon (Caloenas), the crowned pigeon (Goura) and the tooth-billed pigeon (Didunculus (Figs 1, 2) in order of increasing distance.
Figure 2. Figures of the Didunculus skeleton. This taxon is transitional between ocean-going skuas and island-dwelling adzebills, and something similar was basal to dodos and solitaires.
By contrast
the large reptile tree (LRT, 1191 taxa) found Didunculus to be basal to the solitaire (Pezophaps), the dodo (Raphus) but more closely to another large flightless island bird, the adzebill (Aptornis). Pigeons, like Columba and Caloenas, nested is another clade, one that also includes the black vulture (Coragyps) and its new sister, Goura, the crested pigeon. So, once again, we have a DNA/trait mismatch. Close, but no cigar.
Descendants of ocean-going skuas
(genus: Catharacta) could have populated the remote and widespread islands (Fig. 4) on which many of the taxa in figure 3 can be found. I have not yet found a skua or another taxon closer to the pigeons and New World vultures, so, for now, Catharacta will have to suffice as a model. Suggestions are welcome.
Figure 4. Skuas fly from Antarctica to Alaska and probably populated the widespread remote islands on which many of the large flightless birds listed here are known, evolving in isolation.
The skua, Catharacta
(Fig. 5) also joins the LRT.
Figure 5. The great skua, Catharacta, is close to the ancestry of dodos, pigeons, Old World Vultures, petrels, auks and puffins based on its traits.
References
Shapiro B et al. (7 co-authors) 2002. Flight of the Dodo. Science Brevia 295:1683.
The Pterosaur Heresies 