We modified the Worthy et al. dataset for the description of Asteriornis, and as our version includes potentially key taxa such as Conflicto, Gallinuloides, and of course Asteriornis, it might be a useful test for this... For the published version of our analysis, we removed the flightless neognaths, because they seemed to be returning probable artifactual results and weren't the focus of our study, but it was simple enough for me to reintroduce them to the dataset, conservatively score them for the few characters we added, and implement Agnolin's scoring changes.
When analyzed in TNT with the extant taxa (and the moa) under a molecular scaffold, I get:
-With all taxa included: Brontornis, Gastornis, dromornithids, and Patagornis form a flightless neoavian clade most closely related to Cariama... (Right, this was why we took them out...) Brontornis is most closely related to Gastornis in this topology.
-With flightless neognaths except Brontornis excluded: Brontornis is sister to Cariama.
-With flightless neognaths except the two Gastornis species excluded: Gastornis is either a stem-anseriform (forming a clade with Vegavis)... or a neoavian outside the a clade formed by the extant neoavians sampled (in those trees, Vegavis, Anatalavis + Conflicto, and presbyornithids form a clade of stem anseriforms).
-With flightless neognaths except dromornithids excluded: dromornithids are... stem paleognaths, hmm... Lithornithids become crown paleognaths (sister to Tinamus), and Conflicto hops over to the galliform stem?!
-Same as previous but with flightless paleognaths also excluded: dromornithids are stem anseriforms, sometimes forming a clade with Vegavis. (Other times, Vegavis is a stem bird, as in our published topology.)
-With flightless neognaths except Patagornis excluded: Patagornis is sister to Cariama.
-With flightless neognaths except Sylviornis and Megavitiornis excluded: The two form a clade of stem galliforms, crownward of Gallinuloides.
-With all flightless neognaths except Brontornis included: Same results as the first analysis.
-With all flightless neognaths except Brontornis and Patagornis included: Gastornithiforms are stem galliforms, forming a clade with Vegavis. Asteriornis jumps into crown galliforms, on the stem of Cracidae + Phasianidae... or as a phasianid... (This actually isn't as unexpected as it might seem; in some of our preliminary analyses, Asteriornis ended up either in those positions or as a megapode; it has individual skull features that particularly resemble certain extant species.)
-With all taxa included, plus Gastornis and dromornithids constrained to be pan-galloanserans and Patagornis constrained to be sister to Cariama: Gastornithiforms are stem galliforms, Brontornis is a gastornithiform (closer to dromornithids than to Gastornis), strict consensus is super unresolved because Asteriornis jumps around between being a stem anseriform and a phasianid, lithornithids are crown paleognaths, and Anatalavis + Conflicto, Vegavis, and presbyornithids form a clade of stem anseriforms (sometimes with Asteriornis in the mix). (As an aside, the MPTs here are only three steps longer than those from the first analysis.)
-Implied weighting (k = 3) with all taxa included: Patagornis, Gastornis, Brontornis, and dromornithids form a clade of stem galliforms (Brontornis is closest to dromornithids), Vegavis is a stem bird, lithornithids are crown paleognaths, and Asteriornis is a stem galliform or stem megapode.