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Re: Polytomies in cladistics: Good, Bad, or Ugly?

It was too late at night... I wanted to use "good", "ugly" and "bad" instead of "1)", "2)" and "3)" :-}

Yeah, probably a bad choice of words on my part.  I was thinking of the
effect of user input options in PAUP, such like Bayes, Strict Consensus,
bad choice of outgroup taxa, poor choice of a root taxon, etc., etc., and
if these user choices are significant in "creating" polytomies (or
"destroying" them, depending on the option that the user selects).

A strict consensus of different trees cannot help containing polytomies.
If the outgroup is too far away from the ingroup, it can probably produce polytomies.
If there are several taxa in the outgroup, and a taxon that should form a clade with (part of) the outgroup is in the ingroup, that taxon will typically come out next to the ingroup taxon with which it shares the most convergences. (The big Diapsida phylogeny by Müller 2004 has an OTU called "Parareptilia" in the outgroup and the turtles in the ingroup...) I guess when there is no clear candidate for such a most convergent taxon, a polytomy will result.
PAUP* cannot use Bayesian methods...

Mickey M. also mentioned that polytomies tend to show up in cladograms
where character data is sparse for certain groups, as you also noted.

Ironically, too sparse data can occasionally produce a better resolved tree. This can happen when the noise is not evenly spread around the signal. (This in turn does not need to be based on the bias of the one who compiled the matrix. Having enough correlated characters, like size-related or ontogeny-related ones, will easily cause the noise to conspire against the signal.) Adding more data to such a matrix should first decrease and then reincrease the resolution of the tree.