Hi Genevieve,
BUCKy only sees the trees you input, so ambiguity character codings in the sequence data never come into play.
As far as I know (and I may not be updated on this), MrBayes does not use ambiguity codings (e.g., R, Y, etc.) in an analysis. Even if you have them in your data set, they are treated as unknown characters (i.e., N). So, if you have a lot of polymorphic
character positions, these are uninformative for your gene tree reconstructions.
It sounds like you are saying that your individual gene tree posterior distributions have many (thousands) of distinct topologies, which would be indicative of very little phylogenetic information in the data sets. This may mean that you should
not expect BUCKy to be very informative about levels of concordance across loci.
I have not run BUCKy on that many loci before, but my recommendation would be to randomly subsample your loci and perform analyses on smaller sets of loci. Start with something small, like 50 loci, and work your way up to determine how many you
can run in a single analysis. Perhaps you could repeat this a bunch of times to gauge average estimates of concordance. Just a thought.
Dave