UPGMA trees are not ultrametric

[James Angus Chandler]

The jackknifed_beta_diversity.py workflow builds trees using UPGMA clustering. UPGMA is only valid if the data is ultrametric. The resulting dendrogram from ultrametric data has equal distances from root to tip for all samples. Looking at my own data, I find that the UPGMA dendrograms are not ultrametric. In the QIIME 454 overview tutorial, the example UPGMA dendrogram shown in FigTree also is not ultrametric. Likewise Figure 10.7.1 of the Current Protocols in Bioinformatics tutorial has a non-ultrametric UPGMA dendrogram. Nobably, when looking at the original UniFrac papers and dendrograms that I generated many years ago using the UniFrac web application, I find that these dendrograms are indeed ultrametric.

Does anybody have an idea as to how UPGMA clustering in QIIME can lead to dendrograms that have unequal distances from root to tip for different samples, even though this is a violation of an assumptions necessary to do UPGMA clustering?

Thanks,

Angus

[justink]

Hmm, first, I'm going to use ultrametric here as a synonym for 'all tips have the same root to tip distance' to avoid confusion.

Then, I think that the reason that http://qiime.org/_images/UPGMAbytreatment.png and Figure 10.7.1 of the Current Protocols in Bioinformatics aren't ultrametric is because they're actually consensus trees build from multiple UPGMA trees, and even though each UPGMA tree is ultrametric, the consensus isn't.

I looked over some UPGMA trees I've created with qiime, and they all seem to be ultrametric (master_tree.tre isn't, but e.g. upgma_weighted_unifrac_rarefaction_110_7.tre is ultrametric).

Best!

[James Angus Chandler]

Thanks justink! I hadn't looked at the individual trees, I had only looked at the consensus. You are correct that the individual trees have an equal distance from root to tip for all samples.

Do you have any insight into how the consensus tree is made then? I usually think of a consensus topology, but this suggests that these trees have a "consensus" branch length as well. How is this length generated? Is it the average length to the shallowest node for each sample?

Thanks,

Angus

[Justin Kuczynski]

Hey, I think the length of a rootward branch from nodeA with tips {a,b} in the consensus tree is:

the average length of the corresponding branch from the support trees, including only those support trees that have a node with tips exactly {a,b} and no others.

But I'm not certain. I did note that the documentation for the consensus function in pycogent's phylo/consensus.py states that it uses the "majority rules method of Margush and McMorris 1981"

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