Losing information in phylogenetic consensus

Any summary loses information, by definition. That is, a summary is used to extract the "main" information from a larger set of information. Exactly how "main" is defined and detected varies from case to case, and some summary methods work better for certain purposes than for others.

A thought experiment that I used to play with my experimental-design students was to imagine that they were all given the same scientific publication, and were asked to provide an abstract of it. Our obvious expectation is that there would be a lot of similarity among those abstracts, which would represent the "important points" from the original — that is, those points of most interest to the majority of the students. However, there would also be differences among the abstracts, as each student would find different points that they think should also be included in the summary. In one sense, the worst abstract would be the one that has the least in common with the other abstracts, since it would be summarizing things that are of less general interest.

The same concept applies to mathematical summaries (aka "averages"), such as the mean, median and mode, which reduce the central location of a dataset to a single number. It also applies to summaries of the variation in a dataset, such as the variance and inter-quartile range. (Note that a confidence interval or standard error is an indication of the precision of the estimate of the central location, not a summary of the dataset variation — this is a point that seems to confuse many people.)

So, it is easy to summarize data and thereby lose important information. For example, if my dataset has two exactly opposing time patterns, then the data average will appear to remain constant through time. I might thus conclude from the average that "nothing is happening" through time when, in fact, two things are happening. I will never find out about my mistake by simply looking at the data summary — I also need to look at the original data patterns.

So, what has this got to do with phylogenetics? Well, a phylogenetic tree is a summary of a dataset, and that summary is, by definition, missing some of the patterns in the data. These patterns might be of interest to me, if I knew about them.

Even worse, phylogenetic data analyses often produce multiple phylogenetic trees, all of which are mathematically equal as summaries of the data. What are we then to do?

One thing that people often do is to compute a Consensus Tree (eg. the majority consensus), which is a summary of the summaries — that is, it is a tree that summarizes the other trees. It would hardly be surprising if that consensus tree is an inadequate summary of the original data. In spite of this, how often do you see published papers that contain any evaluation of their consensus tree as a summary of the original data?

This issue has recently been addressed in a paper uploaded to the BioRxiv:

Anti-consensus: detecting trees that have an evolutionary signal that is lost in consensus
Daniel H. Huson, Benjamin Albrecht, Sascha Patz, Mike Steel

Not unexpectedly, given the background of the authors, they explore this issue in the context of phylogenetic networks. As they note:

A consensus tree, such as the majority consensus, is based on the set of all splits that are present in more than 50% of the input trees. A consensus network is obtained by lowering the threshold and considering all splits that are contained in 10% of the trees, say, and then computing the corresponding splits network. By construction and in practice, a consensus network usually shows the majority tree, extended by a number of rectangles that represent local rearrangements around internal nodes of the consensus tree. This may lead to the false conclusion that the input trees do not differ in a significant way because "even a phylogenetic network" does not display any large discrepancies.

That is, sometimes authors do attempt to evaluate their consensus tree, by looking at a network. However, even the network may turn out to be inadequate, because a phylogenetic tree is a much more complex summary than is a simple mathematical average. This is sad, of course.

So, the new suggestion by the authors is:

To harness the full potential of a phylogenetic network, we introduce the new concept of an anti-consensus network that aims at representing the largest interesting discrepancies found in a set of trees.

This should reveal multiple large patterns, if they exist in the original dataset. Phylogenetic analyses keep moving forward, fortunately.