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I have a dataset of molecular sequences from which I have inferred a phylogenetic tree (a.k.a a dendrogram) with various algorithms (maximum parsimony, neighbor-joining, and maximum likelihood). What I would like to know is whether there is a way to measure the effect that either one character or several characters has on the inference of the phylogenetic tree.

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There is one way that this can be quite naturally done in the maximum likelihood case: because the log likelihood of the alignment is calculated as the sum of the log likelihood of the individual sites (or equivalently, the likelihood is the product of the site-specific likelihoods), most ML inference programs will allow you to print the site-specific log likelihoods themselves. You can then see which sites are contributing a lot of signal (on a likelihood basis) to the topology.

You can extend this to two- and three-way by comparing the difference in site-specific log likelihoods between two topologies, which can allow you to detect outlier sites strongly supporting one resolution, in a manner analogous to what is conducted in this paper.

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