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Trees that illustrate patterns of ancestry and evolution are a central tool in many areas of biology. Comparing evolutionary trees to each other has widespread applications in comparing the evolutionary stories told by different sources of data, assessing the quality of inference methods, and highlighting areas where patterns of ancestry are uncertain. While these tasks are complicated by the fact that trees are high-dimensional structures encoding a large amount of information, there are a number of metrics suitable for comparing evolutionary trees whose tips have the same set of unique labels. There are also metrics for comparing trees where there is no relationship between their labels: in 'unlabelled' tree metrics the tree shapes are compared without reference to the tip labels. In many interesting applications, however, the taxa present in two or more trees are related but not identical, and it is informative to compare the trees whilst retaining information about their tips' relationships. We present methods for comparing trees whose labels belong to a pre-defined set of categories. The methods include a measure of distance between two such trees, and a measure of concordance between one such tree and a hierarchical classification tree of the unique categories. We demonstrate the intuition of our methods with some toy examples before presenting an analysis of Mycobacterium tuberculosis trees, in which we use our methods to quantify the differences between trees built from typing versus sequence data.

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