The Bourque Distances for Mutation Trees of Cancers

Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson-Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients usually contain different sets of mutation labels. Here, we generalize the Robinson-Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson-Foulds distance and the nearest neighbor interchange distance is also presented.