The Asymmetric Cluster Affinity Cost.

Tree comparison costs are sophisticated tools used to compare the results of different phylogenetic hypotheses and reconstruction methods and to evaluate the robustness of a tree to data perturbations. The Robinson-Foulds distance is a widely used measure for comparing the topologies of two trees, but it is highly sensitive to tree error. Consequently, tree differences may be over-estimated, leading to incorrect inference. An approach to overcome this shortcoming is the Cluster Affinity distance, which is a refinement of the Robinson-Foulds distance. These distances are symmetric and thus designed to compare the same type of trees. However, it is common to compare different types of trees, such as gene trees compared with species trees, or the integration of different datasets into a supertree: these comparisons are inherently asymmetric. Here, we introduce the asymmetric Cluster Affinity cost, a relaxation of the original Affinity cost to compare heterogeneous trees. We demonstrate that the characteristics of this cost are similar to the symmetric Cluster Affinity distance. Further, for the asymmetric affinity cost we describe efficient algorithms, derive the exact diameters, and use these to standardize the cost to be applicable in practice.