Deformity Index: A Semi-Reference Clade-Based Quality Metric of Phylogenetic Trees

Measuring the dissimilarity of a phylogenetic tree with respect to a reference tree or the hypotheses is a fundamental task in the phylogenetic study. A large number of methods have been proposed to compute the distance between the reference tree and the target tree. Due to the presence of unresolved relationships among the species, it is challenging to obtain a precise and an accurate reference tree for a selected dataset. As a result, the existing tree comparison methods may behave unexpectedly in various scenarios. In this paper, we introduce a novel scoring function, called the deformity index, to quantify the dissimilarity of a tree based on the list of clades of a reference tree. The strength of our proposed method is that it depends on the list of clades that can be acquired either from the reference tree or from the hypotheses. We investigate the distributions of different modules of the deformity index and perform different goodness-of-fit tests to understand the cumulative distribution. Then, we examine, in detail, the robustness as well as the scalability of our measure by performing different statistical tests under various models. Finally, we experiment on different biological datasets and show that our proposed scoring function overcomes the limitations of the conventional methods.