Deformity Index: A semi-reference quality metric of phylogenetic trees based on their clades

abstract Measuring the correctness of a phylogenetic tree is one of the most fundamental tasks in phylogenetic study. A large number of methods have been proposed to measure the correctness of a tree. Such methods completely depend on the reference tree and they compute the distance between reference the tree and the target tree. But it is very difficult to obtain a precise and an accurate reference tree for a selected dataset. As a result, the existing methods for comparing the phylogenetic trees can behave unexpectedly in various scenarios. In this paper, we introduce a scoring function, called the Deformity Index, to measure the correctness of a tree based on the biological knowledge of the clades. The strength of our proposed method is that it does not consider any reference tree. We have also investigated the range and the distributions of the different modules of Deformity Index. Furthermore, we perform different goodness of fit tests to understand its cumulative distribution. We have also examined in detail the robustness as well as the scalability of our measure by different statistical tests under the Yule and the uniform models. Moreover, we show that our proposed scoring function can overcome the limitations of the conventional methods of tree comparing by experimenting on different biological datasets.