The Clade Displacement Index: how to detect hotizontal gene transfers in unrooted gene trees

While most genes of any organism are inherited vertically - i.e. from its parent organisms - sometimes they can be exchanged between unrelated species in a process known as the horizontal gene transfer (HGT). Studies of HGT contribute to our knowledge about the mechanisms of evolution, including the emergence of new pathogens, and a great deal of effort has been put into different methods of finding transferred genes. The golden standard of HGT detection is the analysis of the incongruence between the gene and the species trees. Those methods typically require rooted trees, in which the direction of evolution is known. Gene trees are typically unrooted, and rooting them is yet another step in HGT analysis, prone to errors which may lead to wrong conclusions. A natural question arises: can HGTs be detected in gene trees without rooting them at all? It turns out that, for a particular, yet broad, class of transfers, the answer to this question is: yes. It also turns out that the same methodology can be applied to complement the bootstrap support in assessing the stability of gene tree topology. In this article, we present the Clade Displacement Index, a measure of shift of a given clades location between two trees. We derive algorithms to compute it and give several examples of its applications to HGT detection and gene tree stability analysis. We finish by pointing out directions for further studies and an example that shows that not all HGTs are detectable without knowing the location of the root of the gene tree. A Jupyter Notebook with the implementation and applications of CDI described in this paper is available at https://github.com/mciach/CDI