Isometric gene tree reconciliation revisited

Background Isometric gene tree reconciliation is a gene tree/species tree reconciliation problem where both the gene tree and the species tree include branch lengths, and these branch lengths must be respected by the reconciliation. The problem was introduced by Ma et al. in 2008 in the context of reconstructing evolutionary histories of genomes in the infinite sites model. Results In this paper, we show that the original algorithm by Ma et al. is incorrect, and we propose a modified algorithm that addresses the problems that we discovered. We have also improved the running time from O(N^2) to O(Nlog N) , where N is the total number of nodes in the two input trees. Finally, we examine two new variants of the problem: reconciliation of two unrooted trees and scaling of branch lengths of the gene tree during reconciliation of two rooted trees. Conclusions We provide several new algorithms for isometric reconciliation of trees. Some questions in this area remain open; most importantly extensions of the problem allowing for imprecise estimates of branch lengths.