Reconciling multiple genes trees via segmental duplications and losses

Abstract

Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families is interconnected. In this paper, we extend a previous approach to reconcile a set of gene trees with a species tree based on segmental macro-evolutionary events, where segmental duplication events and losses are associated with cost $\delta$ and $\lambda$ , respectively. We show that the problem is polynomial-time solvable when $\delta \le \lambda$ (via LCA-mapping), while if $\delta >\lambda$ the problem is NP-hard, even when $\lambda =0$ and a single gene tree is given, solving a long standing open problem on the complexity of multi-gene reconciliation. On the positive side, we give a fixed-parameter algorithm for the problem, where the parameters are $\delta /\lambda$ and the number d of segmental duplications, of time complexity $O\left({\lceil \frac{\delta }{\lambda }\rceil }^d,·,n,·,\frac{\delta }{\lambda }\right)$ . Finally, we demonstrate the usefulness of this algorithm on two previously studied real datasets: we first show that our method can be used to confirm or raise doubt on hypothetical segmental duplications on a set of 16 eukaryotes, then show how we can detect whole genome duplications in yeast genomes.

Keywords: Fixed-parameter tractability; Gene trees; NP-hardness; Phylogenetics; Reconciliation; Segmental duplications; Species trees; Whole genome duplications.