Reconciling Multiple Genes Trees via Segmental Duplications and Losses

TL;DR

This paper develops a polynomial-time solution for reconciling multiple gene trees with a species tree considering segmental duplications and losses, and introduces a fixed-parameter algorithm for more complex cases, validated on real datasets.

Contribution

It extends gene tree reconciliation to include segmental macro-evolutionary events and solves the NP-hard case with a fixed-parameter algorithm, addressing a longstanding open problem.

Findings

Polynomial-time solution when duplication cost ≤ loss cost

NP-hardness when duplication cost > loss cost

Effective algorithm validated on eukaryote and yeast datasets

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 $\delta \leq \lambda$ (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 the reconciliation problem. 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 $O(\lceil \frac{\delta}{\lambda} \rceil^{d} \cdot n \cdot \frac{\delta}{\lambda})$. 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 refute hypothetical segmental duplications on a set of 16 eukaryotes, then show how we can detect whole genome duplications in yeast genomes.