Consistency of orthology and paralogy constraints in the presence of gene transfers

TL;DR

This paper investigates the consistency of orthology and paralogy relations with species networks allowing gene transfers, providing complexity results and fixed-parameter algorithms for these problems.

Contribution

It formalizes the problem of relation consistency with gene transfers and offers new algorithmic solutions and complexity analyses.

Findings

Deciding relation graph consistency with a species network is NP-hard.

The problem is W[1]-hard with respect to the number of transfers.

An FPT algorithm is proposed based on the degree of the associated DS-tree.

Abstract

Orthology and paralogy relations are often inferred by methods based on gene similarity, which usually yield a graph depicting the relationships between gene pairs. Such relation graphs are known to frequently contain errors, as they cannot be explained via a gene tree that both contains the depicted orthologs/paralogs, and that is consistent with a species tree $S$. This idea of detecting errors through inconsistency with a species tree has mostly been studied in the presence of speciation and duplication events only. In this work, we ask: could the given set of relations be consistent if we allow lateral gene transfers in the evolutionary model? We formalize this question and provide a variety of algorithmic results regarding the underlying problems. Namely, we show that deciding if a relation graph $R$ is consistent with a given species network $N$ is NP-hard, and that it is W[1]-hard under the parameter "minimum number of transfers". However, we present an FPT algorithm based on the degree of the $DS$-tree associated with $R$. We also study analogous problems in the case that the transfer highways on a species tree are unknown.