Robinson-Foulds Reticulation Networks

Abstract

Phylogenetic (hybridization) networks allow investigation of evolutionary species histories that involve complex phylogenetic events other than speciation, such as reassortment in virus evolution or introgressive hybridization in invertebrates and mammals. Reticulation networks can be inferred by solving the reticulation network problem, typically known as the hybridization network problem. Given a collection of phylogenetic input trees, this problem seeks a minimum reticulation network with the smallest number of reticulation vertices into which the input trees can be embedded exactly. Unfortunately, this problem is limited in practice, since minimum reticulation networks can be easily obfuscated by even small topological errors that typically occur in input trees inferred from biological data. We adapt the reticulation network problem to address erroneous input trees using the classic Robinson-Foulds distance. The RF embedding cost allows trees to be embedded into reticulation networks inexactly, but up to a measurable error. The adapted problem, called the Robinson-Foulds reticulation network (RF-Network) problem is, as we show and like many other problems applied in molecular biology, NP-hard. To address this, we employ local search strategies that have been successfully applied in other NP-hard phylogenetic problems. Our local search method benefits from recent theoretical advancements in this area. Further, we introduce inpractice effective algorithms for the computational challenges involved in our local search approach. Using simulations we experimentally validate the ability of our method, RF-Net, to reconstruct correct phylogenetic networks in the presence of error in input data. Finally, we demonstrate how RF-networks can help identify reassortment in influenza A viruses, and provide insight into the evolutionary history of these viruses. RF-Net was able to estimate a large and credible reassortment network with 164 taxa.

RF-Net 2: Fast Inference of Virus Reassortment and Hybridization Networks

“…Markin et al ., 2019 proposed a ‘layered’ approach to RF-Network inference. In particular, we call a set of all networks with exactly k reticulations a k-th layer and it is denoted by 𝒩 k .…”

“…Note that RF-Net implements two major algorithmic advancements as described in Markin et al ., 2019. These algorithms (1) make the computation of the total embedding cost for each network significantly faster, and (2) accelerate SNPR neighborhood traversals for each local search iteration.…”

“…This method had the utility of being able to objectively embed input gene trees into reticulation networks inexactly, but up to a measurable error, and was able to accurately infer phylogenetic networks while directly accounting for errors in the input gene trees. Unfortunately, while the Markin et al ., 2019 method, RF-Net, can handle hundreds of taxa, it cannot address networks with large numbers of reticulations (e.g., greater than 10); a limitation common to most other network inference methods (Wen et al ., 2016; Markin et al ., 2019).…”

“…In this work, we expand the functionality of RF-Net (Markin et al ., 2019) to advance its practical applicability. We develop the Fast-RF-Net approach that is not bound to a limited number of reticulations which resolves a major drawback in the base RF-Net method.…”

“…Markin et al ., 2019 demonstrated that computing δ ( G, N ) is NP-hard even when N is tree-child. This means that computing the embedding cost exactly when the number of reticulations is high (i.e., greater that 10 − 11) is computationally impractical for datasets with hundreds of taxa (see Section 3.2).…”