[Paper Review] Solving Phylogenetic Network Containment Problems using Cherry-picking Sequences

Remie Janssen, Yukihiro Murakami|arXiv (Cornell University)|Dec 19, 2018

Genomics and Phylogenetic Studies4 citations

TL;DR

This paper introduces cherry-picking sequences to characterize when a tree-child network is embedded in another, enabling linear-time decision of the Network Containment problem. It further develops a linear-time isomorphism algorithm for tree-child networks and generalizes the framework to cherry-picking networks, which are uniquely defined by their minimal cherry-picking sequences.

ABSTRACT

Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks: to distinguish different networks, and to see when one network is embedded in another. We show that the tree-child sequences introduced by Linz and Semple characterize when a tree is embedded in a tree-child network. We take this one step further and show that the sequences can be used to characterize when a tree-child network is embedded in another tree-child network ({\sc Network Containment}), and that this can be decided in linear time. Following this, we provide a linear time algorithm for deciding whether two tree-child networks are isomorphic. We also generalize tree-child sequences to cherry-picking sequences, and consequently define the class of cherry-picking networks -- the networks that can be reduced by cherry-picking sequences. These networks are uniquely defined by their smallest minimal cherry-picking sequences, and due to this, the isomorphism result also follows for cherry-picking networks.

Motivation & Objective

• To characterize when one tree-child network is embedded in another using tree-child sequences.
• To develop a linear-time algorithm for the Network Containment problem in tree-child networks.
• To generalize tree-child sequences into cherry-picking sequences for broader network classes.
• To establish a linear-time isomorphism test for tree-child networks.
• To define cherry-picking networks as those uniquely reconstructible from their minimal cherry-picking sequences.

Proposed method

• Leverages tree-child sequences to encode network embeddings and characterize tree-child network containment.
• Extends tree-child sequences to cherry-picking sequences for general network reduction.
• Uses minimal cherry-picking sequences to uniquely define cherry-picking networks.
• Applies sequence-based reduction to design linear-time algorithms for containment and isomorphism.
• Proves that isomorphism of tree-child networks reduces to comparing their minimal cherry-picking sequences.
• Establishes that the structure of cherry-picking networks is fully determined by their smallest minimal cherry-picking sequences.

Experimental results

Research questions

• RQ1 Can tree-child sequences be used to determine if one tree-child network is contained within another?
• RQ2 Is the Network Containment problem for tree-child networks decidable in linear time using sequence-based methods?
• RQ3 Can the concept of tree-child sequences be generalized to define a broader class of networks?
• RQ4 Do cherry-picking networks admit a unique characterization via their minimal cherry-picking sequences?
• RQ5 Can isomorphism between tree-child networks be decided efficiently using sequence comparison?

Key findings

• The Network Containment problem for tree-child networks can be solved in linear time using cherry-picking sequences.
• Tree-child networks are uniquely characterized by their minimal cherry-picking sequences.
• Isomorphism between two tree-child networks can be decided in linear time by comparing their minimal cherry-picking sequences.
• Cherry-picking networks are defined as those that can be reduced via cherry-picking sequences, and are uniquely determined by their smallest such sequences.
• The isomorphism result for tree-child networks extends to the broader class of cherry-picking networks due to their unique sequence-based characterization.
• The framework provides a unified sequence-based approach to network containment and isomorphism in phylogenetic networks.