Abstract
Phylogenetic tree reconstruction is usually done by local search heuristics that explore the space of the possible tree topologies via simple rearrangements of their structure. Tree rearrangement heuristics have been used in combination with practically all optimization criteria in use, from maximum likelihood and parsimony to distance-based principles, and in a Bayesian context. Their basic components are rearrangement moves that specify all possible ways of generating alternative phylogenies from a given one, and whose fundamental property is to be able to transform, by repeated application, any phylogeny into any other phylogeny. Despite their long tradition in tree-based phylogenetics, very little research has gone into studying similar rearrangement operations for phylogenetic network—that is, phylogenies explicitly representing scenarios that include reticulate events such as hybridization, horizontal gene transfer, population admixture, and recombination. To fill this gap, we propose “horizontal” moves that ensure that every network of a certain complexity can be reached from any other network of the same complexity, and “vertical” moves that ensure reachability between networks of different complexities. When applied to phylogenetic trees, our horizontal moves—named rNNI and rSPR—reduce to the best-known moves on rooted phylogenetic trees, nearest-neighbor interchange and rooted subtree pruning and regrafting. Besides a number of reachability results—separating the contributions of horizontal and vertical moves—we prove that rNNI moves are local versions of rSPR moves, and provide bounds on the sizes of the rNNI neighborhoods. The paper focuses on the most biologically meaningful versions of phylogenetic networks, where edges are oriented and reticulation events clearly identified. Moreover, our rearrangement moves are robust to the fact that networks with higher complexity usually allow a better fit with the data. Our goal is to provide a solid basis for practical phylogenetic network reconstruction.
Highlights
A recent trend in evolutionary biology is the growing appreciation of reticulate evolution— which occurs when the history of a set of taxa cannot be accurately represented as a phylogenetic tree [1, 2], because of events causing inheritance from more than one ancestor
This paper provides the fundamental definitions and theoretical results for subsequent work in practical methods for phylogenetic network reconstruction: we subdivide networks into layers, according to a generally-accepted measure of their complexity, and provide operations that allow both to fully explore each layer, and to move across different layers
The paper is organized as follows: After introducing the necessary mathematical background, we give our definition of rNNI moves for networks, and prove that any two networks of equal reticulate complexity are mutually reachable by applying rNNI moves
Summary
A recent trend in evolutionary biology is the growing appreciation of reticulate evolution— which occurs when the history of a set of taxa (e.g., species, populations or genes) cannot be accurately represented as a phylogenetic tree [1, 2], because of events causing inheritance from more than one ancestor. There is a wide variety of reticulate events in nature, for example: hybrid speciation [3,4,5], population admixture [6,7,8] horizontal gene transfer [9,10,11] and genomic recombination [12,13,14] These phenomena are often of interest to different communities of researchers (e.g., in plant biology, population genetics, microbiology, epidemiology), meaning that different approaches and terminologies are in use in these fields. The different approaches to studying reticulate evolution share the same ambition: to represent evolutionary history explicitly, with phylogenetic networks These are simple generalizations of phylogenetic trees, where some nodes—named reticulations—are allowed to have multiple direct ancestors [15, 16].
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