Abstract
Species networks generalize the notion of species trees to allow for hybridization or other lateral gene transfer. Under the network multispecies coalescent model, individual gene trees arising from a network can have any topology, but arise with frequencies dependent on the network structure and numerical parameters. We propose a new algorithm for statistical inference of a level-1 species network under this model, from data consisting of gene tree topologies, and provide the theoretical justification for it. The algorithm is based on an analysis of quartets displayed on gene trees, combining several statistical hypothesis tests with combinatorial ideas such as a quartet-based intertaxon distance appropriate to networks, the NeighborNet algorithm for circular split systems, and the Circular Network algorithm for constructing a splits graph.
Highlights
In this paper we provide the theory supporting a new, statistically consistent method of inferring most topological features of a level-1 hybridization network under the network multispecies coalescent (NMSC) model
The theory we present is based on consideration of the quartets displayed on a collection of gene trees arising under the NMSC, but it differs in important ways from the more purely combinatorial work, such as [13], on undirected networks of level-1 and higher
We implemented Steps 1, 2, and 3 of the NANUQ algorithm in an R package MSCquartets, with a function accepting an input file of Newick gene trees, and producing an output file of the network quartet distances computed from this data
Summary
In this paper we provide the theory supporting a new, statistically consistent method of inferring most topological features of a level-1 hybridization network under the network multispecies coalescent (NMSC) model. Quartet concordance factors The NMSC model is often used to obtain the probability (or density) of observing a specific gene tree (metric or topological, rooted or unrooted) in a species network. A first observation is that for a tree-like CF arising from a quartet network N − with a 32-cycle, say with descendants a, b of the hybrid node as, Nc− has topology ab|cd.
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