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ASTRAL is a powerful and widely used tool for species tree inference, known for its computational speed and robustness under incomplete lineage sorting. The method has often been used as an initial step in species network inference to provide a backbone tree structure upon which hybridization events are later added to such a tree via other methods. However, we show empirically and theoretically, that this methodology can yield flawed results. Specifically, we demonstrate that under the Network Multispecies Coalescent model – including non-anomalous scenarios – ASTRAL can produce a tree that does not correspond to any topology displayed by the true underlying network. This finding highlights the need for caution when using ASTRAL-based inferences in suspected hybridization cases. 

The tree of blobs of a species network shows only the tree-like aspects of relationships of taxa on a network, omitting information on network substructures where hybridization or other types of lateral transfer of genetic information occur. By isolating such regions of a network, inference of the tree of blobs can serve as a starting point for a more detailed investigation, or indicate the limit of what may be inferrable without additional assumptions. Building on our theoretical work on the identifiability of the tree of blobs from gene quartet distributions under the Network Multispecies Coalescent model, we develop an algorithm, TINNiK, for statistically consistent tree of blobs inference. We provide examples of its application to both simulated and empirical datasets, utilizing an implementation in the MSCquartets 2.0 R package. 

IQ-TREE (http://www.iqtree.org) is a widely used open-source software tool for efficiently inferring phylogenetic trees under maximum likelihood. Here, we present IQ-TREE version 3, the third major release of the software. IQ-TREE 3 significantly extends version 2 with new features, including mixture models as an alternative to partitioned models, gene and site concordance factors to quantify discordance between genomic regions, and a fully-featured sequence simulator. The IQ-TREE 3 source code is available at https://github.com/iqtree/iqtree3. 

Abstract When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors—the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network. Addressing these identifiability issues is essential for designing statistically consistent inference methods. 

Reticulations in a phylogenetic network represent processes such as gene flow, admixture, recombination and hybrid speciation. Extending definitions from the tree setting, an anomalous network is one in which some unrooted tree topology displayed in the network appears in gene trees with a lower frequency than a tree not displayed in the network. We investigate anomalous networks under the Network Multispecies Coalescent Model with possible correlated inheritance at reticulations. Focusing on subsets of 4 taxa, we describe a new algorithm to calculate quartet concordance factors on networks of any level, faster than previous algorithms because of its focus on 4 taxa. We then study topological properties required for a 4-taxon network to be anomalous, uncovering the key role of 32-cycles: cycles of 3 edges parent to a sister group of 2 taxa. Under the model of common inheritance, that is, when each gene tree coalesces within a species tree displayed in the network, we prove that 4-taxon networks are never anomalous. Under independent and various levels of correlated inheritance, we use simulations under realistic parameters to quantify the prevalence of anomalous 4-taxon networks, finding that truly anomalous networks are rare. At the same time, however, we find a significant fraction of networks close enough to the anomaly zone to appear anomalous, when considering the quartet concordance factors observed from a few hundred genes. These apparent anomalies may challenge network inference methods.