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Allman ES, Baños H, Garrote-Lopez M, Rhodes JA. Identifiability of Level-1 Species Networks from Gene Tree Quartets. Bull Math Biol 2024; 86:110. [PMID: 39052074 PMCID: PMC11272829 DOI: 10.1007/s11538-024-01339-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2024] [Accepted: 07/01/2024] [Indexed: 07/27/2024]
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.
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Affiliation(s)
- Elizabeth S Allman
- Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK, USA.
| | - Hector Baños
- Department of Mathematics, California State University San Bernadino, San Bernadino, CA, USA
| | | | - John A Rhodes
- Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK, USA
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Allman ES, Baños H, Mitchell JD, Rhodes JA. TINNiK: Inference of the Tree of Blobs of a Species Network Under the Coalescent. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.04.20.590418. [PMID: 38712257 PMCID: PMC11071406 DOI: 10.1101/2024.04.20.590418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2024]
Abstract
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. MSC Classification 92D15, 92D20.
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Ané C, Fogg J, Allman ES, Baños H, Rhodes JA. Anomalous networks under the multispecies coalescent: theory and prevalence. J Math Biol 2024; 88:29. [PMID: 38372830 DOI: 10.1007/s00285-024-02050-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2023] [Revised: 01/18/2024] [Accepted: 01/21/2024] [Indexed: 02/20/2024]
Abstract
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 [Formula: see text]-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.
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Affiliation(s)
- Cécile Ané
- Department of Statistics, University of Wisconsin - Madison, Madison, WI, 53706, USA.
- Department of Botany, University of Wisconsin - Madison, Madison, WI, 53706, USA.
| | - John Fogg
- Department of Statistics, University of Wisconsin - Madison, Madison, WI, 53706, USA
| | - Elizabeth S Allman
- Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775-6660, USA
| | - Hector Baños
- Department of Biochemistry & Molecular Biology, Dalhousie University, Halifax, NS, Canada
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada
| | - John A Rhodes
- Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775-6660, USA
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Allman ES, Baños H, Garrote-Lopez M, Rhodes JA. IDENTIFIABILITY OF LEVEL-1 SPECIES NETWORKS FROM GENE TREE QUARTETS. ARXIV 2024:arXiv:2401.06290v1. [PMID: 38259350 PMCID: PMC10802673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
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.
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Frankel LE, Ané C. Summary Tests of Introgression Are Highly Sensitive to Rate Variation Across Lineages. Syst Biol 2023; 72:1357-1369. [PMID: 37698548 DOI: 10.1093/sysbio/syad056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Revised: 07/07/2023] [Accepted: 08/29/2023] [Indexed: 09/13/2023] Open
Abstract
The evolutionary implications and frequency of hybridization and introgression are increasingly being recognized across the tree of life. To detect hybridization from multi-locus and genome-wide sequence data, a popular class of methods are based on summary statistics from subsets of 3 or 4 taxa. However, these methods often carry the assumption of a constant substitution rate across lineages and genes, which is commonly violated in many groups. In this work, we quantify the effects of rate variation on the D test (also known as ABBA-BABA test), the D3 test, and HyDe. All 3 tests are used widely across a range of taxonomic groups, in part because they are very fast to compute. We consider rate variation across species lineages, across genes, their lineage-by-gene interaction, and rate variation across gene-tree edges. We simulated species networks according to a birth-death-hybridization process, so as to capture a range of realistic species phylogenies. For all 3 methods tested, we found a marked increase in the false discovery of reticulation (type-1 error rate) when there is rate variation across species lineages. The D3 test was the most sensitive, with around 80% type-1 error, such that D3 appears to more sensitive to a departure from the clock than to the presence of reticulation. For all 3 tests, the power to detect hybridization events decreased as the number of hybridization events increased, indicating that multiple hybridization events can obscure one another if they occur within a small subset of taxa. Our study highlights the need to consider rate variation when using site-based summary statistics, and points to the advantages of methods that do not require assumptions on evolutionary rates across lineages or across genes.
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Affiliation(s)
- Lauren E Frankel
- Department of Botany, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Cécile Ané
- Department of Botany, University of Wisconsin-Madison, Madison, WI 53706, USA
- Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706, USA
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Ané C, Fogg J, Allman ES, Baños H, Rhodes JA. ANOMALOUS NETWORKS UNDER THE MULTISPECIES COALESCENT: THEORY AND PREVALENCE. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.18.553582. [PMID: 37662314 PMCID: PMC10473666 DOI: 10.1101/2023.08.18.553582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/05/2023]
Abstract
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.
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Affiliation(s)
- Cécile Ané
- Department of Statistics, University of Wisconsin - Madison, WI, 53706, USA
- Department of Botany, University of Wisconsin - Madison, WI, 53706, USA
| | - John Fogg
- Department of Statistics, University of Wisconsin - Madison, WI, 53706, USA
| | - Elizabeth S Allman
- Department of Mathematics and Statistics, University of Alaska - Fairbanks, AK, 99775-6660, USA
| | - Hector Baños
- Department of Biochemistry & Molecular Biology, Dalhousie University, Halifax, Nova Scotia, Canada
- Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada
| | - John A Rhodes
- Department of Mathematics and Statistics, University of Alaska - Fairbanks, AK, 99775-6660, USA
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