{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T23:10:27Z","timestamp":1774912227781,"version":"3.50.1"},"reference-count":55,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"H. I. Romnes faculty fellowship"},{"DOI":"10.13039\/100001395","name":"Wisconsin Alumni Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100001395","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1902892"],"award-info":[{"award-number":["DMS 1902892"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,5,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>With growing genome-wide molecular datasets from next-generation sequencing, phylogenetic networks can be estimated using a variety of approaches. These phylogenetic networks include events like hybridization, gene flow or horizontal gene transfer explicitly. However, the most accurate network inference methods are computationally heavy. Methods that scale to larger datasets do not calculate a full likelihood, such that traditional likelihood-based tools for model selection are not applicable to decide how many past hybridization events best fit the data. We propose here a goodness-of-fit test to quantify the fit between data observed from genome-wide multi-locus data, and patterns expected under the multi-species coalescent model on a candidate phylogenetic network.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We identified weaknesses in the previously proposed TICR test, and proposed corrections. The performance of our new test was validated by simulations on real-world phylogenetic networks. Our test provides one of the first rigorous tools for model selection, to select the adequate network complexity for the data at hand. The test can also work for identifying poorly inferred areas on a network.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>Software for the goodness-of-fit test is available as a Julia package at https:\/\/github.com\/cecileane\/QuartetNetworkGoodnessFit.jl.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btaa863","type":"journal-article","created":{"date-parts":[[2020,9,22]],"date-time":"2020-09-22T23:49:33Z","timestamp":1600818573000},"page":"634-641","source":"Crossref","is-referenced-by-count":24,"title":["Assessing the fit of the multi-species network coalescent to multi-locus data"],"prefix":"10.1093","volume":"37","author":[{"given":"Ruoyi","family":"Cai","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Wisconsin - Madison , Madison, WI 53706, USA"}]},{"given":"C\u00e9cile","family":"An\u00e9","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin - Madison , Madison, WI 53706, USA"},{"name":"Department of Botany, University of Wisconsin - Madison , Madison, WI 53706, USA"}]}],"member":"286","published-online":{"date-parts":[[2020,12,7]]},"reference":[{"key":"2023051800332219800_btaa863-B1","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1007\/s00285-010-0355-7","article-title":"Identifying the rooted species tree from the distribution of unrooted gene trees under the coalescent","volume":"62","author":"Allman","year":"2011","journal-title":"J. Math. Biol"},{"key":"2023051800332219800_btaa863-B2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/s13015-019-0159-2","article-title":"NANUQ: a method for inferring species networks from gene trees under the coalescent model","volume":"14","author":"Allman","year":"2019","journal-title":"Algorithms Mol. Biol"},{"key":"2023051800332219800_btaa863-B3","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1093\/molbev\/msl170","article-title":"Bayesian estimation of concordance among gene trees","volume":"24","author":"An\u00e9","year":"2007","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B4","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1093\/sysbio\/syy005","article-title":"Inference of adaptive shifts for multivariate correlated traits","volume":"67","author":"Bastide","year":"2018","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B5","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s11222-011-9236-1","article-title":"Slope heuristics: overview and implementation","volume":"22","author":"Baudry","year":"2012","journal-title":"Stat. Comput"},{"key":"2023051800332219800_btaa863-B6","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1002\/tax.562013","article-title":"Concordance trees, concordance factors, and the exploration of reticulate genealogy","volume":"56","author":"Baum","year":"2007","journal-title":"Taxon"},{"key":"2023051800332219800_btaa863-B7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1137\/141000671","article-title":"Julia: a fresh approach to numerical computing","volume":"59","author":"Bezanson","year":"2017","journal-title":"SIAM Review"},{"key":"2023051800332219800_btaa863-B8","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1093\/sysbio\/syz056","article-title":"Phylogenetic trees and networks can serve as powerful and complementary approaches for analysis of genomic data","volume":"69","author":"Blair","year":"2020","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B9","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1093\/sysbio\/syy023","article-title":"HyDe: a Python package for genome-scale hybridization detection","volume":"67","author":"Blischak","year":"2018","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1146\/annurev-ecolsys-110617-062249","article-title":"Evaluating model performance in evolutionary biology","volume":"49","author":"Brown","year":"2018","journal-title":"Annu. Rev. Ecol. Evol. Syst"},{"key":"2023051800332219800_btaa863-B11","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1093\/sysbio\/syy019","article-title":"The biogeography of deep time phylogenetic reticulation","volume":"67","author":"Burbrink","year":"2018","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B12","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1109\/TCBB.2016.2638911","article-title":"Efficient quartet representations of trees and applications to supertree and summary methods","volume":"15","author":"Davidson","year":"2018","journal-title":"IEEE\/ACM Trans. Comput. Biol. Bioinformatics"},{"key":"2023051800332219800_btaa863-B13","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1093\/sysbio\/syy040","article-title":"Modeling hybridization under the network multispecies coalescent","volume":"67","author":"Degnan","year":"2018","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B14","doi-asserted-by":"crossref","first-page":"2239","DOI":"10.1093\/molbev\/msr048","article-title":"Testing for ancient admixture between closely related populations","volume":"28","author":"Durand","year":"2011","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B15","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/978-3-030-10837-3_13","volume-title":"Bioinformatics and Phylogenetics: Seminal Contributions of Bernard Moret","author":"Elworth","year":"2019"},{"key":"2023051800332219800_btaa863-B16","doi-asserted-by":"crossref","first-page":"e1003905","DOI":"10.1371\/journal.pgen.1003905","article-title":"Robust demographic inference from genomic and SNP data","volume":"9","author":"Excoffier","year":"2013","journal-title":"PLoS Genet"},{"key":"2023051800332219800_btaa863-B17","doi-asserted-by":"crossref","first-page":"106878","DOI":"10.1016\/j.ympev.2020.106878","article-title":"Phylogenomic insights into the temporal-spatial divergence history, evolution of leaf habit and hybridization in Stachyurus (Stachyuraceae)","volume":"150","author":"Feng","year":"2020","journal-title":"Mol. Phylogenetics Evol"},{"key":"2023051800332219800_btaa863-B18","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1002\/ajb2.1018","article-title":"New prospects in the detection and comparative analysis of hybridization in the tree of life","volume":"105","author":"Folk","year":"2018","journal-title":"Am. J. Bot"},{"key":"2023051800332219800_btaa863-B19","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1126\/science.1188021","article-title":"A draft sequence of the Neandertal genome","volume":"328","author":"Green","year":"2010","journal-title":"Science"},{"key":"2023051800332219800_btaa863-B20","doi-asserted-by":"crossref","first-page":"2878","DOI":"10.1093\/molbev\/msz178","article-title":"A three-sample test for introgression","volume":"36","author":"Hahn","year":"2019","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B21","first-page":"242","author":"Hejase","year":"2018"},{"key":"2023051800332219800_btaa863-B22","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1111\/2041-210X.12285","article-title":"Intrinsic inference difficulties for trait evolution with Ornstein-Uhlenbeck models","volume":"5","author":"Ho","year":"2014","journal-title":"Methods Ecol. Evol"},{"key":"2023051800332219800_btaa863-B23","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1093\/sysbio\/syz073","article-title":"Reticulate evolution helps explain apparent homoplasy in floral biology and pollination in baobabs (Adansonia; Bombacoideae; Malvaceae)","volume":"69","author":"Karimi","year":"2020","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B24","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1111\/2041-210X.12534","article-title":"Fast and accurate detection of evolutionary shifts in Ornstein-Uhlenbeck models","volume":"7","author":"Khabbazian","year":"2016","journal-title":"Methods Ecol. Evol"},{"key":"2023051800332219800_btaa863-B25","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1111\/jse.12519","article-title":"Diversification of Hawaiian Cyrtandra (Gesneriaceae) under the influence of incomplete lineage sorting and hybridization","volume":"57","author":"Kleinkopf","year":"2019","journal-title":"J. Syst. Evol"},{"key":"2023051800332219800_btaa863-B26","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1093\/sysbio\/syp055","article-title":"Identifying hybridization events in the presence of coalescence via model selection","volume":"58","author":"Kubatko","year":"2009","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B27","doi-asserted-by":"crossref","first-page":"2910","DOI":"10.1093\/bioinformatics\/btq539","article-title":"BUCKy: gene tree\/species tree reconciliation with Bayesian concordance analysis","volume":"26","author":"Larget","year":"2010","journal-title":"Bioinformatics"},{"key":"2023051800332219800_btaa863-B28","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0167-7152(94)00234-8","article-title":"A new family of goodness-of-fit statistics for discrete multivariate data","volume":"25","author":"Lorenzen","year":"1995","journal-title":"Stat. Probabil. Lett"},{"key":"2023051800332219800_btaa863-B29","doi-asserted-by":"crossref","DOI":"10.1145\/3307339.3342151","article-title":"Robinson-Foulds reticulation networks","author":"Markin","year":"2019","journal-title":"In: Proceedings of the 10th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics, BCB \u201919, 77\u201386, New York, USA: Association for Computing Machinery"},{"key":"2023051800332219800_btaa863-B30","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1111\/jbi.13542","article-title":"Reticulate evolution in nuclear Middle America causes discordance in the phylogeny of palm-pitvipers (Viperidae: Bothriechis)","volume":"46","author":"Mason","year":"2019","journal-title":"J. Biogeogr"},{"key":"2023051800332219800_btaa863-B31","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.tpb.2008.10.004","article-title":"Detecting hybrid speciation in the presence of incomplete lineage sorting using gene tree incongruence: a model","volume":"75","author":"Meng","year":"2009","journal-title":"Theor. Popul. Biol"},{"key":"2023051800332219800_btaa863-B32","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1093\/sysbio\/syv045","article-title":"Resolving evolutionary relationships in closely related species with whole-genome sequencing data","volume":"64","author":"Nater","year":"2015","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B33","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1093\/sysbio\/syaa005","article-title":"Implementing large genomic single nucleotide polymorphism data sets in phylogenetic network reconstructions: a case study of particularly rapid radiations of cichlid fish","volume":"69","author":"Olave","year":"2020","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B34","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1002\/ajb2.1016","article-title":"Quartet sampling distinguishes lack of support from conflicting support in the green plant tree of life","volume":"105","author":"Pease","year":"2018","journal-title":"Am. J. Bot"},{"key":"2023051800332219800_btaa863-B35","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1093\/bioinformatics\/btv684","article-title":"Reliable ABC model choice via random forests","volume":"32","author":"Pudlo","year":"2016","journal-title":"Bioinformatics"},{"key":"2023051800332219800_btaa863-B36","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1111\/mec.14491","article-title":"Combining allele frequency and tree-based approaches improves phylogeographic inference from natural history collections","volume":"27","author":"Ruffley","year":"2018","journal-title":"Mol. Ecol"},{"key":"2023051800332219800_btaa863-B37","author":"Semple","year":"2003"},{"key":"2023051800332219800_btaa863-B38","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1093\/biolinnean\/bly067","article-title":"Testing for the presence of cryptic diversity in tail-dropper slugs (Prophysaon) using molecular data","volume":"124","author":"Smith","year":"2018","journal-title":"Biol. J. Linn. Soc"},{"key":"2023051800332219800_btaa863-B39","doi-asserted-by":"crossref","first-page":"e1005896","DOI":"10.1371\/journal.pgen.1005896","article-title":"Inferring phylogenetic networks with maximum pseudolikelihood under incomplete lineage sorting","volume":"12","author":"Sol\u00eds-Lemus","year":"2016","journal-title":"PLoS Genet"},{"key":"2023051800332219800_btaa863-B40","doi-asserted-by":"crossref","first-page":"3292","DOI":"10.1093\/molbev\/msx235","article-title":"Phylonetworks: a package for phylogenetic networks","volume":"34","author":"Sol\u00eds-Lemus","year":"2017","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B41","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1093\/sysbio\/syv039","article-title":"Exploring tree-like and non-tree-like patterns using genome sequences: an example using the inbreeding plant species Arabidopsis thaliana (L.) Heynh","volume":"64","author":"Stenz","year":"2015","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B42","first-page":"5","article-title":"An overview of composite likelihood methods","volume":"21","author":"Varin","year":"2011","journal-title":"Stat. Sin"},{"key":"2023051800332219800_btaa863-B43","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1093\/sysbio\/syx085","article-title":"Coestimating reticulate phylogenies and gene trees from multilocus sequence data","volume":"67","author":"Wen","year":"2018","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B44","doi-asserted-by":"crossref","first-page":"e1006006","DOI":"10.1371\/journal.pgen.1006006","article-title":"Bayesian inference of reticulate phylogenies under the multispecies network coalescent","volume":"12","author":"Wen","year":"2016","journal-title":"PLoS Genet"},{"key":"2023051800332219800_btaa863-B45","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1089\/cmb.2013.0072","article-title":"An algorithm for constructing parsimonious hybridization networks with multiple phylogenetic trees","volume":"20","author":"Wu","year":"2013","journal-title":"J. Comput. Biol"},{"key":"2023051800332219800_btaa863-B46","doi-asserted-by":"crossref","first-page":"S10","DOI":"10.1186\/1471-2164-16-S10-S10","article-title":"A maximum pseudo-likelihood approach for phylogenetic networks","volume":"16","author":"Yu","year":"2015","journal-title":"BMC Genomics"},{"key":"2023051800332219800_btaa863-B47","doi-asserted-by":"crossref","first-page":"e1002660","DOI":"10.1371\/journal.pgen.1002660","article-title":"The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection","volume":"8","author":"Yu","year":"2012","journal-title":"PLoS Genet"},{"key":"2023051800332219800_btaa863-B48","doi-asserted-by":"crossref","first-page":"S6","DOI":"10.1186\/1471-2105-14-S15-S6","article-title":"Fast algorithms and heuristics for phylogenomics under ILS and hybridization","volume":"14","author":"Yu","year":"2013","journal-title":"BMC Bioinformatics"},{"key":"2023051800332219800_btaa863-B49","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1093\/sysbio\/syt037","article-title":"Parsimonious inference of hybridization in the presence of incomplete lineage sorting","volume":"62","author":"Yu","year":"2013","journal-title":"Syst. Biol"},{"key":"2023051800332219800_btaa863-B50","doi-asserted-by":"crossref","first-page":"16448","DOI":"10.1073\/pnas.1407950111","article-title":"Maximum likelihood inference of reticulate evolutionary histories","volume":"111","author":"Yu","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023051800332219800_btaa863-B51","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1093\/molbev\/msz112","article-title":"Phylogenomics reveals an ancient hybrid origin of the Persian walnut","volume":"36","author":"Zhang","year":"2019","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B52","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1093\/molbev\/msx307","article-title":"Bayesian inference of species networks from multilocus sequence data","volume":"35","author":"Zhang","year":"2018","journal-title":"Mol. Biol. Evol"},{"key":"2023051800332219800_btaa863-B53","doi-asserted-by":"crossref","first-page":"i376","DOI":"10.1093\/bioinformatics\/bty295","article-title":"Inference of species phylogenies from bi-allelic markers using pseudo-likelihood","volume":"34","author":"Zhu","year":"2018","journal-title":"Bioinformatics"},{"key":"2023051800332219800_btaa863-B54","doi-asserted-by":"crossref","first-page":"i370","DOI":"10.1093\/bioinformatics\/btz359","article-title":"A divide-and-conquer method for scalable phylogenetic network inference from multilocus data","volume":"35","author":"Zhu","year":"2019","journal-title":"Bioinformatics"},{"key":"2023051800332219800_btaa863-B55","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1186\/s12859-015-0721-y","article-title":"Hybrid-lambda: simulation of multiple merger and kingman gene genealogies in species networks and species trees","volume":"16","author":"Zhu","year":"2015","journal-title":"BMC Bioinformatics"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btaa863\/34751160\/btaa863.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/37\/5\/634\/50356257\/btaa863.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/37\/5\/634\/50356257\/btaa863.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:34:38Z","timestamp":1684370078000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/37\/5\/634\/5919071"}},"subtitle":[],"editor":[{"given":"Schwartz","family":"Russell","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,7]]},"references-count":55,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,5,5]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btaa863","relation":{},"ISSN":["1367-4803","1367-4811"],"issn-type":[{"value":"1367-4803","type":"print"},{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,3,1]]},"published":{"date-parts":[[2020,12,7]]}}}