New substitution models for rooting phylogenetic trees
Open accessAbstract
The root of a phylogenetic tree is fundamental to its biological interpretation, but standard substitution models do not provide any information on its position. Here, we describe two recently developed models that relax the usual assumptions of stationarity and reversibility, thereby facilitating root inference without the need for an outgroup. We compare the performance of these models on a classic test case for phylogenetic methods, before considering two highly topical questions in evolutionary biology: the deep structure of the tree of life and the root of the archaeal radiation. We show that all three alignments contain meaningful rooting information that can be harnessed by these new models, thus complementing and extending previous work based on outgroup rooting. In particular, our analyses exclude the root of the tree of life from the eukaryotes or Archaea, placing it on the bacterial stem or within the Bacteria. They also exclude the root of the archaeal radiation from several major clades, consistent with analyses using other rooting methods. Overall, our results demonstrate the utility of non-reversible and non-stationary models for rooting phylogenetic trees, and identify areas where further progress can be made.
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Bacterial hyperthermophiles such as Aquificales and Thermotogales can artificially be attracted to the root of the tree due to phylogenetic artifacts.
“For instance, previous work has shown that bacterial hyperthermophiles such as Aquificales and Thermotogales can artificially be attracted to the root of the tree due to phylogenetic artifacts (Williams et al. 2015) (Fig. 3A).”
From The Emergence of Life (2019) · cites this paper as Williams et al. 2015
In “The relationship between Thermus and Deinococcus” (Figure 1; page unavailable), the paper shows that a standard model incorrectly groups the thermophiles Aquifex and Thermotoga with Thermus because of similar sequence composition. It does not show that these bacteria are artificially attracted to the root: the most-supported root split separates Aquifex from the other taxa under both models. (LLM, conf=0.86)
Experimental — accuracy not yet measuredLocating the root in the current tree of life is essential for reconstructing the early evolutionary history of life.
“In this regard, it is important to locate the root in the current tree of life as this is essential for reconstructing the early evolutionary history of life (Williams et al. 2015).”
From The Emergence of Life (2019) · cites this paper as Williams et al. 2015
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“Indeed, the monophyly of DPANN was not recovered by in depth phylogenomic analyses (Brochier-Armanet et al., 2011; Petitjean et al., 2014; Williams et al., 2015).”
Church, D. L., Cerutti, L., Gürtler, A., Griener, T. P., Zelazny, A. M., & Emler, S. (2020) · Clinical Microbiology Reviews · doi:10.1128/cmr.00053-19 · Cited by 351 · see citing works
“Rooting a phylogenetic tree using a somewhat distantly related sequence of a different genus can help to build more stable clusters of very similar sequences; bootstrapping will indicate the robustness of a branch but is generally low for highly similar sequences from genes, such as the 16S (129).”
Genomic exploration of the diversity, ecology, and evolution of the archaeal domain of life
Spang, A., Caceres, E. F., & Ettema, T. J. G. (2017) · Science · doi:10.1126/science.aaf3883 · Cited by 346 · see citing works
“Sophisticated Bayesian models to root the archaeal tree without the need for an outgroup retrieved a root between TACK archaea and a clade comprising Euryarchaeota/DPANN (82).”
STRIDE: Species Tree Root Inference from Gene Duplication Events
Emms, D. M., & Kelly, S. (2017) · Molecular Biology and Evolution · doi:10.1093/molbev/msx259 · Cited by 311 · see citing works
“Although time-irreversible models of sequence evolution exist, they do not provide a method for accurately inferring the direction of time in a tree (Huelsenbeck et al. 2002; Williams et al. 2015).”
Phylogenomics provides robust support for a two-domains tree of life
Williams, T. A., Cox, C. J., Foster, P. G., Szöllősi, G. J., & Embley, T. M. (2019) · Nature Ecology & Evolution · doi:10.1038/s41559-019-1040-x · Cited by 274 · see citing works
Self-citationIntegrative modeling of gene and genome evolution roots the archaeal tree of life
Williams, T. A., Szöllősi, G. J., Spang, A., Foster, P. G., Heaps, S. E., Boussau, B., Ettema, T. J. G., & Embley, T. M. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1618463114 · Cited by 233 · see citing works
“under standard models of sequence evolution, which do not directly infer the root (55, 56).”
Self-citationPhylogenetic rooting using minimal ancestor deviation
Tria, F. D. K., Landan, G., & Dagan, T. (2017) · Nature Ecology & Evolution · doi:10.1038/s41559-017-0193 · Cited by 241 · see citing works
“In the non-reversible models approach the transition probabilities are asymmetric and require a specification of the ancestor-descendant relation for each branch 6 .”
Genomic diversity, lifestyles and evolutionary origins of DPANN archaea
Dombrowski, N., Lee, J.-H., Williams, T. A., Offre, P., & Spang, A. (2019) · FEMS Microbiology Letters · doi:10.1093/femsle/fnz008 · Cited by 230 · see citing works
“While site- and branch-heterogeneous models have been described (Blanquart and Lartillot 2008; Heaps et al. 2014; Williams et al. 2015; Cherlin et al. 2018) and implemented, they are currently computationally intractable even on modestly”
Self-citationMinimum variance rooting of phylogenetic trees and implications for species tree reconstruction
Mai, U., Sayyari, E., & Mirarab, S. (2017) · PLoS ONE · doi:10.1371/journal.pone.0182238 · Cited by 81 · see citing works
Camprubí, E., de Leeuw, J. W., House, C. H., Raulin, F., Russell, M. J., Spang, A., Tirumalai, M. R., & Westall, F. (2019) · Space Science Reviews · doi:10.1007/s11214-019-0624-8 · Cited by 84 · see citing works
“In this regard, it is important to locate the root in the current tree of life as this is essential for reconstructing the early evolutionary history of life (Williams et al. 2015).”
InfluentialRedmond, A. K., Zou, J., Secombes, C. J., Macqueen, D. J., & Dooley, H. M. (2019) · Frontiers in Immunology · doi:10.3389/fimmu.2019.01558 · Cited by 72 · see citing works
“Fortunately, it can often be counteracted by breaking long branches with additional taxa (43) (44) (45) , applying site-heterogeneous models of evolution (42, 46) , removing fast-evolving sites (47) , and/or identifying the best outgroup (48) (49) (50) (51) , in addition to using outgroupfree methods (41, (52) (53) (5…”
Cavalier‐Smith, T., & Chao, E. E. Y. (2020) · PROTOPLASMA · doi:10.1007/s00709-019-01442-7 · Cited by 68 · see citing works
“None of our trees placed the root within non-DPANN euryarchaeotes as did Raymann et al. (2015) or within Filarchaeota, but both the position of DPANNs which appeared as one or more often two clades and of the root were sensitive to taxon sampling and method, the root often seeming within or beside DPANNs; we think thi…”
InfluentialNaser-Khdour, S., Minh, B. Q., & Lanfear, R. (2021) · Systematic Biology · doi:10.1093/sysbio/syab067 · Cited by 58 · see citing works
“2018) or relatively small empirical data sets (Yang and Roberts 1995; Yap and Speed 2005; Jayaswal et al. 2011; Heaps et al. 2014; Williams et al. 2015; Cherlin et al. 2018).”
Genome size evolution in the Archaea
Kellner, S., Spang, A., Offre, P., Szöllősi, G. J., Petitjean, C., & Williams, T. A. (2018) · Emerging Topics in Life Sciences · doi:10.1042/etls20180021 · Cited by 48 · see citing works
Self-citationInvestigating the Origins of Membrane Phospholipid Biosynthesis Genes Using Outgroup-Free Rooting
Coleman, G. A., Pancost, R. D., & Williams, T. A. (2019) · Genome Biology and Evolution · doi:10.1093/gbe/evz034 · Cited by 47 · see citing works
Self-citationThe Evolutionary Origins of Extreme Halophilic Archaeal Lineages
Feng, Y., Neri, U., Gosselin, S., Louyakis, A. S., Papke, R. T., Gophna, U., & Gogarten, J. P. (2021) · Genome Biology and Evolution · doi:10.1093/gbe/evab166 · Cited by 37 · see citing works
Akaryotes and Eukaryotes are independent descendants of a universal common ancestor
Harish, A., & Kurland, C. G. (2017) · Biochimie · doi:10.1016/j.biochi.2017.04.013 · Cited by 33 · see citing works
Empirical genome evolution models root the tree of life
Harish, A., & Kurland, C. G. (2017) · Biochimie · doi:10.1016/j.biochi.2017.04.014 · Cited by 33 · see citing works
Devos, D. P. (2021) · Molecular Biology and Evolution · doi:10.1093/molbev/msab186 · Cited by 33 · see citing works
Inferring the Deep Past from Molecular Data
Williams, T. A., Schrempf, D., Szöllősi, G. J., Cox, C. J., Foster, P. G., & Embley, T. M. (2021) · Genome Biology and Evolution · doi:10.1093/gbe/evab067 · Cited by 31 · see citing works
Self-citationAssessing the accuracy of phylogenetic rooting methods on prokaryotic gene families
Wade, T. E., Rangel, L. T., Kundu, S., Fournier, G. P., & Bansal, M. S. (2020) · PLoS ONE · doi:10.1371/journal.pone.0232950 · Cited by 30 · see citing works
“This category includes strict molecular clock rooting [17], Bayesian molecular clock rooting [18], methods based on non-reversible and/or non-stationary evolutionary models [19–23], and relaxed clock models [24, 25].”
Nuclear Pore-Like Structures in a Compartmentalized Bacterium
Sagulenko, E., Nouwens, A. S., Webb, R. I., Green, K., Yee, B., Morgan, G., Leis, A. P., Lee, K., Butler, M. K., Chia, N., et al. (2017) · PLoS ONE · doi:10.1371/journal.pone.0169432 · Cited by 30 · see citing works
Reconstruction of the sialylation pathway in the ancestor of eukaryotes
Petit, D. P., Teppa, E., Cenci, U., Ball, S. G., & Harduin‐Lepers, A. (2018) · Scientific Reports · doi:10.1038/s41598-018-20920-1 · Cited by 30 · see citing works
Gruenstaeudl, M. (2019) · Plant Systematics and Evolution · doi:10.1007/s00606-019-01610-5 · Cited by 27 · see citing works
Changing ideas about eukaryotic origins
Williams, T. A., & Embley, T. M. (2015) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2014.0318 · Cited by 26 · see citing works
Self-citationRecoding Amino Acids to a Reduced Alphabet may Increase or Decrease Phylogenetic Accuracy
Foster, P. G., Schrempf, D., Szöllősi, G. J., Williams, T. A., Cox, C. J., & Embley, T. M. (2022) · Systematic Biology · doi:10.1093/sysbio/syac042 · Cited by 24 · see citing works
Self-citationArchaea‐First and the Co‐Evolutionary Diversification of Domains of Life
Staley, J. T., & Caetano‐Anollés, G. (2018) · BioEssays · doi:10.1002/bies.201800036 · Cited by 19 · see citing works
From pairs of most similar sequences to phylogenetic best matches
Stadler, P. F., Geiß, M., Schaller, D., Sánchez, A. L., Laffitte, M. E. G., Valdivia, D. I., Hellmuth, M., & Hernández-Rosales, M. (2020) · Algorithms for Molecular Biology · doi:10.1186/s13015-020-00165-2 · Cited by 15 · see citing works
Staley, J. T., & Fuerst, J. A. (2017) · Research in Microbiology · doi:10.1016/j.resmic.2017.01.001 · Cited by 12 · see citing works
A road map for phylogenetic models of species trees
Cornuault, J., & Sanmartín, I. (2022) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2022.107483 · Cited by 12 · see citing works
Bremer, N., Knopp, M. R., Martin, W. F., & Tria, F. D. K. (2022) · Life · doi:10.3390/life12070995 · Cited by 11 · see citing works
“Methods commonly used for rooting include: (i) the outgroup [1], including the special case of tree rooting with ancient gene duplications [2]; (ii) the midpoint criterion [3]; (iii) the minimal ancestor deviation (MAD) approach [4]; (iv) molecular clock models [5]; and (v) time-irreversible models [6].”
Practical Guide and Review of Fossil Tip-Dating in Phylogenetics
Heckeberg, N. S., Capobianco, A., Khakurel, B., Darlim, G., & Höhna, S. (2025) · Systematic Biology · doi:10.1093/sysbio/syaf050 · Cited by 11 · see citing works
“Although we focus here on time-reversible models, there are numerous non-time-reversible models that can potentially be defined ( Yang 1994 ; Huelsenbeck et al. 2002 ; Williams et al. 2015 ).”
Naser-Khdour, S., Minh, B. Q., & Lanfear, R. (2020) · ANU Open Research (Australian National University) · doi:10.5061/dryad.fj6q573rx · Cited by 12 · see citing works
Molecular phylogeny of two Aliinostoc isolates from a paddy field
Nowruzi, B., & Lorenzi, A. S. (2023) · Plant Systematics and Evolution · doi:10.1007/s00606-023-01848-0 · Cited by 8 · see citing works
Fast speciations and slow genes: uncovering the root of living canids
Lamarca, A. P., & Schrago, C. G. (2019) · Biological Journal of the Linnean Society · doi:10.1093/biolinnean/blz181 · Cited by 7 · see citing works
Phylogenetic Analysis That Models Compositional Heterogeneity over the Tree
Foster, P. G. (2022) · Methods in molecular biology · doi:10.1007/978-1-0716-2691-7_6 · Cited by 9 · see citing works
Kerk, D., Valdés‐Tresanco, M. E., Toth, R., Noskov, S. Y., Ng, K. K.-S., & Moorhead, G. B. G. (2021) · BBA Advances · doi:10.1016/j.bbadva.2021.100005 · Cited by 6 · see citing works
Naser-Khdour, S., Minh, B. Q., & Lanfear, R. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.07.31.230144 · Cited by 6 · see citing works
Rangel, L. T., Soucy, S. M., Setúbal, J. C., Gogarten, J. P., & Fournier, G. P. (2021) · Genome Biology and Evolution · doi:10.1093/gbe/evab187 · Cited by 4 · see citing works
Rooting Species Trees Using Gene Tree-Species Tree Reconciliation
Harris, B. J., Sheridan, P. O., Davín, A., Gubry‐Rangin, C., Szöllősi, G. J., & Williams, T. A. (2022) · Methods in molecular biology · doi:10.1007/978-1-0716-2691-7_9 · Cited by 3 · see citing works
Self-citationPhylogenomic Testing of Root Hypotheses
Tria, F. D. K., Landan, G., Picazo, D. R., & Dagan, T. (2023) · Genome Biology and Evolution · doi:10.1093/gbe/evad096 · Cited by 2 · see citing works
Incorporating compositional heterogeneity into Lie Markov models for phylogenetic inference
Hannaford, N. E., Heaps, S. E., Nye, T. M. W., Williams, T. A., & Embley, T. M. (2020) · The Annals of Applied Statistics · doi:10.1214/20-aoas1369 · Cited by 3 · see citing works
“In earlier work, where we developed non-homogeneous, non-stationary extensions of the (reversible) HKY85 and GTR models (Heaps et al., 2014; Williams et al., 2015), this was achieved by keeping the exchangeability parameters fixed across the tree, so that only the stationary probabilities varied.”
Self-citationGeneralizing rate heterogeneity across sites in statistical phylogenetics
Heaps, S. E., Nye, T. M. W., Boys, R. J., Williams, T. A., Cherlin, S., & Embley, T. M. (2020) · Statistical Modelling · doi:10.1177/1471082x19829937 · Cited by 1 · see citing works
“ersible rate matrix Q (b) which factorises into a composition vector ˇ (b) and a set of exchangeability parameters ˆthat are assumed constant across the tree. We use the formulation of the model from Williams et al. (2015) in which the composition vector on the root edge of the underlying unrooted topology is the same…”
Self-citationRooting the deep divergence of land plantsPreprint
Chen, H., & de Vries, J. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.11.29.691271 · Cited by 2 · see citing works
“…(MAD) rooting 65 , 3) minimum variance rooting 66 , 4) molecular clock-based rooting 67 , 5) non-reversible substitution model-based rooting 68 , 6) paralogue-based rooting 69 , 7) multispecies coalescent model-based rooting 70 , 8) gene family evolution model-based rooting 71 , such as…”
Rooting Gene Trees via Phylogenetic Networks
Tiuryn, J., Rutecka, N., & Górecki, P. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-22105-7_37 · Cited by 1 · see citing works
Phylogenetic network-assisted rooting of unrooted gene trees
Tiuryn, J., Rutecka, N., & Górecki, P. (2024) · Journal of Combinatorial Optimization · doi:10.1007/s10878-024-01181-3 · Cited by 1 · see citing works
“Here, the root is inferred directly with the phylogenetic tree (Lepage et al. 2007; Williams et al. 2015).”
Generalizing rate heterogeneity across sites in statistical phylogenetics
Heaps, S. E., Nye, T. M. W., Boys, R. J., Williams, T. A., Cherlin, S., & Embley, T. M. (2019) · Statistical Modelling · doi:10.1177/1471082x18829937 · Cited by 1 · see citing works
Self-citationNon-phylogenetic identification of co-evolving genes for reconstructing the archaeal Tree of LifePreprint
Rangel, L. T., Soucy, S. M., Setúbal, J. C., Gogarten, J. P., & Fournier, G. P. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.10.16.343293 · Cited by 1 · see citing works
Resolving the origins of membrane phospholipid biosynthesis genes using outgroupfree rootingPreprint
Coleman, G. A., Pancost, R. D., & Williams, T. A. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/312991 · Cited by 1 · see citing works
“2010), but some analyses have supported an alternative placement of the root within Bacteria (CavalierSmith 2006; Lake et al. 2009; Williams et al. 2015).”
Self-citationGruenstaeudl, M. (2019) · Preprints.org · doi:10.20944/preprints201905.0002.v1
Phylogenetic Analysis of Pathogens
Morrison, D. A. (2017) · Elsevier eBooks · doi:10.1016/b978-0-12-799942-5.00008-1
From Best Hits to Best MatchesPreprint
Stadler, P. F., Geiß, M., Schaller, D., Sánchez, A. L., González, M. E., Valdivia, D. I., Hellmuth, M., & Hernández-Rosales, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.00958
The Clade Displacement Index: how to detect horizontal gene transfers in unrooted gene treesPreprint
Ciach, M. A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.06.24.449756
Additional file 2 of From pairs of most similar sequences to phylogenetic best matches
Stadler, P. F., Geiß, M., Schaller, D., Sánchez, A. L., Laffitte, M. E. G., Valdivia, D. I., Hellmuth, M., & Hernández-Rosales, M. (2020) · Figshare · doi:10.6084/m9.figshare.12109566
Shah, P. T., & Xing, L. (2024) · Viruses · doi:10.3390/v16060928
“Further understanding of the molecular phylogenetics can be gained by referring to [13–15].”
Maximum Likelihood Phylogenetic Inference
Lamarca, A. P., Schrago, C. G., & Mello, B. (2024) · Elsevier eBooks · doi:10.1016/b978-0-443-15750-9.00085-9
Additional file 1 of From pairs of most similar sequences to phylogenetic best matches
Stadler, P. F., Geiß, M., Schaller, D., Sánchez, A. L., González-Laffitte, M., Valdivia, D. I., Hellmuth, M., & Hernández-Rosales, M. (2020) · Figshare · doi:10.6084/m9.figshare.12109560
Modelling compositional and exchange rate changes over time
Foster, P. G. (2026) · Evolutionary Journal of the Linnean Society · doi:10.1093/evolinnean/kzag001
- Authors
- Williams, T. A., Heaps, S. E., Cherlin, S., Nye, T. M. W., Boys, R. J., & Embley, T. M.
- Affiliations
- Newcastle University (GB)
- Corresponding author
- Williams, Tom A.
- Venue
- Philosophical Transactions of the Royal Society B: Biological Sciences
- Publisher
- The Royal Society
- Published
- 2015-09-26
- Volume
- 370
- Issue
- 1678
- Pages
- 20140336
- ISSN
- 0962-8436 (ISSN-L)
- 1471-2970
- PMC
- PMC4571574
- OpenAlex
- W1771294277
- Cited by
- 61
- References
- 66
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 3 · 2023: 2 · 2022: 6 · 2021: 7 · 2020: 11 · 2019: 9 · 2018: 7 · 2017: 12 · 2015: 1
- FWCI
- 2.90
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Philosophical Transactions of the Royal Society B Biological Sciences (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Durham Research Online (Durham University) (submittedVersion, cc-by)
- Explore Bristol Research (submittedVersion)
- Newcastle University ePrints (Newcastle Univesity) (cc-by)
- Funders
- Wellcome Trust (045404)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protist diversity and phylogeny
- Keywords
- substitution models, non-stationary models, tree of life, eukaryotes, molecular phylogeny
- MeSH terms
- Archaea, Bacteria, Computer Simulation, Models, Genetic, Phylogeny, Genetic Variation
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