Terraces in phylogenetic tree space
Abstract
Analysis of terraces in phylogenetic space can inform on phylogenetic relationships with greater computational efficiency
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Missing data can create phylogenetic terraces, where for two or more species trees the associated sets of induced single-locus trees are identical, leading to identical likelihoods under an edge-unlinked partitioned model.
“Missing data can create phylogenetic terraces (Sanderson et al. 2011), where for two or more species trees the associated sets of induced single-locus trees are identical, leading to identical likelihoods under an edge-unlinked partitioned model.”
From IQ-TREE 2: New Models and Efficient Methods for Phylogenetic Inference in the Genomic Era (2020) · cites this paper as Sanderson et al. 2011
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IQ-TREE 2: New Models and Efficient Methods for Phylogenetic Inference in the Genomic Era
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“Missing data can create phylogenetic terraces (Sanderson et al. 2011), where for two or more species trees the associated sets of induced single-locus trees are identical, leading to identical likelihoods under an edge-unlinked partitioned model.”
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“The EUL partition model, where each partition has its own set of branch lengths, is the most However, due to missing data an EUL model may general. lead 997 (Sanderson et al. 2011), where different tree topologies have the same score (likelihood parsimony).”
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“The set S is also a terrace when likelihood is the optimality criterion if the likelihood is determined by a model for each locus in the partition, P , that is “unlinked” (Sanderson et al. 2011).”
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“…been an ongoing topic of theoretical and empirical research and debate (e.g., Wiens 2003; Philippe et al. 2004; Lemmon et al. 2009; Cho et al. 2011; Sanderson et al. 2010, 2011, 2015; Wiens and Morrill 2011; Roure et al. 2013; Jiang et al. 2014; Hosner et al. 2016; Streicher et al. 2016; Xi et al.…”
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Prediction of missing sequences and branch lengths in phylogenomic data
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“Firstly, depending on the structure of the missing data blocks and under certain model parameter configurations (most importantly unlinked branch lengths), gappy datasets can give rise to so-called terraces in tree space (Sanderson et al., 2011).”
BackgroundLost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks
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“phylogenetic trees [22, 51], to identify horizontal gene transfer events [21], to resolve ambiguity in terraces in phylogenetic tree space [69], and as a consensus approach [14].”
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“Finally, there is a relationship between decisiveness and “phylogenetic terraces”, which occurs when there are multiple trees that have the same optimality score [111, 110, 35].”
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“The landscape of treespace, representing support for all the possible topologies given the data, is often hidden from our view (Sanderson et al. 2011; St. John 2017).”
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The prevalence of terraced treescapes in analyses of phylogenetic data sets
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“One potential explanation would be the large amount of missing data, which is known to create “islands” of similarly scoring trees, hampering the exploration of the tree space (Sanderson et al. 2011; Roch and Steel 2015; Suvorov et al. 2022).”
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Chernomor, O., Minh, B. Q., & von Haeseler, A. (2015) · Journal of Computational Biology · doi:10.1089/cmb.2015.0146 · Cited by 16 · see citing works
“Since the number of trees on one terrace can be quite large (Sanderson et al., 2011), accounting for terraces in tree search algorithms can potentially save a lot of computation time.”
InfluentialPearse, W. D., Chase, M. W., Crawley, M. J., Dolphin, K., Fay, M. F., Joseph, J. A., Powney, G. D., Preston, C. D., Rapacciuolo, G., Roy, D. B., et al. (2015) · PLoS ONE · doi:10.1371/journal.pone.0126524 · Cited by 16 · see citing works
“In particular, the three distinct groupings in Fig 3b suggest that three islands in treespace were sampled (discussed in [42]); since each island seems equally likely, there may be no correct score for such species.”
BackgroundOn simulated annealing phase transitions in phylogeny reconstruction
Strobl, M. A. R., & Barker, D. (2016) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2016.05.001 · Cited by 15 · see citing works
“Data was analysed in R (http://www.R-project.org), with default parameters for boxplots.”
MethodThe combinatorics of discrete time-trees: theory and open problems
Gavryushkin, A., Whidden, C., & Matsen, F. A., IV (2017) · Journal of Mathematical Biology · doi:10.1007/s00285-017-1167-9 · Cited by 15 · see citing works
Total evidence and sensitivity phylogenetic analyses of egg‐brooding frogs (Anura: Hemiphractidae)
Echevarría, L. Y., la Riva, I. D., Venegas, P. J., Rojas‐Runjaic, F. J. M., Dias, I. R., & Castroviejo‐Fisher, S. (2020) · Cladistics · doi:10.1111/cla.12447 · Cited by 14 · see citing works
Two C++ libraries for counting trees on a phylogenetic terrace
Biczok, R., Bozsoky, P., Eisenmann, P., Ernst, J., Ribizel, T., Scholz, F., Trefzer, A. C., Weber, F., Hamann, M., & Stamatakis, A. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty384 · Cited by 14 · see citing works
Transcriptome Ortholog Alignment Sequence Tools (TOAST) for phylogenomic dataset assembly
Wcisel, D. J., Howard, J. T., Yoder, J. A., & Dornburg, A. (2020) · BMC Evolutionary Biology · doi:10.1186/s12862-020-01603-w · Cited by 13 · see citing works
STBase: One Million Species Trees for Comparative Biology
McMahon, M. M., Deepak, A., Fernández‐Baca, D., Boss, D., & Sanderson, M. J. (2015) · PLoS ONE · doi:10.1371/journal.pone.0117987 · Cited by 13 · see citing works
Self-citationHumphries, P. J., & Wu, T. (2013) · IEEE Transactions on Computational Biology and Bioinformatics · doi:10.1109/tcbb.2013.66 · Cited by 12 · see citing works
Tochihara, Y., & Hosoya, T. (2022) · MycoKeys · doi:10.3897/mycokeys.87.73082 · Cited by 9 · see citing works
“Sequence matrix containing missing data typically yield multiple trees residing on a phylogenetic terrace (Sanderson et al. 2011; Biczok et al. 2018).”
BackgroundDumm, W., Barker, M., Howard-Snyder, W., DeWitt, W. S., & Matsen, F. A., IV (2023) · Journal of Mathematical Biology · doi:10.1007/s00285-023-02006-3 · Cited by 9 · see citing works
“This is related to the idea of characterizing the trees in a single optimal “terrace” in phylogenetic tree space, with respect to parsi-mony (Sanderson et al. 2011, 2015).”
BackgroundMahbub, S., Sawmya, S., Saha, A., Reaz, R., Rahman, M. S., & Bayzid, M. S. (2022) · Journal of Computational Biology · doi:10.1089/cmb.2022.0212 · Cited by 9 · see citing works
“Incomplete gene trees may decrease the species tree accuracy [27, 31, 35] and introduce ambiguity in the tree search [36, 37].”
BackgroundBias in Tree Searches and its Consequences for Measuring Group Supports
Goloboff, P. A., & Simmons, M. P. (2014) · Systematic Biology · doi:10.1093/sysbio/syu051 · Cited by 9 · see citing works
“by (Sanderson et al., 2011), tree terraces (or some approximation of them, when non-partitioned models are used) are to be expected often when combining data for different genes with uneven taxon representation.”
BackgroundInfluentialCapoferri, A. A., Bale, M. J., Simonetti, F. R., & Kearney, M. F. (2019) · The Lancet HIV · doi:10.1016/s2352-3018(19)30051-7 · Cited by 9 · see citing works
Dias, G. R., Dupim, E. G., Vanderlinde, T., Mello, B., & Carvalho, A. B. (2020) · BMC Evolutionary Biology · doi:10.1186/s12862-020-01703-7 · Cited by 9 · see citing works
Biological causes and impacts of rugged tree landscapes in phylodynamic inference
Gao, J., Brusselmans, M., Carvalho, L. M., Suchard, M. A., Baele, G., & Matsen, F. A., IV (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2510938123 · Cited by 7 · see citing works
Gregório, B. D. S., de Carvalho, C. S., Ramos, G., Rocha, L., Stirton, C. H., de Lima, H. C., Zartman, C. E., Lewis, G. P., TORKE, B. M., Snak, C., et al. (2023) · Botanical Journal of the Linnean Society · doi:10.1093/botlinnean/boad059 · Cited by 7 · see citing works
Computational Reproducibility of Molecular Phylogenies
Kumar, S., Tao, Q., Lamarca, A. P., & Tamura, K. (2023) · Molecular Biology and Evolution · doi:10.1093/molbev/msad165 · Cited by 7 · see citing works
“related to the presence of many local optima (Sanderson et al. 2011; John 2017).”
BackgroundMethodFarah, I. T., Islam, M., Zinat, K. T., Rahman, A. H., & Bayzid, M. S. (2021) · Systematic Biology · doi:10.1093/sysbio/syab026 · Cited by 7 · see citing works
Phylo2Vec: A Vector Representation for Binary Trees
Penn, M. J., Scheidwasser, N., Khurana, M. P., Duchêne, D. A., Donnelly, C. A., & Bhatt, S. (2024) · Systematic Biology · doi:10.1093/sysbio/syae030 · Cited by 7 · see citing works
“Another critical challenge is the size of the tree space: for a tree with n leaves, there are (2𝑛−3)⋅(2𝑛−5)⋅ …⋅5⋅3⋅1 possible rooted binary trees (Cavalli‑Sforza and Edwards 1967).”
InfluentialA Review of Approaches for Optimizing Phylogenetic Likelihood Calculations
Stamatakis, A. (2019) · Computational biology · doi:10.1007/978-3-030-10837-3_1 · Cited by 7 · see citing works
Leaping through Tree Space: Continuous Phylogenetic Inference for Rooted and Unrooted Trees
Penn, M. J., Scheidwasser, N., Penn, J., Donnelly, C. A., Duchêne, D. A., & Bhatt, S. (2023) · Genome Biology and Evolution · doi:10.1093/gbe/evad213 · Cited by 7 · see citing works
“Second, all the aforementioned tree arrangements are prone to being trapped in local optima and even if a global optimum is found, terraces of trees with identical quality exist (Sanderson et al. 2011).”
BackgroundAre the Duplication Cost and Robinson-Foulds Distance Equivalent?
Zheng, Y., & Zhang, L. (2014) · Journal of Computational Biology · doi:10.1089/cmb.2014.0021 · Cited by 6 · see citing works
“Given a metric defined in the species tree space, the set of species trees with the same metric score from a species tree is called a terrace (Sanderson et al., 2011).”
Estimating the mean in the space of ranked phylogenetic trees
Berling, L., Collienne, L., & Gavryushkin, A. (2024) · Bioinformatics · doi:10.1093/bioinformatics/btae514 · Cited by 4 · see citing works
Mahbub, S., Sawmya, S., Saha, A., Reaz, R., Rahman, M. S., & Bayzid, M. S. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-04749-7_10 · Cited by 4 · see citing works
Molecular Systematics and the Evolution of Arthropods
Hoy, M. A. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-415874-0.00012-3 · Cited by 4 · see citing works
A navigation system for tree space
Mark, S., McLeod, J. C., & Steel, M. (2016) · Journal of Graph Algorithms and Applications · doi:10.7155/jgaa.00392 · Cited by 4 · see citing works
Self-citationLarge-Scale Species Tree Estimation
Molloy, E. K., & Warnow, T. J. (2023) · Princeton University Press eBooks · doi:10.2307/j.ctv2wr4wdf.8 · Cited by 4 · see citing works
Inferring and Postprocessing Huge Phylogenies
Smith, S. A., & Stamatakis, A. (2013) · doi:10.1002/9781118617151.ch46 · Cited by 4 · see citing works
Geodesics to characterize the phylogenetic landscape
Khodaei, M., Owen, M., & Beerli, P. (2023) · PLoS ONE · doi:10.1371/journal.pone.0287350 · Cited by 3 · see citing works
Silva, A. S. (2024) · Journal of Systematic Palaeontology · doi:10.1080/14772019.2024.2321620 · Cited by 3 · see citing works
“H € ohna & Drummond, 2011; Lakner et al., 2008; Olmstead et al., 1993; Sanderson et al., 2011) and the summary of inferred trees (e.g. Sharkey & Leathers, 2001; Serra Silva & Wilkinson, 2021a; Sumrall et al., 2001), it is not unreasonable to expect that topology-based taxonomic instability…”
BackgroundAn Automated Convergence Diagnostic for Phylogenetic MCMC Analyses
Berling, L., Bouckaert, R., & Gavryushkin, A. (2024) · IEEE Transactions on Computational Biology and Bioinformatics · doi:10.1109/tcbb.2024.3457875 · Cited by 3 · see citing works
Terraces in species tree inference from gene trees
Habib, M., Roy, K., Hasan, S., Rahman, A. H., & Bayzid, M. S. (2024) · BMC Ecology and Evolution · doi:10.1186/s12862-024-02309-z · Cited by 3 · see citing works
“[21] first formally investigated this and showed that when phylogenetic trees are estimated from sequence alignments using maximum likelihood (ML), multiple distinct trees can have exactly the same likelihood score due to missing data (i.e., missing genes) – a phenomenon which was referred to as…”
BackgroundMethodInfluentialDai, J., & Molloy, E. K. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-90252-9_8 · Cited by 2 · see citing works
Checking Phylogenetics Decisiveness in Theory and in Practice.
Parvini, G., Braught, K., & Fernández‐Baca, D. (2022) · PubMed · doi:10.1109/tcbb.2021.3128381 · Cited by 6 · see citing works
Coping with Ineffective Overlap in Multilocus Phylogenetics
Silva, A. S., Siu-Ting, K., Creevey, C. J., Pisani, D., & Wilkinson, M. (2025) · Systematic Biology · doi:10.1093/sysbio/syaf044 · Cited by 2 · see citing works
“Taxon coverage decisiveness underpins the concept of phylogenetic terraces in multilocus data, where terraces are sets of exactly equally optimal trees such that each data partition (tree) induces identical sub-trees ( Sanderson et al. 2011 ).”
The origin and diversification of Amaryllidaceae: A phylogenetic and biogeographic analysis
Dennehy-Carr, Z., Könyves, K., Yesson, C., David, J. C., & Culham, A. (2025) · American Journal of Botany · doi:10.1002/ajb2.70092 · Cited by 2 · see citing works
“The number of Amaryllidaceae taxa included in this analysis was reduced to decrease the e ff ect of missing data and the size of the data set, subsequently enhancing the signal ‐ to ‐ noise ratio and reducing the time needed to su ffi ciently explore tree space (Sanderson and Sha ff er, 2002; Sanderson et al., 2011; Roure…”
Dai, J., & Molloy, E. K. (2025) · Journal of Computational Biology · doi:10.1177/15578666251386082 · Cited by 2 · see citing works
“These data characteristics have been shown to lead to phylogenetic terraces of many equally optimal trees (Sanderson et al., 2011).”
Enumerating all maximal frequent subtrees in collections of phylogenetic trees
Deepak, A., & Fernández‐Baca, D. (2014) · Algorithms for Molecular Biology · doi:10.1186/1748-7188-9-16 · Cited by 2 · see citing works
“MASTs are used, among other things, as a metric for comparing phylogenetic trees [2-4], computing their congruence index [5,6], to identify horizontal gene transfer events [7], for resolving ambiguity in terraces in phylogenetic tree space [8], and as a consensus approach [9].”
Empirical Analysis of Phylogenetic Quasi-TerracesPreprint
Breitling, P., Stamatakis, A., Chernomor, O., Bettisworth, B., & Reszczynski, L. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/810309 · Cited by 2 · see citing works
“The size (the number of trees in P) can vary between 1 tree (a trivial set) and more than a billion of trees (Sanderson et al., 2011).”
BackgroundMethod
- Authors
- Sanderson, M. J., McMahon, M. M., & Steel, M.
- Affiliations
- University of Arizona (US)
- University of Canterbury (NZ)
- Corresponding author
- Sanderson, Michael J.
- Venue
- Science
- Published
- 2011-07-22
- Volume
- 333
- Issue
- 6041
- Pages
- 448-450
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2095523744
- Cited by
- 144
- References
- 28
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 12 · 2023: 11 · 2022: 6 · 2021: 8 · 2020: 20 · 2019: 8 · 2018: 6 · 2017: 5 · 2016: 14 · 2015: 11 · 2014: 13 · 2013: 10 · 2012: 9
- FWCI
- 4.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
- Physical Sciences › Earth and Planetary Sciences › Paleontology › Evolution and Paleontology Studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic diversity and population structure
- Keywords
- multilocus phylogeny, tree reconstruction, maximum agreement subtree
- MeSH terms
- Algorithms, Animals, Arthropods, Bayes Theorem, Data Interpretation, Statistical, Biological Evolution, Poaceae, Phylogeny, Models, Statistical, Likelihood Functions, Sequence Alignment, Colubridae, Magnoliopsida, Genomics
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