Mike Steel

See some of my co-authors hard at work (mostly in the South Island of New Zealand).

Disclaimer: The listing of papers on this webpage is for my own use. Some of these files are probably covered by publisher copyrights. Please ensure that your institution has the appropriate subscription before reading any of these .pdfs.

Selected publications (non-phylogenetic)

All publications

In press/submitted

- last updated March 6, 2023

  1. Download PDFManson, K. and Steel, M. (2023). Spaces of phylogenetic diversity indices: combinatorial and geometric properties (submitted). BioRxiv. abstract
  2. Download PDFFrancis, A. and Steel, M. (2023) Labelleable phylogenetic networks (submitted). doi: 10.1101/2023.02.09.527917. abstract
  3. Download PDFOverwater, M. and Steel, M. (2023). The expected loss of feature diversity (versus phylogenetic diversity) following rapid extinction at the present. (submitted). DOI: 10.1101/2022.10.09.511499. abstract
  4. Download PDFRosindell, J., Manson, K., et al (2022). Phylogenetic Biodiversity Metrics Should Account for Both Accumulation and Attrition of Evolutionary Heritage. Submitted. BioRxiv. abstract
  5. Download PDFKatriel, G., Mahanaymi, U., Koutschan, C., Zeilberger, D., Steel, M. and Snir, S. (2022). Gene Transfer-based Phylogenetics: Analytical Expressions and Additivity via Birth–Death Theory. BioRxiv. abstract


  1. Download PDFGumbs, R., Gray, C.L., Böhm, M., Burfield, I.J., Couchman, O.R., Faith, D.P., et al. (2023). The EDGE2 protocol: Advancing the prioritisation of Evolutionarily Distinct and Globally Endangered species for practical conservation action. PLoS Biol. 21(2): e3001991, doi: 10.1371/journal.pbio.3001991. abstract


  1. Download PDFHordijk, W., Steel, M. and Kauffman, S. (2022). Autocatalytic sets arising in a combinatorial model of chemical evolution. Life 12(11), 1703. abstract
  2. Download PDFBocharov, S., Harris, S., Kominek, E., Mooers, A. O. and Steel, M. (2022). Predicting long pendant edges in model phylogenies, with applications to biodiversity and tree inference. Systematic Biology: syac059, doi: 10.1093/sysbio/syac059.
  3. PDF coming soonGabora, L. & Steel, M. (2022) From uncertainty to insight: An autocatalytic framework. In: Uncertainty: A Catalyst for Creativity, Learning and Development (Beghetto, R. & Jaeger, G., Eds.), 125-156, Berlin: Springer
  4. Download PDFMehta, R. S., Steel, M. and Rosenberg, N. A. (2022). The probability of joint monophyly of all species in an arbitrary species tree. Journal of Computational Biology 29(7): 679-703. doi: 10.1089/cmb.2021.0647.
  5. Download PDFManson, K. Semple, S. and Steel, M. (2022). Counting and optimising maximum phylogenetic diversity sets. Journal of Mathematical Biology 85:11
  6. PDF coming soonGabora, L., Beckage, N. and Steel, M. (2022). An autocatalytic network model of conceptual change. Topics in cognitive Science 14: 163-188, doi: 10.1111/tops.12583.
  7. Download PDFWertheim, J. O., Steel, M. and Sanderson, M. J. (2022). Accuracy in near-perfect virus phylogenies. Systematic Biology 71(2): 426-438, doi: 10.1093/sysbio/syab069. bioRxiv. abstract
  8. Download PDFBienvenu, F., Lambert, A. and Steel, M. (2022). Combinatorial and stochastic properties of ranked tree-child networks. arxiv. Random Structures and Algorithms 60(4): 653-689. abstract


  1. Download PDFWeller-Davies, O., Steel, M. and Hein, J. (2021) Combinatorics of polymer-based models of early metabolism. SIAM Journal of Discrete Mathematics 35 (4): 2304-2316 abstract
  2. Download PDF Gabora, L and Steel, M. (2021). An evolutionary process without variation and selection. J. R. Soc. Interface 18: 20210334. BioRxiv. abstract
  3. Download PDF Francis, A., Huson, D. and Steel, M. (2021) Normalising phylogenetic networks. Molecular Phylogenetics and Evolution 163: 107215. arxiv. abstract
  4. Download PDFSusko, E., Steel, M., and Roger, A. J. (2021). Conditions under which distributions of edge length ratios on phylogenetic trees can be used to order evolutionary events. Journal of Theoretical Biology 526: 110788. bioRxiv. abstract
  5. Download PDF Steel, M. (2021). Modelling aspects of consciousness: a topological perspective. Journal of Theoretical Biology 523: 110713, doi: 10.1016/j.jtbi.2021.110713. abstract
  6. Download PDFWicke, K., Mooers, A. and Mike Steel (2021). Formal Links between Feature Diversity and Phylogenetic Diversity. Systematic Biology, 70(3): 480-490, doi: 10.1093/sysbio/syaa062. abstract
  7. Download PDF Kauffman, S. and Steel, M. (2021). The expected number of viable autocatalytic sets in chemical reaction systems. Artificial Life 27:1-14, doi: artl_a_00333. abstract
  8. Download PDFBai, A., Erdös, P.L., Semple, C. and Steel, M. (2021). Defining phylogenetic networks using ancestral profiles. Mathematical Biosciences, 332: 108537. abstract


  1. Download PDF Sanderson, M.J. McMahon, M.M. and Steel, M. (2020). Terraces in gene tree reconciliation-based species tree inference. bioRxiv. abstract
  2. Download PDFGabora, L. and Steel, M. (2020). A model of the transition to behavioral and cognitive modernity using reflexively autocatalytic networks. J. R. Soc. Interface.1720200545, doi: 10.1098/rsif.2020.0545. abstract
  3. Download PDFGabora, L. and Steel, M. (2020). Modeling a cognitive transition at the origin of cultural evolution using autocatalytic networks. Cognitive Science. 44(9): e12878, doi: 10.1111/cogs.12878. abstract
  4. Download PDFSteel, M., Xavier, J. C., and Huson, D. H. (2020). The structure of autocatalytic networks, with application to early biochemistry. J. Royal Society Interface, 17: 20200488, doi: 10.1098/rsif.2020.0488. abstract
  5. Download PDFWeller-Davies, O., Steel, M. and Hein, J. (2020) Complexity results for autocatalytic network models. Mathematical Biosciences. 325(2020): 108365. abstract
  6. Download PDFXavier, J. C., Hordijk, W., Kauffman, S., Steel M. and Martin, W. F. (2020). Autocatalytic chemical networks at the origin of metabolism. Proc. Roy. Soc. B. 287: 2019237, doi: 10.1098/rspb.2019.2377. abstract
  7. Download PDFWicke, K. and Steel, M. (2020). Combinatorial properties of phylogenetic diversity indices for rooted and unrooted trees. J. Math. Biol. 80: 687-715. abstract
  8. Download PDFSteel, M., Hordijk, W. and Kauffman, S. (2020). Dynamics of a birth-death process based on combinatorial innovation. J. Theor. Biol. 491: 110187. abstract
  9. Download PDFSteel, M. (2020). Lambert and Stadler (2013): A unifying framework for modelling evolutionary trees. Theor. Pop. Biol. 133: 38-39. first paragraph
  10. Download PDFGascuel, O. and Steel, M. (2020). A Darwinian uncertainty principle. Systematic Biology, 69(3): 521-529 (, abstract


  1. Download PDFHuson, D. H., Albrecht, B., Patz, S. and Steel, M. (2020). Anti-consensus: detecting trees that have an evolutionary signal that is lost in consensus. BioRxiv., abstract
  2. Download PDFSevillya, G. Lerner, Y., Doerr, D., Stoye, J., Steel, M., and Snir, S. (2019). Horizontal Gene Transfer Phylogenetics: A Random Walk Approach. Mol. Biol. Evol. 37(5): 1470-1479,, abstract
  3. Download PDFStadler, T. and Steel, M. (2019). Swapping birth and death: Symmetries and transformations in phylodynamic models. Systematic Biology, Volume 68(5): 852-858. abstract
  4. Download PDFErdös, P. L., Semple, C. and Steel, M. (2019). A class of phylogenetic networks reconstructable from ancestral profiles. Mathematical Biosciences, 313: 33-40. abstract
  5. Download PDFL. Herbst, T. Li and M. Steel. (2019). Quantifying the accuracy of ancestral state prediction in a phylogenetic tree under maximum parsimony. J. Math. Biol. 78:1953-1979. abstract
  6. Download PDFHoppe, A., Türpitz, S. and Steel, M. (2019). Species notions that combine phylogenetic trees and phenotypic partitions. Journal of Mathematical Biology 78:117-134 abstract
  7. Download PDFPons, J. C., Semple, C. and Steel, M. (2019). Tree-based networks: characterisations, metrics, and support trees. Journal of Mathematical Biology 78(4): 899-918. abstract
  8. Download PDFHordijk, W., Steel, M. and Kauffman, S. A. (2019). Molecular Diversity Required for the Formation of Autocatalytic Sets. Life 9: 23. abstract
  9. Download PDFHuber, K. T., Moulton, V. and Steel, M. (2019). Phylogenetic flexibility via Hall-type inequalities and submodularity. Bull. Math. Biol. 81(2): 598-617. abstract
  10. Download PDFSteel, M., Hordijk, W. and Xavier, J. C. (2019). Autocatalytic networks in biology: structural theory and algorithms. J. Royal Society Interface 16: 20180808. abstract, supplementary material


  1. Download PDFHordijk, W. and Steel, M. (2018). Autocatalytic networks at the basis of life's origin and organization. Life 8(4): 62. abstract
  2. Download PDFBordewich, M., Deutschmann, I. M., Fischer, M., Kasbohm, E., Semple, C., Steel, M. (2018). On the information content of discrete phylogenetic characters. J. Math. Biol. 77(3): 527-544. abstract
  3. Download PDFGrunewald, S., Huber, K. T., Moulton, V., and Steel, M. Combinatorial properties of triplet covers for binary trees. Adv. Appl. Math. 99: 59-82. abstract
  4. Download PDF Hordijk, W., Steel, M. and Dittrich, P. (2018). Autocatalytic sets and chemical organizations: Modeling self-sustaining reaction networks at the origin of life. New Journal of Physics 20:015011. abstract
  5. Download PDFSteel, M., Pourfaraj, V., Chaudhary, A. and Mooers, A. (2018). Evolutionary isolation and phylogenetic diversity loss under random extinction events. Journal of Theoretical Biology, 438: 151-155. abstract
  6. Download PDF Francis, A., Semple, C. and Steel, M. (2018). New characterisations of tree-based networks and proximity measures. Adv. Appl. Math. 93: 93-107. abstract
  7. Download PDF Steel, M. and Kauffman, S. (2018). A note on random catalytic branching processes. Journal of Theoretical Biology, 437: 222-224. abstract


  1. Download PDF Huber, K. T., Moulton, V. and Steel, M. (2017). Minimum triplet covers of binary phylogenetic X-trees. J. Math. Biol. 75: 1827-1840. abstract
  2. Download PDFGabora, L. and Steel, M. (2017), Autocatalytic networks in cognition and the origin of culture. J. Theor. Biol. 431: 87-95. abstract
  3. Download PDF Bryant, D., Francis, A. and Steel, M. (2017). Can we "future-proof" consensus trees? Syst. Biol. 66(4): 611-619. abstract
  4. Download PDF Casanellas, M. and Steel, M. (2017), Phylogenetic mixtures and linear invariants for equal input models J. Math. Biol., 74(5): 1107-1138. abstract
  5. Download PDF Huson, D. H., Steel, M., El-Hadidi, M., Mitra, S., Silke, P. and Willmann, M. (2017). A simple statistical test of taxonomic or functional homogeneity using replicated microbiome sequencing samples. Journal of Biotechnology, 250: 45-50. abstract
  6. Download PDF Steel, M. and Leuenberger, C. (2017). The optimal rate for resolving a near-polytomy in a phylogeny. J. Theor. Biol., 420: 174-179. abstract
  7. Download PDF Hordijk, W. and Steel, M. (2017). Chasing the tail: The emergence of autocatalytic networks. Biosystems, 152:1-10. abstract
  8. Download PDF Matschiner, M., Musilová, Z., Barth, J. M. I., Starostová, Z., Salzburger, W., Steel, M. and Bouckaert, R. (2017). Bayesian phylogenetic estimation of clade ages supports trans-atlantic dispersal of cichlid fishes, Systematic Biology, 66 (1): 3-22. abstract
  9. Download PDF Sober, E. and Steel, M. (2017). Similarities as Evidence for Common Ancestry — A Likelihood Epistemology. British J. Phil. Sci. 68(3): 617-638. abstract


  1. Download PDF J. V. de Jong, J. C. McLeod, and M. Steel. (2016). Neighbourhoods of phylogenetic trees: exact and asymptotic counts. SIAM Journal on Discrete Mathematics, 30(4): 2265-2287. abstract
  2. Download PDF Huber, K. T., Moulton, V., Steel, M. and Wu, T. (2016). Folding and unfolding phylogenetic trees and networks. J. Math. Biol. 73(6): 1761-1780. abstract
  3. No PDF Steel, M. (2016). Phylogeny: Discrete and random processes in evolution (Book), CBMS-NSF Regional conference series in Applied Mathematics. SIAM. 303 pages. table of contents, 9-page review at SIAM Reviews, 7-page review at Bulletin of the American Mathematical Society, errata
  4. Download PDF Hordijk, W. and Steel, M. (2016). Autocatalytic sets in polymer networks with variable catalysis distributions, J. Math. Chem., 54(10): 1997-2021. abstract
  5. Download PDF Mark, S., McLeod, J.C., and Steel, M. (2016). A navigation system for tree space. Journal of Graph Algorithms and Applications, 20(2): 247-268. abstract
  6. Download PDF Gascuel, O. and Steel, M. (2016). A 'stochastic safety radius' for distance-based tree reconstruction. Algorithmica, 74: 1386-1403. abstract
  7. Download PDF Hordijk, W. and Steel, M. (2016). Comment on "Tibor Gánti and Robert Rosen" by Athel Cornish-Bowden. J. Theor. Biol., 392: 122-123. introduction


  1. Download PDF Bernstein, D.I., Ho, L.S.T, Long, C., Steel, M. St John, K. and Sullivant, S. (2015). Bounds on the expected size of the maximum agreement subtree. SIAM J Discr. Math. 29(4): 2065-2074. abstract
  2. Download PDF McTavish, E.J., Steel, M. and Holder, M.T. (2015). Twisted trees and inconsistency of tree estimation when gaps are treated as missing data — the impact of model mis-specification in distance corrections. Mol. Phyl. Evol. 93:289-295. abstract
  3. Download PDF Francis, A. and Steel, M. (2015). Which phylogenetic networks are merely trees with additional arcs? Syst. Biol. 64 (5): 768-777. abstract
  4. Download PDF Steel, M. (2015). Self-sustaining autocatalytic networks within open-ended reaction systems. Journal of Mathematical Chemistry, 53(8): 1687-1701. abstract
  5. Download PDF Sanderson, M.J., McMahon, M.M., Stamatakis, A., Zwickl, D.J., and Steel, M. (2015). Impacts of terraces on phylogenetic inference. Systematic Biology 64 (5): 709-726 abstract
  6. Download PDF Hordijk, W., Smith, J. I. and Steel, M. (2015). Algorithms for detecting and analysing autocatalytic sets. Algorithms in Molecular Biology 10: 15. abstract
  7. Download PDF Chor, B. and Steel, M. (2015). Do tree split probabilities determine the branch lengths? J. Theor. Biol. 374: 54-59 abstract
  8. Download PDF Steel, M. (2015). Reflections on the extinction-explosion dichotomy. Theor. Pop. Biol. 101: 61-66. abstract
  9. Download PDF Sober, E. and Steel, M. (2015). How probable is common ancestry according to different evolutionary processes? J. Theor. Biol. 373: 111-116. abstract
  10. Download PDF Gravel, S. and Steel, M. (2015). The existence and abundance of ghost ancestors in biparental populations. Theor. Pop. Biol. 101: 47-53. abstract
  11. Download PDF Scotland, R.W. and Steel, M. (2015). Circumstances in which parsimony but not compatibility will be provably misleading. Systematic Biology 64 (3): 492-504 abstract
  12. Download PDF Francis, A.R. and Steel, M. (2015). Tree-like reticulation networks -- When do tree-like distances also support reticulation evolution? Math. Biosci. 259: 12-19. abstract
  13. Download PDF Hagen, O., Hartmann, K., Steel, M. and Stadler, T. (2015). Age-dependent speciation can explain the shape of empirical phylogenies. Syst. Biol. 64 (3): 432-440 abstract
  14. Download PDF Roch, S. and Steel, M. (2015). Likelihood-based tree reconstruction on a concatenation of aligned sequence data sets can be statistically inconsistent. Theoretical Population Biology, 100: 56-62. abstract
  15. Download PDF Sousa, F.L., Hordijk, W., Steel, M. and Martin, W. (2015). Autocatalytic sets in E. coli metabolism. J. Syst. Chem. 6: 4. abstract
  16. Download PDF Hordijk, W. and Steel, M. (2015). Autocatalytic sets and boundaries. J. Syst. Chem. 6:1. DOI 10.1186/s13322-014-0006-2. abstract
  17. Download PDF Molitor, D., Steel, M. and Taylor, A. (2015). The structure of symmetric n-player games when influence and independence collide. Adv. Appl. Math. 62: 15-40. abstract
  18. Download PDF Steel, M. (2015). Capturing a phylogenetic tree when the number of character states varies with the number of leaves. (ArXiV). abstract
  19. Download PDF Steel, M. (2015). A consistency lemma in statistical phylogenetics. (ArXiv). abstract


  1. Download PDF Hordijk, W. and Steel, M. (2015). Conditions for evolvability of autocatalytic sets: a formal example and analysis. Origins of Life and Evolution of Biospheres 44(2): 111-124. abstract
  2. Download PDFMossel, E. and Steel, M. (2014). Majority rule has transition ratio 4 on Yule trees under a 2-state symmetric model. Journal of Theoretical Biology 360: 315-318. abstract
  3. Download PDFFischer, M., Galla, M., Herbst, L. and Steel, M. (2014). The most parsimonious tree for random data. Molecular Phylogenetics and Evolution 80: 165-168. abstract
  4. Download PDFDress, A., Huber, K. and Steel, M. (2014). A matroid associated with a phylogenetic tree. Discrete Mathematics and Theoretical Computer Science 16(2): 41-56. abstract
  5. Download PDFSteel, M. and Velasco, J. (2014). Axiomatic opportunities and obstacles for inferring a species tree from gene trees. Syst. Biol. 63(5): 772-778. abstract
  6. Download PDFSteel, M. (2014). Tracing evolutionary links between species. American Mathematical Monthly 121(9): 771-792. abstract
  7. Download PDFSober, E. and Steel, M. (2014). Time and knowability in evolutionary processes. Philosophy of Science 81(4): 558-579 abstract
  8. Download PDFHuber, K. and Steel, M. (2014). Reconstructing fully-resolved trees from triplet cover distances. Electronic Journal of Combinatorics 21(2): p2.15 abstract
  9. Download PDFSmith, J.I., Steel, M. and Hordijk, W. (2014). Autocatalytic sets in a partitioned biochemical network. Journal of Systems Chemistry 5:2 abstract
  10. Download PDFGascuel, O. and Steel, M. (2014). Predicting the ancestral character changes in a tree is typically easier than predicting the root state. Systematic Biology. 63(3): 421-435 abstract
  11. Download PDFHordijk, W., Wills, P. and Steel, M. (2014). Autocatalytic Sets and Biological Specificity. Bulletin of Mathematical Biology 76(1): 201-224. abstract


  1. Download PDFBecker, M., Gruenheit, N., Steel, M., Voelckel, C., Deusch,O., Heenan, P.B., McLenachan, P.A., Kardailsky, O., Leigh, J.W. and Lockhart, P.J. (2013). Hybridization may facilitate in situ survival of endemic species through periods of climate change. Nature Climate Change 3, 1039-1043. abstract
  2. Download PDFHordijk, W., Steel, M. and Kauffman. (2013). The origin of life, evolution, and functional organization. pp. 49-60 in Evolutionary Biology: Exobiology and Evolutionary Mechanisms, Pierre Pontarotti (Editor), Springer. abstract
  3. Download PDFSteel, M. (2013). Consistency of Bayesian inference of resolved phylogenetic trees. Journal of Theoretical Biology. 336: 246-249. abstract
  4. Download PDFBapteste, E., van Iersel, L., Janke, A., Kelchner, S., Kelk, S., McInerney, J., Morrison, D., Nakhleh, L., Steel, M., Stougie, L., Whitfield, J. (2013). Networks: Expanding evolutionary thinking. Trends in Genetics 29(8): 439-441. first paragraph
  5. Download PDFLambert, A. and Steel, M. (2013). Predicting the loss of phylogenetic diversity under non-stationary diversification models. Journal of Theoretical Biology. 337: 111-124. abstract
  6. Download PDFRadel, D., Sand, A. and Steel, M. (2013). Hide and seek: placing and finding an optimal tree for thousands of homoplasy-rich sequences. Molecular Phylogenetics and Evolution. 69(3): 1186-1189. abstract
  7. Download PDFSand, A. and Steel, M. (2013). The standard lateral gene transfer model is statistically consistent for pectinate four-taxon trees. Journal of Theoretical Biology, 335: 295-298. abstract
  8. Download PDFSteel, M., Hordijk, W., and Smith, J. (2013). Minimal autocatalytic networks. Journal of Theoretical Biology 332: 96-107. abstract
  9. Download PDFZhu, S. and Steel, M. (2013). Does Random Tree Puzzle produce Yule-Harding trees in the many-taxon limit? Mathematical Biosciences. 243: 109-116. abstract
  10. Download PDFHordijk, W. and Steel, M. (2013). A formal model of autocatalytic sets emerging in an RNA replicator system. J. Systems Chemistry 4:3. abstract
  11. Download PDFSteel, M., Linz, S., Huson, D.H. and Sanderson, M.J. (2013). Identifying a species tree subject to random lateral gene transfer. Journal of Theoretical Biology. 322: 81-93. abstract
  12. Download PDFSober, E. and Steel, M. (2013). Screening-off and causal incompleteness: a no-go theorem. British J. Philos. Sci. 64(3): 513-550. doi: 10.1093/bjps/axs021. abstract


  1. Download PDFNelson-Saithi, S., Dagan, T., Landan, G. Janssen, A., Steel, M. McInerney, J.O., Deppenmeier, U. and Martin W.F. (2012). Acquisition of 1,000 eubacterial genes physiologically transformed a methanogen at the origin of Haloarchaea. Proceedings of the National Academy of Sciences USA 109: 20537-20542. abstract
  2. Download PDFMartyn, I. and Steel, M. (2012). The impact and interplay of long and short branches on phylogenetic information content. Journal of Theoretical Biology 314: 157-163. abstract
  3. Download PDFHordijk, W., Steel, M. and Kauffman, S. (2012). The Structure of Autocatalytic Sets: Evolvability, Enablement, and Emergence. Acta Biotheoretica, 60: 379-392. abstract
  4. Download PDFHordijk, W. and Steel, M. (2012). Autocatalytic Sets Extended: Dynamics, Inhibition, and a Generalization. Journal of Systems Chemistry, 3:5 (12 pp.). abstract
  5. Download PDFSteel M. (2012). Root location in random trees: A polarity property of all sampling consistent phylogenetic models except one. Molecular Phylogenetics and Evolution 65: 345-348. abstract
  6. Download PDFSoubrier, J., Steel, M. Lee, M. Der Sarkissian, C. Guindon, S., Ho, S.Y.W., Cooper, A. (2012). The influence of rate heterogeneity among sites on the time dependence of molecular rates. Molecular Biology and Evolution 29(11): 3345-3358. abstract
  7. Download PDFDress, A.W.M., Huber, K.T. and Steel, M. (2012). 'Lassoing' a phylogenetic tree I: Basic properties, shellings, and covers. Journal of Mathematical Biology 65(1): 77-105. abstract
  8. Download PDFBryant, D. and Steel, M. (2012). 'Bureaucratic' set systems, and their role in phylogenetics. Applied Mathematics Letters 25: 1148-1152. abstract
  9. Download PDFHordijk, W. and Steel, M. (2012). Predicting template-based catalysis rates in a simple catalytic reaction model. Journal of Theoretical Biology 295: 132-138. abstract
  10. Download PDFStadler, T. and Steel, M. (2012). Distribution of branch lengths and phylogenetic diversity under homogeneous speciation models. Journal of Theoretical Biology. 297: 33-40. abstract
  11. Download PDFFaller, B. and Steel, M. (2012). Trait-dependent extinction leads to greater expected biodiversity loss. SIAM Journal on Discrete Mathematics 26(2): 472-481. abstract
  12. Download PDFMoulton, V. and Steel, M. (2012). The 'Butterfly effect' in Cayley graphs with applications to genomics. Journal of Mathematical Biology, 65(6-7): 1267-1284. abstract
  13. Download PDFMooers, A., Gascuel, O., Stadler, T., Li, H. and Steel, M. (2012). Branch lengths on Birth-Death trees and the expected loss of phylogenetic diversity. Systematic Biology 61(2): 195-203. abstract


  1. Download PDFSanderson, M.J., McMahon, M.M. and Steel, M. (2011). Terraces in phylogenetic tree space. Science 333: 448-450. abstract
  2. Download PDFSteel, M. (2011). Can we avoid 'SIN' in the House of 'No Common Mechanism'? Systematic Biology 60(1): 96-109. abstract
  3. Download PDFSober, E. and Steel, M. (2011). Entropy increase and information loss in Markov models of evolution. Biology and Philosophy 26(2): 223-250. abstract
  4. Download PDFZhu, S., Degnan, J.H., and Steel, M. (2011). Clades, clans and reciprocal monophyly under neutral evolutionary models. Theoretical Population Biology 79: 220-227. abstract
  5. Download PDFHolder, M.T. and Steel, M. (2011). Estimating phylogenetic trees from pairwise likelihoods and posterior probabilities of substitution counts. Journal of Theoretical Biology 280: 159-166. abstract
  6. Download PDFHordijk, W., Kauffman, S., and Steel, M. (2011). Required levels of catalysis for the emergence of autocatalytic sets in models of chemical reaction systems. International Journal of Molecular Sciences (Special issue: Origin of Life 2011) 12: 3085-3101. abstract
  7. Download PDFSteel, M. (2011). Can maths help us glimpse the future? NZ Science Teacher 126: 6-7(non-peer reviewed). first paragraph


  1. Download PDFvan Iersel, L., Semple, C. and Steel, M. (2010). Quantifying the extent of lateral gene transfer required to avert a 'Genome of Eden'. Bulletin of Mathematical Biology. 72: 1783-1798. abstract
  2. Download PDFSteel, M. and Mooers, A. (2010). Expected length of pendant and interior edges of a Yule tree. Applied Mathematics Letters 23(11): 1315-1319. abstract
  3. Download PDFGascuel, O. and Steel, M. (2010). Inferring ancestral sequences in taxon-rich phylogenies. Mathematical Biosciences, 227: 125-135. abstract
  4. Download PDFSanderson, M.J., McMahon, M.M. and Steel, M. (2010). Phylogenomics with incomplete taxon coverage: the limits to inference. BMC Evolutionary Biology 10: 155. abstract
  5. Download PDFDress, A.W.M., Moulton, V., Steel, M. and Wu, T. (2010) Species, clusters and the 'Tree of Life': A graph-theoretic perspective. Journal of Theoretical Biology 265(4): 535-542. abstract
  6. Download PDFHordijk, W., Hein, J. and Steel, M. (2010). Autocatalytic Sets and the Origin of Life, Entropy 12(7): 1733-1744. abstract
  7. Download PDFMagnuson-Ford, K., Mooers, A., Rioux Paquette S, Steel, M. (2010). Comparing strategies to preserve evolutionary diversity. Journal of Theoretical Biology 266(1): 107-116. abstract
  8. Download PDFMihaescu, R. and Steel, M. (2010). Logarithmic bounds on the posterior divergence time of two sequences. Applied Mathematics Letters 23: 975-979. abstract
  9. Download PDFIngram, T. and Steel, M. (2010). Modelling the unpredictability of biodiversity in ecological networks. Journal of Theoretical Biology 264: 1047-1056. abstract
  10. Download PDFSteel, M. and Sanderson, M.J. (2010). Characterizing phylogenetically decisive taxon coverage. Applied Mathematics Letters 23, 82-86. abstract
  11. Download PDFvan Iersel, L. Semple, C. and Steel, M. (2010). Locating a tree in a phylogenetic network. Information Processing Letters 110: 1037-1043. abstract
  12. Download PDFSteel, M. and Penny, D. (2010). Origins of life: Common ancestry put to the test. Nature 465: 168-169. abstract
  13. Download PDFBook review of 'The phylogenetic handbook: A practical approach to phylogenetic analysis and hypothesis testing', Biometrics, 66(1): 324-325, 2010. first 2 paragraphs


  1. Download PDFSteel, M. A. and Szekely, L. (2009). Inverting random functions (III): Discrete MLE revisited. Annals of Combinatorics 13(3): 365-382. abstract
  2. Download PDFDress, A. and Steel, M. (2009). A Hall-type theorem for triplet set systems based on medians in trees. Appl. Math. Lett. 22, 1789-1792. abstract
  3. Download PDFSzekely, L. and Steel, M. (2009). An improved bound on the Maximum Agreement Subtree problem. Applied Mathematics Letters 22: 1778-1780. abstract
  4. Download PDFBryant, D. and Steel, M. (2009). Computing the distribution of a tree metric. IEEE/ACM Transactions in Computational Biology and Bioinformatics 16(3): 420-426. abstract
  5. Download PDFSteel, M. and Faller, B. (2009). Markovian log-supermodularity, and its applications in phylogenetics. Applied Mathematics Letters 22 (7): 1141-1144. abstract
  6. Download PDFSteel, M., Szekely, L. and Mossel, E. (2009). Phylogenetic information complexity: Is testing a tree easier than finding it? Journal of Theoretical Biology 258: 95-102. abstract
  7. Download PDFSteel, M. (2009). The 'Penny Ante': Mathematical biology or biological mathematics?. New Zealand Science Review 66(1): 11-12. first paragraph
  8. Math HorizonsSemple, C. and Steel, M. (Feb. 2009). Mathematical aspects of the 'Tree of life'. Math Horizons. first paragraph
  9. Download PDFHuson, D., Moulton, V. and Steel, M. (2009). Special Section: Phylogenetics. IEEE/ACM Transactions in computational biology and bioinformatics 6(1): 4-6. ISSN: 1545-5963. first paragraph
  10. Download PDFMossel, E., Roch, S. and Steel, M. (2009). Shrinkage effect in ancestral maximum likelihood. IEEE/ACM Transactions in computational biology and bioinformatics 6(1): 126-133. ISSN: 1545-5963. abstract
  11. Download PDFWu, T., Moulton, V., and Steel, M. (2009). Refining phylogenetic trees given additional data: Algorithms based on parsimony. IEEE/ACM Transactions in computational biology and bioinformatics 6(1): 118-125. ISSN: 1545-5963. abstract
  12. Download PDFFischer, M. and Steel, M. (2009). Sequence length bounds for resolving a deep phylogenetic divergence. Journal of Theoretical Biology 256: 247-252. abstract
  13. Download PDFSteel, M. (2009). A basic limitation on inferring phylogenies by pairwise sequence comparisons. Journal of Theoretical Biology 256: 467-472. abstract


  1. Download PDFWhitfield, J., Cameron, S., Huson, D., and Steel, M. (2008). Filtered z-closure supernetworks for extracting and visualizing recurrent signal from incongruent gene trees. Systematic Biology 57(6): 939-947. first paragraph
  2. Download PDFHuson, D, Moulton, V., Steel, M., Freiberger, M. (2008). Reconstructing the tree of life. PLUS magazine. first 3 paragraphs
  3. Download PDFGernhard, T., Hartmann, K., and Steel, M. (2008). Stochastic properties of generalised Yule models, with biodiversity applications. Journal of Mathematical Biology 57: 713-735. first paragraph
  4. Download PDFLi, G., Steel, M. and Zhang, L. (2008). More taxa are not necessarily better for the reconstruction of ancestral character states. Systematic Biology 57(4):647-653. abstract
  5. Download PDFGruenheit, N., Lockhart, P. J., Steel, M. and Martin, W. (2008). Difficulties in testing for covarion-like properties of sequences under the confounding influence of changing proportions of invariable sites. Molecular Biology and Evolution 25: 1512-1520. abstract
  6. Download PDFGill, J., Linusson, S., Moulton, V. and Steel, M. (2008). A regular decomposition of the edge-product space of phylogenetic trees. Advances in Applied Mathematics 41: 158-176. abstract
  7. Download PDFMatsen, F. A., Mossel, E. and Steel, M. (2008). Mixed-up trees: The structure of phylogenetic mixtures. Bulletin of Mathematical Biology 70(4), 1115-1139. abstract
  8. Download PDFSteel, M. and Rodrigo, A. (2008). Maximum likelihood supertrees. Systematic Biology 57(2): 243-250, 2008. abstract
  9. Download PDFThatte, B. and Steel, M. (2008). Reconstructing pedigrees: A stochastic perspective. Journal of Theoretical Biology, 251(3): 440-449. abstract
  10. Download PDFFischer, M. and Steel, M. (2008). Expected anomalies in the fossil record. Evolutionary bioinformatics online 4: 61-67. abstract
  11. Download PDFThierer, T., Bryant, D. and Steel, M. (2008). Counting ancestral reconstructions in a fixed phylogeny, Annals of Combinatorics 12: 123-132. abstract
  12. Download PDFFaller, B. Pardi, F. and Steel, M. (2008) Distribution of phylogenetic diversity under random extinction. Journal of Theoretical Biology 251, 286-296. abstract


  1. Download PDFSteel, M. and Szekely, L. (2007) Teasing apart two trees. Combinatorics, Probability and Computing 16, 903-922. abstract
  2. Download PDFSteel, M., Mimoto, A and Mooers, A. O. (2007). Hedging our bets: the expected contribution of species to future phylogenetic diversity. Evolutionary Bioinformatics 3: 237-244. abstract
  3. Download PDFMatsen, F. A. and Steel, M. (2007). Phylogenetic mixtures on a single tree can mimic a tree of another topology. Systematic Biology 56(5): 767-775. abstract

  4. bookGascuel, O and Steel, M. (eds). (2007). Reconstructing Evolution: New Mathematical and Computational Advances . Book (340 pp). Oxford University Press. Publication date: June 2007. [ Search inside this book]
  5. Download PDFHartmann, K. and Steel, M. (2007). Phylogenetic diversity: From combinatorics to ecology. Book chapter for: Reconstructing evolution: New mathematical and computational approaches (eds. O. Gascuel and M. Steel) Oxford University Press. abstract
  6. Download PDFGrunewald, S., Steel, M. and Swenson, M.Shel. (2007). Closure operations in phylogenetics. Mathematical Biosciences 208, 521-537. abstract

  7. Download PDFDress, A. and Steel, M. (2007). Phylogenetic diversity over an abelian group Annals of Combinatorics 11, 143-160. abstract

  8. Download PDFMoulton, V., Semple, C. and Steel, M. (2007). Optimizing phylogenetic diversity under constraints. Journal of Theoretical Biology 246, 186-194. abstract
  9. Download PDFSteel, M. and Matsen, E. (2007). The Bayesian 'star paradox' persists for long finite sequences. Molecular Biology and Evolution 24: 1075-1079. abstract

  10. Download PDFSteel, M. (2007). Tools to construct and study big trees: A mathematical perspective. Chapter 7 (pp. 97-112) in Reconstructing the Tree of Life: Taxonomy and Systematics of Species Rich Taxa (eds. Trevor Hodkinson, John Parnell and Steve Waldren) CRC Press (Taylor and Francis). abstract


  1. Download PDFGernhard, T., Ford, D., Vos, R. and Steel, M. (2006). Estimating the relative order of speciation or coalescence events on a given phylogeny. Evolutionary Bioinformatics 2: 309-317. abstract
  2. Download PDFBordewich, M., Semple, C. and Steel, M. (2006). Identifying X-trees with few characters. Electronic Journal of Combinatorics 13 #R83 abstract

  3. Download PDFSteel, M. and Szekely, L. (2006). On the variational distance of two trees, Annals of Applied Probability 16(3): 1563-1575. abstract
  4. Download PDFGascuel, O. and Steel, M. (2006). Neighbor-Joining revealed. Molecular Biology and Evolution 23(11): 1997-2000. abstract
  5. Download PDFHuson, D., Steel, M. and Whitfield, J. (2006). Reducing distortion in phylogenetic networks. Proceedings of WABI (Workshop on algorithms in bioinformatics) 2006. P. Buecher and BME Moret (eds). Lecture Notes in Bioinformatics 475, pp. 150-161, Springer-Verlage Berlin Heidelberg. abstract
  6. Download PDFHartmann, K. and Steel, M. (2006). Maximimizing phylogenetic diversity in biodiverstity conservation: greedy solutions to the Noah's Ark problem. Systematic Biology 55(4), 644-651. abstract
  7. Download PDFBaroni, M. and Steel, M. (2006). Accumulation phylogenies. Annals of Combinatorics 10: 19-30. abstract

  8. Download PDFDress, A. and Steel, M. (2006). Mapping edge sets to splits in trees: the path index and parsimony. Annals of Combinatorics 10: 77-96 abstract

  9. Download PDFBaroni, M., Semple, C. and Steel, M. (2006). Hybrids in real time. Systematic Biology 44(1): 46-56. abstract

  10. Download PDFSteel, M. and Hein, J. (2006). Reconstructing pedigrees: a combinatorial perspective. Journal of Theoretical Biology 240(3) 360-367. abstract
  11. Download PDFSteel, M and Pickett, K. M. (2006). On the impossibility of uniform priors on clade size. Molecular Phylogenetics and Evolution 39(2), 585-586. abstract

  12. Download PDFSemple, C. and Steel, M. (2006). Unicyclic networks: compatibility and enumeration. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(1), 84-91. abstract
  13. Download PDFM. Steel and D. Penny. (2005). Maximum parsimony and the phylogenetic information in multi-state characters. Pp. 163-178 In Parsimony, phylogeny and genomics (ed. V. Albert), Oxford University Press. abstract


  1. Download PDFP. Lockhart and M. Steel. (2005). A tale of two processes. Systematic Biology, 54(6): 948-951. abstract

  2. Download PDFM. Steel. (2005). Phylogenetic diversity and the greedy algorithm. Systematic Biology 54(4): 527-529. abstract

  3. Download PDFD.H. Huson, T. Kloepper, Pete J. Lockhart, Mike Steel. (2005). Reconstruction of reticulate networks from gene trees. RECOMB 2005. LNBI 3500. (S. Miyano et al. eds). pp 233-249. Springer-Verlag Heidelberg. abstract
  4. Download PDFM. Steel. (2005). Should phylogenetic models be trying to 'fit an elephant'? Trends in Genetics 21(6), 307-309. abstract
  5. Download PDFK. Huber, V. Moulton and M. Steel. (2005). Four characters suffice to convexly define a phylogenetic tree. SIAM Journal on Discrete Mathematics 18(4): 835-843. abstract
  6. Download PDFE. Mossel and M. Steel. (2005). How much can evolved characters tell us about the tree that generated them? pp. 384-412 In Mathematics of Evolution and Phylogeny (Olivier Gascuel ed.), Oxford University Press. abstract
  7. Download PDFE. Mossel and M. Steel. (2005). Random biochemical networks and the probability of self-sustaining autocatalysis. Journal of Theoretical Biology 233(3), 327-336. abstract
  8. Download PDFK.T. Huber, V. Moulton, C.Semple and M. Steel. (2005). Recovering a phylogenetic tree using pairwise closure operations. Applied Mathematics Letters 18(3): 361-366. abstract


  1. Download PDFW. Hordijk, and M. Steel. (2004). Detecting autocatalyctic, self-sustaining sets in chemical reaction systems. Journal of Theoretical Biology 227(4): 451-461. abstract

  2. Download PDFDaniel H. Huson, Tobias Dezulian, Tobias Klöpper, Mike A. Steel. (2004). Phylogenetic Super-Networks from Partial Trees IEEE/ACM Transactions on Computational Biology and Bioinformatics. Vol 1(4): 151-158. abstract
  3. Download PDFM. Baroni, C. Semple, and M. Steel. (2004). A framework for representing reticulate evolution. Annals of Combinatorics. Vol 8(4): 391-408. abstract
  4. Download PDFD. Huson and M. Steel. (2004). Phylogenetic trees based on gene content. Bioinformatics 20: 2044-2049. abstract
  5. Download PDFV. Moulton and M. Steel. (2004). Peeling phylogenetic 'oranges'. Advances in Applied Mathematics 33(4): 710-727. abstract

  6. Download PDFE. Mossel and M. Steel. (2004). A phase transition for a random cluster model on phylogenetic trees. Mathematical Biosciences. 187: 189-203. abstract
  7. Download PDFSemple, C., Daniel, P., Hordijk, W., Page, R.D.M. and Steel, M. (2004). Supertree algorithms for ancestral divergence dates and nested taxa. Bioinformatics 20(15): 2355-2360. abstract
  8. Download PDFJ.D. Bashford, P.D. Jarvis, J. Sumner and M. Steel. (2004). U(1) x U(1) x U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes. Journal of Physics (A) 37(8): L81-L89. abstract
  9. Download PDFD. Bryant, C. Semple and M. Steel. (2004). Supertree methods for ancestral dates and other applications. In Phylogenetic Supertrees: Combining information to reveal the tree of life. (O.R.P. Bininda-Emonds ed.) Kluwer. pp. 129-150. abstract
  10. Download PDFC. Semple and M. Steel. (2004). Cyclic permutations and evolutionary trees. Advances in Applied Mathematics 32(4): 669-680. abstract

  11. Download PDFD. H. Huson and M. Steel. (2004). Distances that perfectly mislead, Systematic Biology 53(2): 327-332. abstract

  12. Download PDFM. Steel and D. Penny. (2004). Two further links between MP and ML under the Poisson Model. Applied Mathematics Letters 17(7): 785-790. abstract
  13. Download PDFT. Dezulian and M. Steel. (2004). Phylogenetic closure operations and homoplasy-free evolution. In Classification, clustering, and data mining applications (Proceedings of the meeting of the International Federation of Classification Societies (IFCS) 2004). (ed. D. Banks, L. House, F.R. McMorris, P. Arabie, and W. Gaul), pp. 395-416. Springer-Verlag, Berlin. abstract
  14. Download PDFEsser et al. (2004). A genome phylogeny for mitochondria among ±-proteobacteria and a predominantly eubacterial ancestry of yeast nuclear genes. Mol.Biol.Evol. 21(9): 1643-1660. abstract
  15. Download PDFM. Steel. (2004). Inferring Phylogenies - an epic worth the wait (Book Review) Trends in Ecology and Evolution 19(4): 173-174. abstract


  1. bookSemple, C. and Steel, M. (2003). Phylogenetics [Book, 250 pages] Oxford University Press (Mathematics and its Applications series, No. 22). [ Search inside this book]
  2. Download PDFD. Bryant, A. McKenzie and M. Steel. (2003). The size of a maximum agreement subtree for random binary trees. In BioConsensus (Dimacs Series in discrete mathematics and theoretical computer science), American Mathematical Society 61: 55-65. abstract


  1. Download PDFBininda-Emonds, O.R.P., Gittleman, J.L. and Steel, M.A. (2002). The (super) tree of life: procedures, problems, and prospects. Ann. Rev. Ecol. Syst. 33: 265-289. abstract
  2. Download PDFSober, E. and Steel, M. (2002). Testing the hypothesis of common ancestry. J. Theor. Biol. 218: 395-408. abstract
  3. Download PDFSteel, M. A. and Szekely, L.A. (2002). Inverting random functions (II): explicit bounds for discrete maximum likelihood estimation, with applications, SIAM J. Discr. Math. 15(4): 562-575. abstract
  4. Download PDFSemple, C. and Steel, M. (2002). A characterisation for a set of partial partitions to define an X-tree, Discrete Mathematics 247: 169-186. abstract
  5. Download PDFSemple, C. and Steel, M. (2002). Tree reconstruction from multi-state characters, Adv. Appl. Math. 28(2): 169-184. abstract
  6. Download PDFSteel, M. (2002). Some statistical aspects of the maximum parsimony method. In Molecular Systematics and Evolution: Theory and Practice (Ed. R. DeSalle, G. Giribet, W. Wheeler). 125-140, Birkhauser. abstract


  1. Download PDFSteel, M. and Hein, J. (2001). Applying the Thorne-Kishino-Felsenstein model to sequence evolution on a star tree. Applied Mathematics Letters. 14(6): 679-684. abstract
  2. Download PDFSteel, M. and McKenzie, A. (2001). Properties of phylogenetic trees generated by Yule-type speciation models. Mathematical Biosciences 170: 91-112. abstract
  3. Download PDFBryant, D. and Steel, M. (2001). Constructing optimal trees from quartets. Journal of Algorithms, 38: 237-259. abstract
  4. Download PDFAllen, B. and Steel, M. (2001). Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Combinatorics 5: 1-13. abstract
  5. Download PDFMeir, A., Moon, J. and Steel, M. (2001). A limiting theorem on 2-coloured trivalent trees. Congressus Numerantium. 150: 43-63. abstract
  6. Download PDFSemple, C. and Steel, M.A. (2001). Tree reconstruction via a closure operation on partial splits. pp 126-134, In Computational Biology (proceedings of JOBIM 2000), LNCS 2066, Springer-Verlag. abstract
  7. Download PDFSteel, M. and McKenzie, A. (2001). The "shape" of phylogenies under simple random speciation models. Proceedings of Biological Evolution and Statistical Physics conference, Max Plank Institute (Dresden, 2000), (Book Chapter P. 165-185). Springer. abstract


  1. Download PDFMcKenzie, A. and Steel, M. (2000). Distributions of cherries for two models of trees. Mathematical Biosciences 164: 81-92. abstract
  2. Download PDFSteel, M. (2000). Sufficient conditions for two tree reconstruction techniques to succeed on sufficiently long sequences. SIAM Journal on Discrete Mathematics. 14(1):36-48. abstract
  3. Download PDFSemple, C. and Steel, M. (2000). A supertree method for rooted trees. Discrete Applied Mathematics 105: 147-158. abstract
  4. Download PDFMoulton, V., Zuker, M. Steel, M., Penny, D. and Pointon, R. (2000). Metrics on RNA Secondary Structures. J. Computational Biology 7(1): 277-292. abstract
  5. Download PDFSteel, M. and Penny, D., (2000). Parsimony, likelihood and the role of models in molecular phylogenetics. Molecular Biology and Evolution 17(6): 839-850. abstract
  6. Download PDFLockhart, P.J., Huson, D., Maier, U. Fraunholz, M. J., Peer, Y. v., Barbrook, A.C., Howe, C. and Steel M.A. (2000). How molecules evolve in Eubacteria. Molecular Biology and Evolution 17(5), 835-838. abstract
  7. Download PDFSteel, M., Huson, D. and Lockhart P.J. (2000). Invariable sites models and their use in phylogeny reconstruction. Systematic Biology 49(2): 225-232. abstract
  8. Download PDFBryant, D., Böcker, S., Dress, A.W.M., and Steel, M. (2000). Algorithmic aspects of tree amalgamation. Journal of Algorithms 37: 522-537. abstract
  9. Download PDFSteel, M., Böcker, S., and Dress, A.W.M. (2000). Simple but fundamental limits for supertree and consensus tree methods. Systematic Biology 49(2): 363-368.abstract
  10. Download PDFMeei, N., Steel, M., and Wormald, N. (2000). The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees. Discrete Applied Mathematics 98: 227-235. abstract
  11. Download PDFSteel, M. (2000). The emergence of a self-catalysing structure in abstract origin-of-life models. Applied Mathematics Letters 13 (3): 91-95. abstract


  1. Download PDFSemple, C. and Steel, M.A. (1999). Tree representations of non-symmetric, group-valued proximities. Advances in Applied Mathematics 23: 300-321. abstract
  2. Download PDFErdös, P.L., Steel, M.A., Székely, L.A. and Warnow, T. (1999). A few logs suffice to build (almost) all trees (Part 2). Theoretical Computer Science 221: 77-118. abstract
  3. Download PDFSteel, M. and Waddell, P.J. (1999). Approximating likelihoods under low but variable rates across sites. Applied Mathematics Letters 12(6): 13-19. abstract
  4. Download PDFMoulton V. and Steel, M.A. (1999). Retractions of finite distance functions onto tree metrics. Discrete Applied Mathematics 91:215-233. abstract
  5. Download PDFErdös, P.L., Steel, M.A., Székely, L.A. and Warnow, T. (1999). A few logs suffice to build (almost) all trees (Part 1). Random Structures and Algorithms 14(2):153-184. abstract
  6. Download PDFBöcker, S., Dress, A.W.M., Steel, M. (1999). Patching up X-trees. Annals of Combinatorics 3:1-12. abstract

  7. Download PDFSteel, M.A., and Székely, L.A. (1999). Inverting random functions. Annals of Combinatorics 3:103-113. abstract


  1. Download PDFBonet, M., Steel, M.A., Warnow, T., and Yooseph, S. (1998). Better methods for solving parsimony and compatibility. Journal of Computational Biology 5(3): 391-407. abstract
  2. Download PDFSteel, M.A. Hendy, M.D. and Penny, D. (1998). Reconstructing phylogenies from nucleotide pattern probabilities - a survey and some new results. Discrete Applied Mathematics 88: 367-396. abstract
  3. Download PDFLockhart, P.J. Steel, M.A., Barbrook, A.C. Huson, D., Charleston, M.A. and Howe, C.J. (1998). A covariotide model explains apparent phylogenetic structure of oxygenic photosynthetic Lineages. Molecular Biology and Evolution 15(9): 1183-1187. abstract


  1. Download PDFWaddell, P.J. and Steel, M.A. (1997). General time reversible distances with unequal rates across sites. Molecular Phylogenetics and Evolution 8(3): 398-414. abstract
  2. Download PDFTuffley, C. and Steel, M.A. (1997). Modelling the covarion hypothesis of nucleotide substitution. Mathematical Biosciences 147: 63-91. abstract
  3. Download PDFHamel, A. and Steel, M.A. (1997). The length of a random leaf coloration on a random tree. SIAM Journal on Discrete Mathematics. 10: 359-372. abstract
  4. Download PDFErdös, P.L. , Steel, M., Székeley, L. and Warnow, T. (1997). Local quartet splits of a binary tree imply all quartet splits under one dyadic inference rule. Computers and Artificial Intelligence 16(2): 217-227. abstract
  5. Download PDFDress, A., Moulton, V. and Steel, M.A. (1997). Trees, taxonomy and strongly compatible multi-state characters. Advances in Applied Mathematics 19(1): 1-30. abstract
  6. Download PDFTuffley, C. and Steel, M. (1997). Links between maximum likelihood and maximum parsimony under a simple model of site substitution. Bulletin of Mathematical Biology 59(3): 581-607. abstract
  7. Download PDFMoulton, V. Steel, M. and Tuffley, C. (1997). Dissimilarity maps and substitution models: some new results. In Mathematical Hierarchies and Biology, DIMACS series in Discrete Mathematics and Theoretical Computer Science, Vol 37, American Mathematical Society, (Book chapters) abstract


  1. PDF coming soonPenny, D. Steel, M.A., Lockhart, P.J. and Hendy, M.D. (1996). Corrected parsimony, minimum evolution and Hadamard conjugations. Systematic Biology 45(4): 596-696.
  2. PDF coming soonLockhart P.J., Steel M.A. & Larkum A.W.D. (1996). Gene Duplication and the Evolution of Photosynthetic Reaction Centers. FEBS Letters 385: 193-196.
  3. Download PDFBaritompa, B. and Steel, M.A. (1996). Bounds on absorption times of directionally biased random sequences. Random Structures and Algorithms 9(3): 279-293. abstract
  4. Download PDFLockhart, P.J., Larkum, W.D., Steel, M.A., Waddell, P, and Penny, D. (1996). Evolution of chlorophyll and bacteriochlorophyll: The problem of invariant sites in sequence analysis. Proceedings National Academy Sciences, USA, 93: 1930-1934. abstract
  5. Download PDFSteel, M.A., Cooper, A. and Penny, D. (1996). Confidence Intervals for the divergence times of two clades. Systematic Biology 45(2): 127-134. abstract
  6. Download PDFHamel, A. and Steel, M.A. (1996). Finding a maximum compatible tree is NP-hard for sequences and trees. Applied Mathematics Letters 9(2): 55-60. abstract
  7. Download PDFSteel, M., Goldstein, L, and Waterman, M.S. (1996). A central limit theorem for the parsimony length of trees. Advances in Applied Probability 28(4): 1051-1071. abstract


  1. Download PDFBryant, D.J. and Steel, M.A. (1995). Extension operations on sets of leaf-labelled trees. Advances in Applied Mathematics 16(4): 425-453. abstract
  2. Download PDFPenny, D. Steel, M.A. Waddell, P.J. and Hendy, M.D. (1995). Improved Analyses of Human mtDNA Sequences Support a Recent African Origin for Homo sapiens. Molecular Biology and Evolution 12(5): 863-882. abstract
  3. Download PDFZabinski, Z. Wood, G. Steel, M.A. and Baritompa, B. (1995). Pure adaptive search for finite global optimization. Mathematical Programming 69: 443-448. abstract
  4. Download PDFBandelt, H.-J. and Steel, M.A. (1995). Symmetric matrices representable by weighted trees over a cancellative abelian monoid. SIAM Journal on Discrete Mathematics 8(4): 517-525. abstract
  5. Download PDFSteel, M.A. and Fu, Y.X. (1995). Classifying and counting linear phylogenetic invariants for the Jukes-Cantor model. Journal of Computational Biology 2(1): 39-47. abstract
  6. Download PDFSteel, M. A. Lockhart, P.J. and Penny, D. (1995). A frequency dependent significance test for parsimony. Molecular Phylogenetics and Evolution 4(1): 64-71. abstract
  7. Download PDFSteel, M.A. and Charleston, M. (1995). Five surprising properties of parsimoniously colored trees. Bulletin of Mathematical Biology 57(2): 367-375. abstract
  8. PDF coming soonPenny, D. Steel, M.A. Lockhart, P.J. and Hendy, M.D. (1995). The role of models in reconstructing evolutionary trees. pp. 211-230. In Models in Phylogeny reconstruction (Oxford University Press, eds. R.W. Scotland, D.J. Siebert, and D.M. Williams ). (Book chapters)


  1. Download PDFSteel, M.A. (1994). The maximum likelihood point for a phylogenetic tree is not unique. Systematic Biology 43(4): 560-564. abstract
  2. Download PDFSzékely, L. Erdös, P.L. and Steel, M.A. (1994). The combinatorics of evolutionary trees - a survey. Journal of Combinatorial Mathematics and Combinatorial Computing 15: 241-254. abstract
  3. Download PDFSteel, M.A. Székely, L. and Hendy, M.D. (1994). Reconstructing trees when sequence sites evolve at variable rates. Journal of Computational Biology 1(2): 153-163. abstract
  4. Download PDFLockhart, P.J. Steel, M.A. Penny, D. and Hendy, M.D. (1994). Recovering evolutionary trees under a more realistic model of sequence evolution. Molecular Biology and Evolution 11(4): 605-612. abstract
  5. Download PDFHendy, M.D., Penny, D. and Steel, M.A. (1994). A discrete Fourier analysis for evolutionary trees. Procedings of the National Academy of Sciences, USA 91: 3339-3343. abstract
  6. Download PDFSteel, M.A. (1994). Recovering a tree from the leaf colourations it generates under a Markov model. Applied Mathematics Letters 7(2): 19-24. abstract


  1. Download PDFSteel, M.A. Penny, D. and Hendy, M.D. (1993). Parsimony can be consistent! Systematic Biology 42: 581-587.
  2. Download PDFSteel, M.A. Lockhart, P. and Penny, D. (1993). Confidence in evolutionary trees from biological sequence data. Nature 364: 440-442. abstract
  3. Download PDFSteel, M.A. and Warnow, T. (1993). Kaikoura tree theorems: computing the maximum agreement subtree. Information Processing Letters 48: 77-82. abstract
  4. Download PDFSteel, M.A. Székely, L. Erdös, P.L. and Waddell, P. (1993). A complete family of phylogenetic invariants for any number of taxa under Kimura's 3ST model. NZ Journal of Botany (conference proceedings) 13(3): 289-296. abstract
  5. Download PDFWood, G.R. and Steel, M.A. (1993). On a problem of Andersson and Perlman. Statistics and Probability Letters 18: 381-382. abstract
  6. Download PDFMoon, J.W. and Steel, M.A. (1993). A limiting theorem for parsimoniously bicoloured trees. Applied Mathematics Letters 6(4): 5-8. abstract
  7. PDF coming soonPenny, D. Steel, M.A. and Watson, E. (1993). Trees from languages and genes are very similar. Systematic Biology 42(3): 382-384.
  8. Download PDFSzékely, L. Steel, M.A. and Erdös, P.L. (1993). Fourier calculus on evolutionary trees. Advances in Applied Mathematics 14: 200-216. abstract
  9. Download PDFSzékely, L. Erdös, P.L. Steel, M.A. and Penny, D. (1993). A fourier inversion formula for evolutionary trees. Applied Mathematics Letters 6(2): 13-17. abstract
  10. Download PDFSteel, M.A. and Penny, D. (1993). Distributions of tree comparison metrics - some new results. Systematic Biology 42(2): 126-141. abstract
  11. Download PDFSteel, M.A. (1993). Decompositions of leaf-coloured binary trees. Advances in Applied Mathematics 14(1): 1-24. abstract
  12. Download PDFSteel, M.A. (1993). Distributions on bicoloured binary trees arising from the principle of parsimony. Discrete Applied Mathematics 41(3): 245-261. abstract

1992 - 1988:

  1. Download PDFSteel, M.A. Hendy, M.D., Székely, L. and Erdös, P.L. (1992). Spectral analysis and a closest tree method for genetic sequences. Applied Mathematics Letters 5(6): 63-67. abstract
  2. Download PDFDress, A. and Steel, M.A. (1992). Convex tree realizations of partitions. Applied Mathematics Letters, 5(3): 3-6. abstract
  3. Download PDFPenny, D. Hendy, M.D. and Steel, M.A. (1992). Progress with methods for constructing evolutionary trees. Trends in Ecology and Evolution 7(3): 73-79.
  4. Download PDFSteel, M.A., Hendy, M.D. and Penny, D. (1992). Significance of the length of the shortest tree. Journal of Classification 9: 71-90. abstract
  5. Download PDFSteel, M. (1992). The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification 9: 91-116. abstract
  6. Download PDFPenny, D. Hendy, M.D. and Steel, M.A. (1991). Testing the theory of descent. In Phylogenetic Analysis of DNA sequences, (eds. M. Miyamoto and J. Cracraft ) Oxford University Press, 155-183. (Book chapters)
  7. Download PDFSteel, M.A. (1990). Distributions on bicoloured evolutionary trees, (PhD abstract). Bulletin of the Australian Mathematical Society 41: 159-160. first paragraph
  8. Download PDFSteel, M.A. (1989). Distributions on bicoloured evolutionary trees. PhD Thesis. Massey University. abstract
  9. Download PDFSteel, M. A., Penny, D. and Hendy, M.D. (1988). Loss of information in genetic distances. Nature 336(6195): 118. first 2 paragraphs
  10. Download PDFSteel, M. A. (1988). Distribution of the symmetric difference metric on phylogenetic trees. SIAM Journal on Discrete Mathematics 1(4): 541-551. abstract
  11. Download PDFHendy, M.D., Steel, M. A., Penny, D and Henderson, I.M. (1988). Families of trees and consensus. In Classification and Related Methods of Data Analysis (ed. H.H. Bock), Elsevier Science Publishers B.V. (North Holland). 355-362. (Book chapters). abstract

Papers published in refereed conference proceedings (partial list)

  1. PDF coming soonBryant, D. and Steel, M. (1999). Fast algorithms for constructing optimal trees from quartets, Proceedings of SODA (Symposium on Discrete Algorithms), Baltimore, USA.
  2. PDF coming soonErdös, P.L., Steel, M.A., Székely, L.A. and Warnow, T. (1997). Constructing big trees from short sequences, ICALP -97 (International Congress on Automata and Language Programming), Bolognia, Italy.
  3. PDF coming soonSteel, M. Reconstructing evolutionary trees under a variety of Markov-style models. (1995). Proceedings of Phylogeny Workshop, Princeton University (DIMACS Technical Report 95-48): 51-54.
  4. Download PDFMcMorris, F.R. and Steel, M.A. (1994). The complexity of the median procedure for binary trees. In Procedings of the International Federation of Classification Societies, 1993, Springer-Verlag, New York. abstract