Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-07T01:27:24.864Z Has data issue: false hasContentIssue false

Understanding the Tripartite Approach to Bayesian Divergence Time Estimation

Published online by Cambridge University Press:  08 December 2020

Rachel C. M. Warnock
Affiliation:
ETH Zürich
April M. Wright
Affiliation:
Southeastern Louisiana University

Summary

Placing evolutionary events in the context of geological time is a fundamental goal in paleobiology and macroevolution. In this Element we describe the tripartite model used for Bayesian estimation of time calibrated phylogenetic trees. The model can be readily separated into its component models: the substitution model, the clock model and the tree model. We provide an overview of the most widely used models for each component and highlight the advantages of implementing the tripartite model within a Bayesian framework.
Get access
Type
Element
Information
Online ISBN: 9781108954365
Publisher: Cambridge University Press
Print publication: 04 February 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abadi, S., Azouri, D., Pupko, T., & Mayrose, I. (2019). Model selection may not be a mandatory step for phylogeny reconstruction. Nature Communications, 10(1), 934.Google Scholar
Álvarez-Carretero, S., Goswami, A., Yang, Z., & dos Reis, M. (2019). Bayesian estimation of species divergence times using correlated quantitative characters. Systematic Biology, syz015. doi: https://doi.org/10.1093/sysbio/syz015CrossRefGoogle Scholar
Andújar, C., Soria-Carrasco, V, Serrano, J., & Gomez-Zurita, J. (2014). Congruence test of molecular clock calibration hypotheses based on Bayes factor comparisons. Methods in Ecology and Evolution, 5(3), 226-242. doi: https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.12151CrossRefGoogle Scholar
Aris-Brosou, S., & Yang, Z. (2002). Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny. Systematic Biology, 51(5), 703714.Google Scholar
Aris-Brosou, S., & Yang, Z. (2003). Bayesian models of episodic evolution support a late Precambrian explosive diversification of the Metazoa. Molecular Biology and Evolution, 20(12), 19471954.Google Scholar
Bapst, D. W., Schreiber, H. A., & Carlson, S. J. (2017). Combined analysis of extant Rhynchonellida (Brachiopoda) using morphological and molecular data. Systematic Biology, 67(1), 3248. doi: https://doi.org/10.1093/sysbio/syx049Google Scholar
Barido-Sottani, J., Aguirre-Fernández, G., Hopkins, M. J., Stadler, T., & Warnock, R. C. M. (2019). Ignoring stratigraphic age uncertainty leads to erroneous estimates of species divergence times under the fossilized birth-death process. Proceedings of the Royal Society B, 286(1902), 20190685.Google Scholar
Barido-Sottani, J., Bošková, V., du Plessis, L., et al. (2018). Taming the beast? A community teaching material resource for BEAST 2. Systematic Biology, 67(1), 170174.Google Scholar
Barido-Sottani, J., Pett, W., O’Reilly, J. E., & Warnock, R. C. M. (2019). FossilSim An R package for simulating fossil occurrence data under mechanistic models of preservation and recovery. Methods in Ecology and Evolution, 10(6), 835840.CrossRefGoogle Scholar
Barido-Sottani, J., Vaughan, T. G., & Stadler, T. (2020). A multi-state birthdeath model for Bayesian inference of lineage-specific birth and death rates. Systematic Biology, 69(5), 973986. doi: https://doi.org/10.1093/sysbio/syaa01Google Scholar
Beaulieu, J. M., Jhwueng, D.-C., Boettiger, C., & O’Meara, B. C. (2012). Modeling stabilizing selection: Expanding the Ornstein–Uhlenbeck model of adaptive evolution. Evolution: International Journal of Organic Evolution, 66(8), 23692383.CrossRefGoogle ScholarPubMed
Beerli, P., & Felsenstein, J. (2001). Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach. Proceedings of the National Academy of Sciences, 98(8), 45634568. doi: https://doi.org/10.1073/pnas.081068098CrossRefGoogle Scholar
Bouckaert, R. R., Vaughan, T. G., Barido-Sottani, J., et al. (2019). BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis. PLoS Computational Biology, 15(4), 128. doi: https://doi.org/10.1371/journal.pcbi.1006650CrossRefGoogle ScholarPubMed
Brandley, M. C., Leaché, A. D., Warren, D. L., & McGuire, J. A. (2006). Are unequal clade priors problematic for Bayesian phylogenetics? Systematic Biology, 55(1), 138146.CrossRefGoogle Scholar
Brandley, M. C., Schmitz, A., & Reeder, T. W. (2005). Partitioned Bayesian analyses, partition choice, and the phylogenetic relationships of scincid lizards. Systematic Biology, 54(3), 373390.CrossRefGoogle ScholarPubMed
Bromham, L., Hua, X., Lanfear, R., & Cowman, P. F. (2015). Exploring the relationships between mutation rates, life history, genome size, environment, and species richness in flowering plants. The American Naturalist, 185(4), 507524.Google Scholar
Bromham, L., Rambaut, A., & Harvey, P. H. (1996). Determinants of rate variation in mammalian DNA sequence evolution. Journal of Molecular Evolution, 43(6), 610621.CrossRefGoogle ScholarPubMed
Brown, J., &ElDabaje, R. (2009). PuMA: Bayesian analysis of partitioned (and unpartitioned) model adequacy. Bioinformatics, 25(4), 537538.Google Scholar
Brown, J. M. (2014). Predictive approaches to assessing the fit of evolutionary models. Systematic Biology, 63(3), 289292.Google Scholar
Butler, M. A., & King, A. A. (2004). Phylogenetic comparative analysis: A modeling approach for adaptive evolution. The American Naturalist, 164(6), 683695.CrossRefGoogle ScholarPubMed
De Baets, K., Antonelli, A., & Donoghue, P. C. (2016). Tectonic blocks and molecular clocks. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1699), 20160098.CrossRefGoogle ScholarPubMed
de Queiroz, K. (1985). The ontogenetic method for determining character polarity and its relevance to phylogenetic systematics. Systematic Zoology, 34(3), 280299.Google Scholar
dos Reis, M., Donoghue, P. C., & Yang, Z. (2016). Bayesian molecular clock dating of species divergences in the genomics era. Nature Reviews Genetics, 17(2), 71.Google Scholar
dos Reis, M., & Yang, Z. (2013). The unbearable uncertainty of Bayesian divergence time estimation. Journal of Systematics and Evolution, 51(1), 3043.Google Scholar
Drummond, A. J., Ho, S. Y., Phillips, M., & Rambaut, A. (2006). Relaxed phylogenetics and dating with confidence. PLoS Biology, 4(5), e88.CrossRefGoogle ScholarPubMed
Drummond, A. J., & Rambaut, A. (2007). BEAST: Bayesian evolutionary analysis sampling trees. BMC Evolutionary Biology, 7, 214.Google Scholar
Drummond, A. J., & Suchard, M. (2010). Bayesian random local clocks, or one rate to rule them all. BMC Biology, 8(1), 114.Google Scholar
Drummond, A. J., Rambaut, A., Shapiro, B., & Pybus, O. G. (2005). Bayesian coalescent inference of past population dynamics from molecular sequences. Molecular Biology and Evolution, 22(5), 11851192. doi: https://doi.org/10.1093/molbev/msi103CrossRefGoogle ScholarPubMed
Drummond, A. J., & Stadler, T. (2016). Bayesian phylogenetic estimation of fossil ages. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1699), 20150129.Google Scholar
Duchêne, D. A., Duchêne, S., Holmes, E. C., & Ho, S. Y. (2015). Evaluating the adequacy of molecular clock models using posterior predictive simulations. Molecular Biology and Evolution, 32(11), 29862995.Google Scholar
du Plessis, L., & Stadler, T. (2015). Getting to the root of epidemic spread with phylodynamic analysis of genomic data. Trends in Microbiology, 23(7), 383386.Google Scholar
Felsenstein, J. (1973). Maximum-likelihood estimation of evolutionary trees from continuous characters. American Journal of Human Genetics, 25(5), 47192.Google ScholarPubMed
Felsenstein, J. (1981). Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of Molecular Evolution, 17(6), 368376.Google Scholar
Felsenstein, J. (1985). Phylogenies and the comparative method. The American Naturalist, 115.Google Scholar
Gaut, B. S., Muse, S. V., Clark, W. D., & Clegg, M. T. (1992). Relative rates of nucleotide substitution at the rbcL locus of monocotyledonous plants. Journal of Molecular Evolution, 35(4), 292303.Google Scholar
Gavryushkina, A., Heath, T. A., Ksepka, D. T., et al. (2017). Bayesian totalevidence dating reveals the recent crown radiation of penguins. Systematic Biology, 66(1), 5773.Google Scholar
Gavryushkina, A., Welch, D., Stadler, T., & Drummond, A. J. (2014). Bayesian inference of sampled ancestor trees for epidemiology and fossil calibration. PLoS Computational Biology, 10(12), e1003919.Google Scholar
Gernhard, T. (2008). The conditioned reconstructed process. Journal of Theoretical Biology, 253(4), 769778.Google Scholar
Gingerich, P. D. (1993). Quantification and comparison of evolutionary rates. American Journal of Science, 293(A), 453.Google Scholar
Goloboff, P. A., Mattoni, C. I., & Quinteros, A. S. (2006). Continuous characters analyzed as such. Cladistics, 22(6), 589601.Google Scholar
Hansen, T. F. (1997). Stabilizing selection and the comparative analysis of adaptation. Evolution, 51(5), 13411351.Google Scholar
Harrison, L. B., & Larsson, H. C. (2015). Among-character rate variation distributions in phylogenetic analysis of discrete morphological characters. Systematic Biology, 64(2), 307324.CrossRefGoogle ScholarPubMed
Hasegawa, M., Kishino, H., & Yano, T. (1985). Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. Journal of Molecular Evolution, 22(2), 160174.Google Scholar
Heath, T. A. (2012). A hierarchical Bayesian model for calibrating estimates of species divergence times. Systematic Biology, 61(5), 793809.CrossRefGoogle ScholarPubMed
Heath, T. A., Huelsenbeck, J. P., & Stadler, T. (2014). The fossilized birth-death process for coherent calibration of divergence-time estimates. Proceedings of the National Academy of Sciences, 111(29), E2957E2966.Google Scholar
Heled, J., & Bouckaert, R. R. (2013). Looking for trees in the forest: Summary tree from posterior samples. BMC Evolutionary Biology, 13(1), 221.CrossRefGoogle ScholarPubMed
Heled, J., & Drummond, A. J. (2010). Bayesian inference of species trees from multilocus data. Molecular Biology and Evolution, 27(3), 570.Google Scholar
Heled, J., & Drummond, A. J. (2012). Calibrated tree priors for relaxed phylogenetics and divergence time estimation. Systematic Biology, 61(1), 138149.CrossRefGoogle ScholarPubMed
Ho, S. Y., & Phillips, M. J. (2009). Accounting for calibration uncertainty in phylogenetic estimation of evolutionary divergence times. Systematic Biology, 58(3), 367380.Google Scholar
Ho, S.Y., Tong, K. J., Foster, C.S., et al. (2015). Biogeographic calibrations for the molecular clock. Biology Letters, 11(9), 20150194.CrossRefGoogle ScholarPubMed
Höhna, S., Coghill, L. M., Mount, G. G., Thomson, R. C., & Brown, J. M. (2017). P3: Phylogenetic posterior prediction in RevBayes. Molecular Biology and Evolution, 35(4), 10281034. doi: https://doi.org/10.1093/molbev/msx286CrossRefGoogle Scholar
Höhna, S., Heath, T. A., Boussau, B., et al. (2014). Probabilistic graphical model representation in phylogenetics. Systematic Biology, 63(5), 753771. doi: https://doi.org/10.1093/sysbio/syu039Google Scholar
Höhna, S., Landis, M. J., Heath, T. A., et al. (2016). RevBayes: Bayesian phylogenetic inference using graphical models and an interactive model-specification language. Systematic Biology, 65(4), 726736. doi: https://doi.org/10.1093/sysbio/syw021Google Scholar
Höhn, S., Stadler, T., Ronquist, F., & Britton, T. (2011). Inferring speciation and extinction rates under different species sampling schemes. Molecular Biology and Evolution, 28(9), 25772589.Google Scholar
Holder, M., & Lewis, P. O. (2003). Phylogeny estimation: Traditional and Bayesian approaches. Nature Reviews Genetics, 4(4), 275.Google Scholar
Holland, S. M. (1995). The stratigraphic distribution of fossils. Paleobiology, 21(1), 92109. doi: https://doi.org/10.1017/S0094837300013099Google Scholar
Hopkins, M. J., Bapst, D. W., Simpson, C., & Warnock, R. C. M. (2018). The inseparability of sampling and time and its influence on attempts to unify the molecular and fossil records. Paleobiology, 44(4), 561574.Google Scholar
Huelsenbeck, J. P., Larget, B., Miller, R., & Ronquist, F. (2002). Potential applications and pitfalls of Bayesian inference of phylogeny. Systematic Biology, 51(5), 673688.Google Scholar
Huelsenbeck, J. P., & Ronquist, F. (2001). MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics, 17(8), 754755.Google Scholar
Jarvis, E. D., Mirarab, S.,Aberer, A. J., et al. (2014). Whole-genome analyses resolve early branches in the tree of life of modern birds. Science, 346(6215), 13201331.Google Scholar
Jukes, T., & Cantor, C. (1969). Evolution of protein molecules. Mammalian Protein Metabolism, 3, 21132.Google Scholar
Kendall, D. G. (1948). On the generalized “birth-and-death” process. The Annals of Mathematical Statistics, 19(1), 115.Google Scholar
Kimura, M. (1980). A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. Journal of Molecular Evolution, 16(2), 111120.Google Scholar
King, B., Qiao, T., Lee, M. S. Y., Zhu, M., & Long, J. A. (2016). Bayesian morphological clock methods resurrect placoderm monophyly and reveal rapid early evolution in jawed vertebrates. Systematic Biology, 66(4), 499516. doi: https://doi.org/10.1093/sysbio/syw107Google Scholar
Kingman, J. F. C. (1982). On the genealogy of large populations. Journal of Applied Probability, 19, 2743.Google Scholar
Kishino, H., Thorne, J. L., & Bruno, W. J. (2001). Performance of a divergence time estimation method under a probabilistic model of rate evolution. Molecular Biology and Evolution, 18(3), 352361.Google Scholar
Klopfstein, S., Ryser, R., Corio, M., & Spasejovic, T. (2019). Mismatch of the morphology model is mostly unproblematic in total-evidence dating: Insights from an extensive simulation study. bioRxiv, 679084.Google Scholar
Kühnert, D., Stadler, T., Vaughan, T. G., & Drummond, A. J. (2016). Phylodynamics with migration: A computational framework to quantify population structure from genomic data. Molecular Biology and Evolution, 33(8), 21022116.Google Scholar
Landis, M. J. (2017). Biogeographic dating of speciation times using paleogeo-graphically informed processes. Systematic Biology, 66(2), 128144. doi: https://doi.org/10.1093/sysbio/syw040Google Scholar
Landis, M. J., Freyman, W. A., & Baldwin, B. G. (2019). Retracing the Hawaiian silversword radiation despite phylogenetic, biogeographic, and paleogeographic uncertainty. Evolution, 72(11), 23432359.Google Scholar
Landis, M. J., Schraiber, J. G., & Liang, M. (2013). Phylogenetic analysis using Lévy processes: Finding jumps in the evolution of continuous traits. Systematic Biology, 62(2), 193204.Google Scholar
Leaché, A. D., Banbury, B. L., Felsenstein, J., de Oca, A. n. M., & Stamatakis, A. (2015). Short tree, long tree, right tree, wrong tree: New acquisition bias corrections for inferring SNP phylogenies. Systematic Biology, 64(6), 10321047.CrossRefGoogle ScholarPubMed
Lee, M.S.Y., Cau, A., Naish, D., & Dyke, G.J. (2014). Morphological clocks in paleontology, and a mid-Cretaceous origin of crown Aves. Systematic Biology, 63(3), 442449. doi: https://doi.org/10.1093/sysbio/syt110Google Scholar
Lewis, P. O. (2001). A likelihood approach to estimating phylogeny from discrete morphological character data. Systematic Biology, 50(6), 913925.Google Scholar
Liu, L. (2008). BEST: Bayesian estimation of species trees under the coalescent model. Bioinformatics, 24(21), 25422543.Google Scholar
Maddison, W. P., & Knowles, L. L. (2006). Inferring phylogeny despite incomplete lineage sorting. Systematic Biology, 55(1), 2130.Google Scholar
Mashayekhi, S., & Beerli, P. (2019). Fractional coalescent. Proceedings of the National Academy of Sciences, 116(13), 62446249. www.pnas.org/content/116/13/6244 doi: https://doi.org/10.1073/pnas.1810239116Google Scholar
Matschiner, M., Musilová, Z., Barth, J. M., Starostová, Z., Salzburger, W., Steel, M., & Bouckaert, R. R. (2017). Bayesian phylogenetic estimation of clade ages supports trans-atlantic dispersal of cichlid fishes. Systematic Biology, 66(1), 322.Google Scholar
Matzke, N. J., & Wright, A. (2016). Inferring node dates from tip dates in fossil Canidae: The importance of tree priors. Biology Letters, 12(8), 20160328.Google Scholar
Mirarab, S., Reaz, R., Bayzid, M. S., Zimmermann, T., Swenson, M. S., & Warnow, T. (2014). ASTRAL: Genome-scale coalescent-based species tree estimation. Bioinformatics, 30(17), i541i548.CrossRefGoogle ScholarPubMed
Nascimento, F. F., dos Reis, M., & Yang, Z. (2017). A biologist’s guide to Bayesian phylogenetic analysis. Nature Ecology & Evolution, 1(10), 14461454.Google Scholar
Nguyen, L.-T., Schmidt, H. A., von Haeseler, A., & Minh, B. Q. (2014). IQ-TREE: A fast and effective stochastic algorithm for estimating maximum-likelihood phylogenies. Molecular Biology and Evolution, 32(1), 268274. doi: https://doi.org/10.1093/molbev/msu300Google Scholar
Nylander, J. A., Ronquist, F., Huelsenbeck, J. P., & Nieves-Aldrey, J. (2004). Bayesian phylogenetic analysis of combined data. Systematic Biology, 53(1), 4767.Google Scholar
Ogilvie, H. A., Vaughan, T. G., Matzke, N. J. et al. (2018). Inferring species trees using integrative models of species evolution. bioRxiv, 242875.Google Scholar
O’Reilly, J. E., & Donoghue, P. C. (2018). The efficacy of consensus tree methods for summarizing phylogenetic relationships from a posterior sample of trees estimated from morphological data. Systematic Biology, 67(2), 354362.CrossRefGoogle ScholarPubMed
O’Reilly, J. E., dos Reis, M., & Donoghue, P. C. (2015). Dating tips for divergence-time estimation. Trends in Genetics, 31(11), 637650.Google Scholar
Parham, J. F., Donoghue, P. C., Bell, C. J., et al. (2012). Best practices for justifying fossil calibrations. Systematic Biology, 67(2), 346359.Google Scholar
Parins-Fukuchi, C. (2017). Use of continuous traits can improve morphological phylogenetics. Systematic Biology, 67(2), 328339.Google Scholar
Paterson, J. R., Edgecombe, G. D., & Lee, M. S. Y. (2019). Trilobite evolutionary rates constrain the duration of the Cambrian explosion. Proceedings of the National Academy of Sciences, 116(10), 43944399.Google Scholar
Peters, S. E. (2005, Aug.). Geologic constraints on the macroevolutionary history of marine animals. Proceedings of the National Academy of Sciences, 102(35), 1232612331. doi: https://doi.org/10.1073/pnas.0502616102Google Scholar
Ronquist, F., & Huelsenbeck, J. P. (2003). MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics, 19(12), 15721574.Google Scholar
Ronquist, F., Huelsenbeck, J. P., & Britton, T. (2004). Bayesian supertrees. Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, 3, 193224.Google Scholar
Ronquist, F., Klopfstein, S., Vilhelmsen, L., et al. (2012). A total-evidence approach to dating with fossils, applied to the early radiation of the Hymenoptera. Systematic Biology, 61(6), 973999.Google Scholar
Schrago, C., Mello, B., & Soares, A. (2013). Combining fossil and molecular data to date the diversification of New World primates. Journal of Evolutionary Biology, 26(11), 24382446.Google Scholar
Silvestro, D., Schnitzler, J., Liow, L. H., Antonelli, A., & Salamin, N. (2014). Bayesian estimation of speciation and extinction from incomplete fossil occurrence data. Systematic Biology, 63(3), 349367, doi: https://doi.org/10.1093/sysbio/syu006.Google Scholar
Slater, G. J. (2015). Iterative adaptive radiations of fossil canids show no evidence for diversity-dependent trait evolution. Proceedings of the National Academy of Sciences, 112(16), 48974902. www.pnas.org/content/112/16/4897 doi: https://doi.org/10.1073/pnas.1403666111Google Scholar
Song, S., Liu, L., Edwards, S. V., & Wu, S. (2012). Resolving conflict in eutherian mammal phylogeny using phylogenomics and the multispecies coalescent model. Proceedings of the National Academy of Sciences, 109(37), 1494214947.Google Scholar
Soul, L. C., & Friedman, M. (2015). Taxonomy and phylogeny can yield comparable results in comparative paleontological analyses. Systematic Biology, 64(4), 608620.Google Scholar
Stadler, T. (2009). On incomplete sampling under birth-death models and connections to the sampling-based coalescent. Journal of Theoretical Biology, 261(1), 5866.Google Scholar
Stadler, T. (2010). Sampling-through-time in birth-death trees. Journal of Theoretical Biology, 267(3), 396404.Google Scholar
Stadler, T. (2011). Mammalian phylogeny reveals recent diversification rate shifts. Proceedings of the National Academy of Sciences, 108(15), 61876192.Google Scholar
Stadler, T., Gavryushkina, A., Warnock, R. C. M., Drummond, A. J., & Heath, T. A. (2018). The fossilized birth-death model for the analysis of stratigraphic range data under different speciation modes. Journal of Theoretical Biology, 447, 4155.Google Scholar
Stadler, T., Kühnert, D., Bonhoeffer, S., & Drummond, A. J. (2013). Birthdeath skyline plot reveals temporal changes of epidemic spread in HIV and hepatitis C virus (HCV). Proceedings of the National Academy of Sciences, 110(1),228233.Google Scholar
Stamatakis, A. (2014). RAxML version 8: A tool for phylogenetic analysis and post-analysis of large phytogenies. Bioinformatics, 30(9), 13121313. doi: https://doi.org/10.1093/bioinformatics/btu033Google Scholar
Suchard, M. A., Lemey, P., Baele, G., et al. (2018). Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10. Virus Evolution, 4(1). doi: https://doi.org/10.1093/ve/vey016 doi: 10.1093/ve/vey016Google Scholar
Swofford, D. L. (2003). PAUP*. Phylogenetic analysis using parsimony (*and other methods). Version 4. Sinauer Associates, Sunderland, Massachusetts. doi: https://paup.phylosolutions.com/documentation/faq/Google Scholar
Tavaré, S. (1986). Some probabilistic and statistical problems in the analysis of DNA sequences. Some Mathematical Questions in Biology: DNA Sequence Analysis, 17, 5786.Google Scholar
Thomas, J. A., Welch, J. J., Woolfit, M., & Bromham, L. (2006). There is no universal molecular clock for invertebrates, but rate variation does not scale with body size. Proceedings of the National Academy of Sciences, 103(19), 73667371.Google Scholar
Thompson, E. (1975). Human evolutionary trees. Cambridge: Cambridge University Press.Google Scholar
Thorne, J. L., Kishino, H., & Painter, I. S. (1998). Estimating the rate of evolution of the rate of molecular evolution. Molecular Biology and Evolution, 15, 16471657.Google Scholar
Thorne, J. L., & Kishino, H. (2002). Divergence time and evolutionary rate estimation with multilocus data. Systematic Biology, 51(5), 689702.Google Scholar
Wagner, P. J. (2011). Modelling rate distributions using character compatibility: Implications for morphological evolution among fossil invertebrates. Biology Letters, 8(1), 143146.Google Scholar
Warnock, R. C. M., Heath, T. A., & Stadler, T. (2020). Assessing the impact of incomplete species sampling on estimates of speciation and extinction rates. Paleobiology, 46(2), 137157, doi: https://doi.org/10.1017/pab.2020.12Google Scholar
Warnock, R. C. M., Parham, J. F., Joyce, W. G., Lyson, T. R., & Donoghue, P. C. (2015). Calibration uncertainty in molecular dating analyses: There is no substitute for the prior evaluation of time priors. Proceedings of the Royal Society B: Biological Sciences, 282(1798), 20141013.Google Scholar
Warnock, R.C.M., Yang, Z., & Donoghue, P.C. (2017). Testing the molecular clock using mechanistic models of fossil preservation and molecular evolution. Proceedings of the Royal Society B: Biological Sciences, 284(1857), 20170227.Google Scholar
Watrous, L. E., & Wheeler, Q. D. (1981). The out-group comparison method of character analysis. SystematicBiology, 30(1), 111.Google Scholar
Wood, H. M., Matzke, N. J., Gillespie, R. G., & Griswold, C. E. (2013). Treating fossils as terminal taxa in divergence time estimation reveals ancient vicariance patterns in the palpimanoid spiders. Systematic Biology, 62(2), 264284.Google Scholar
Wright, A. M. (2019). A Systematist’s guide to estimating bayesian phytogenies from morphological data. Insect Systematics and Diversity, 3(3). doi: https://doi.org/10.1093/isd/ixz006Google Scholar
Wright, A. M., Lloyd, G. T., & Hillis, D. M. (2016). Modeling character change heterogeneity in phylogenetic analyses of morphology through the use of priors. Systematic Biology, 65(4), 602611.Google Scholar
Wright, D. F. (2017). Phenotypic innovation and adaptive constraints in the evolutionary radiation of Palaeozoic crinoids. Scientific Reports, 7(1), 13745. doi: https://doi.org/10.1038/s41598-017-13979-9Google Scholar
Wright, D. F., & Toom, U. (2017). New crinoids from the Baltic region (Estonia): Fossil tip-dating phylogenetics constrains the origin and Ordovician–Silurian diversification of the Flexibilia (Echinoder-mata). Palaeontology, 60(6), 893910. doi: https://onlinelibrary.wiley.com/doi/abs/10.1111/pala.12324Google Scholar
Xie, W., Lewis, P. O., Fan, Y., Kuo, L., & Chen, M. (2011). Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Systematic Biology, 60(2), 150160.Google Scholar
Xu, B., & Yang, Z. (2016). Challenges in species tree estimation under the multispecies coalescent model. Genetics, 204(4), 13531368.CrossRefGoogle ScholarPubMed
Yang, Z. (1994). Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods. Journal of Molecular Evolution, 39(3), 306314.Google Scholar
Yang, Z. (2007). PAML 4: Phylogenetic analysis by maximum likelihood. Molecular Biology and Evolution, 24(8), 15861591. doi: https://doi.org/10.1093/molbev/msm088Google Scholar
Yang, Z., & Rannala, B. (1997). Bayesian phylogenetic inference using DNA sequences: A Markov Chain Monte Carlo Method. Molecular Biology and Evolution, 14(7), 717724.Google Scholar
Yang, Z., & Rannala, B. (2006). Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds. Molecular Biology and Evolution, 23(1), 212226. doi: https://doi.org/10.1093/molbev/msj024Google Scholar
Yang, Z., & Rannala, B. (2012). Molecular phylogenetics: Principles and practice. Nature Reviews Genetics, 13(5), 303314.Google Scholar
Yoder, A. D., & Yang, Z. (2000). Estimation of primate speciation dates using local molecular clocks. Molecular Biology and Evolution, 17(7), 10811090.Google Scholar
Yule, G. (1925). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, FRS. Philosophical Transactions of the Royal Society of London. Series B, 213, 2187.Google Scholar
Zhang, C., Stadler, T., Klopfstein, S., Heath, T. A., &Ronquist, F. (2016). Totalevidence dating under the fossilized birth-death process. Systematic Biology, 65(2), 228249. doi: https://doi.org/10.1093/sysbio/syv080Google Scholar
Zuckerkandl, E., & Pauling, L. (1962). Molecular disease, evolution, and genetic heterogeneity. In Kasha, M. & Pullman, B. (Eds.), Horizons in biochemistry (pp. 189225). New York: Academic Press.Google Scholar
Zuckerkandl, E., & Pauling, L. (1965). Evolutionary divergence and convergence in proteins. Evolving Genes and Proteins, 97, 97166.Google Scholar
Zwickl, D. J. (2006). Genetic algorithm approaches for the phylogenetic analysis of large biological sequence datasets under the maximum likelihood criterion. Unpublished doctoral dissertation, The University of Texas at Austin.Google Scholar

Save element to Kindle

To save this element to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Understanding the Tripartite Approach to Bayesian Divergence Time Estimation
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Understanding the Tripartite Approach to Bayesian Divergence Time Estimation
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Understanding the Tripartite Approach to Bayesian Divergence Time Estimation
Available formats
×