Reviews

Principles, error sources and application suggestions of prevailing molecular dating methods

  • Yangkang Chen ,
  • Yi Wang ,
  • Jialiang Li ,
  • Wentao Wang ,
  • Duanyu Feng ,
  • Kangshan Mao
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  • 1 Key Laboratory of Bio-resources and Eco-environment of Ministry of Education, College of Life Sciences, Sichuan University, Chengdu 610065
    2 College of Mathematics, Sichuan University, Chengdu 610065

Received date: 2020-07-08

  Accepted date: 2020-08-18

  Online published: 2020-10-10

Abstract

Background & Aims: Molecular dating methods have been applied widely in recent years and provide an indispensable and detailed evolutionary timescale for macroevolutionary researches, particularly for studies on the evolutionary history of biodiversity patterns. Bayesian methods and Markov chain Monte Carlo methods can accommodate multi-dimensional and various type of data and parameter settings, which have helped the node-dating methods implemented in softwares such as BEAST, PAML-MCMCTree to become the most widely used molecular dating methods. One of the advantages of Bayesian frameworks is that they can employ complex models to consider a variety of uncertainty factors to make more accurate estimations of evolutionary divergence times.
Progress: We review the principles and main types of Bayesian molecular dating methods and use Bayesian node-dating methods as an example to discuss potential errors in molecular clock models, selection and placement of fossil calibrating points, frequency of sampling, and setting a prior distribution for node calibrations based on fossils. We further describe advantages associated with different Bayesian time tree reconstruction software packages, the discussing principle of node age, and the comparison method of time tree under different models. We also provide suggestions for overcoming the challenges of overestimation and underestimation bias of node ages. Integration of the output of various Bayesian methods and models and selection of the best among them often improve the reliability of molecular dating results.
Prospect: Researchers should explicitly assess the relationship between model output of time tree construction and model parameter settings, which increases transparency and provides documentation and reference for future researches. We recommend that future research simultaneously focus on updating fossil records and improving molecular dating methods.

Cite this article

Yangkang Chen , Yi Wang , Jialiang Li , Wentao Wang , Duanyu Feng , Kangshan Mao . Principles, error sources and application suggestions of prevailing molecular dating methods[J]. Biodiversity Science, 2021 , 29(5) : 629 -646 . DOI: 10.17520/biods.2020273

References

[1] Baele G, Lemey P, Bedford T, Rambaut A, Suchard MA, Alekseyenko AV (2012a) Improving the accuracy of demographic and molecular clock model comparison while accommodating phylogenetic uncertainty. Molecular Biology and Evolution, 29, 2157-2167.
[2] Baele G, Li WLS, Drummond AJ, Suchard MA, Lemey P (2012b) Accurate model selection of relaxed molecular clocks in Bayesian phylogenetics. Molecular Biology and Evolution, 30, 239-243.
[3] Barba-Montoya J, dos Reis M, Yang ZH (2017) Comparison of different strategies for using fossil calibrations to generate the time prior in Bayesian molecular clock dating. Molecular Phylogenetics and Evolution, 114, 386-400.
[4] Beerli P (2006) Comparison of Bayesian and maximum- likelihood inference of population genetic parameters. Bioinformatics, 22, 341-345.
[5] Benton MJ, Donoghue PCJ (2007) Paleontological evidence to date the tree of life. Molecular Biology and Evolution, 24, 26-53.
[6] Bouckaert R, Heled J, Kühnert D, Vaughan T, Wu CH, Xie D, Suchard MA, Rambaut A, Drummond AJ (2014) BEAST 2: A software platform for Bayesian evolutionary analysis. PLoS Computational Biology, 10, e1003537.
[7] Bouckaert RR, Drummond AJ (2017) bModelTest: Bayesian phylogenetic site model averaging and model comparison. BMC Evolutionary Biology, 17, 42.
[8] Brinkmann H, van der Giezen M, Zhou Y, De Raucourt GP, Philippe H (2005) An empirical assessment of long-branch attraction artefacts in deep eukaryotic phylogenomics. Systematic Biology, 54, 743-757.
[9] Bromham L, Duchêne S, Hua X, Ritchie AM, Duchêne DA, Ho SYW (2018) Bayesian molecular dating: Opening up the black box. Biological Reviews, 93, 1165-1191.
[10] Brooks DR, Bilewitch J, Condy C, Evans DC, Folinsbee KE, Fr?bisch J, Halas D, Hill S, McLennan D, Mattern M, Tsuji LA, Ward J, Wahlberg N, Zamparo D, Zanatta D (2007) Quantitative phylogenetic analysis in the 21st century. Revista Mexicana de Biodiversidad, 78, 225-252.
[11] Brower AVZ (2018) Statistical consistency and phylogenetic inference: A brief review. Cladistics, 34, 562-567.
[12] Brown RP, Yang ZH (2011) Rate variation and estimation of divergence times using strict and relaxed clocks. BMC Evolutionary Biology, 11, 271.
[13] Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, 69-92.
[14] Claramunt S, Cracraft J (2015) A new time tree reveals Earth history’s imprint on the evolution of modern birds. Science Advances, 1, e1501005.
[15] Condamine FL, Nagalingum NS, Marshall CR, Morlon H (2015) Origin and diversification of living cycads: A cautionary tale on the impact of the branching process prior in Bayesian molecular dating. BMC Evolutionary Biology, 15, 1-18.
[16] Conroy CJ, van Tuinen M (2003) Extracting time from phylogenies: Positive interplay between fossil and genetic data. Journal of Mammalogy, 84, 444-455.
[17] Cooper N, Thomas GH, Venditti C, Meade A, Freckleton RP (2016) A cautionary note on the use of Ornstein Uhlenbeck models in macroevolutionary studies. Biological Journal of the Linnean Society, 118, 64-77.
[18] Crisp MD, Trewick SA, Cook LG (2011) Hypothesis testing in biogeography. Trends in Ecology & Evolution, 26, 66-72.
[19] Darriba D, Taboada GL, Doallo R, Posada D (2012) jModelTest 2: More models, new heuristics and parallel computing. Nature Methods, 9, 772.
[20] Donoghue MJ, Doyle JA, Gauthier J, Kluge AG, Rowe T (1989) The importance of fossils in phylogeny reconstruction. Annual Review of Ecology and Systematics, 20, 431-460.
[21] Donoghue MJ, Moore BR (2003) Toward an integrative historical biogeography. Integrative and Comparative Biology, 43, 261-270.
[22] dos Reis M, Donoghue PCJ, Yang ZH (2016) Bayesian molecular clock dating of species divergences in the genomics era. Nature Reviews Genetics, 17, 71-80.
[23] dos Reis M, Inoue J, Hasegawa M, Asher RJ, Donoghue PCJ, Yang ZH (2012) Phylogenomic datasets provide both precision and accuracy in estimating the timescale of placental mammal phylogeny. Proceedings of the Royal Society B: Biological Sciences, 279, 3491-3500.
[24] dos Reis M, Thawornwattana Y, Angelis K, Telford MJ, Donoghue PCJ, Yang ZH (2015) Uncertainty in the timing of origin of animals and the limits of precision in molecular timescales. Current Biology, 25, 2939-2950.
[25] Drummond AJ, Ho SYW, Phillips MJ, Rambaut A (2006) Relaxed phylogenetics and dating with confidence. PLoS Biology, 4, e88.
[26] Drummond AJ, Suchard MA, Xie D, Rambaut A (2012) Bayesian phylogenetics with BEAUti and the BEAST 1.7. Molecular Biology and Evolution, 29, 1969-1973.
[27] Duchêne DA, Duchêne S, Ho SYW (2017) New statistical criteria detect phylogenetic bias caused by compositional heterogeneity. Molecular Biology and Evolution, 34, 1529-1534.
[28] Duchêne S, Lanfear R, Ho SYW (2014) The impact of calibration and clock-model choice on molecular estimates of divergence times. Molecular Phylogenetics and Evolution, 78, 277-289.
[29] Fan Y, Wu R, Chen MH, Kuo L, Lewis PO (2011) Choosing among partition models in Bayesian phylogenetics. Molecular Biology and Evolution, 28, 523-532.
[30] Felsenstein J (1981) Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of Molecular Evolution, 17, 368-376.
[31] Fiká?ek M, Beutel RG, Cai C, Lawrence JF, Newton AF, Solodovnikov A, ?lipiński A, Thayer MK, Yamamoto S (2020) Reliable placement of beetle fossils via phylogenetic analyses—Triassic Leehermania as a case study (Staphylinidae or Myxophaga?). Systematic Entomology, 45, 175-187.
[32] Friston KJ, Lawson R, Frith CD (2013) On hyperpriors and hypopriors: Comment on Pellicano and Burr. Trends in Cognitive Sciences, 17, 1.
[33] Good PI, Hardin JW (2012) Common Errors in Statistics (and How to Avoid Them). John Wiley & Sons, Hoboken.
[34] Graham TA, Sottoriva A (2017) Measuring cancer evolution from the genome. The Journal of Pathology, 241, 183-191.
[35] Greenwood DR (1991) The taphonomy of plant macrofossils. In: The Processes of Fossilization (ed. Donovan SK), pp. 141-169. Columbia University Press, New York.
[36] Grimm GW, Kapli P, Bomfleur B, McLoughlin S, Renner SS (2015) Using more than the oldest fossils: Dating Osmundaceae with three Bayesian clock approaches. Systematic Biology, 64, 396-405.
[37] Guillerme T, Cooper N (2016) Assessment of available anatomical characters for linking living mammals to fossil taxa in phylogenetic analyses. Biology Letters, 12, 20151003.
[38] Hall BG (2005) Comparison of the accuracies of several phylogenetic methods using protein and DNA sequences. Molecular Biology and Evolution, 22, 792-802.
[39] Halliday TJ, Goswami A (2016) The impact of phylogenetic dating method on interpreting trait evolution: A case study of Cretaceous-Palaeogene eutherian body-size evolution. Biology Letters, 12, 20160051.
[40] Harwood DM, Nikolaev VA, Winter DM (2007) Cretaceous records of diatom evolution, radiation, and expansion. The Paleontological Society Papers, 13, 33-59.
[41] 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, 160-174.
[42] Heads M (2005) Dating nodes on molecular phylogenies: A critique of molecular biogeography. Cladistics, 21, 62-78.
[43] Heath TA, Huelsenbeck JP, Stadler T (2014) The fossilized birth-death process for coherent calibration of divergence- time estimates. Proceedings of the National Academy of Sciences, USA, 111, E2957-E2966.
[44] Ho SYW, Duchêne S (2014) Molecular-clock methods for estimating evolutionary rates and timescales. Molecular Ecology, 23, 5947-5965.
[45] Ho SYW, Phillips MJ (2009) Accounting for calibration uncertainty in phylogenetic estimation of evolutionary divergence times. Systematic Biology, 58, 367-380.
[46] H?hna S, Landis MJ, Heath TA, Boussau B, Lartillot N, Moore BR, Huelsenbeck JP, Ronquist F (2016) RevBayes: Bayesian phylogenetic inference using graphical models and an interactive model-specification language. Systematic Biology, 65, 726-736.
[47] Jeffreys H (1935) Some tests of significance, treated by the theory of probability. Mathematical Proceedings of the Cambridge Philosophical Society, 31, 203-222.
[48] Jukes TH, Cantor CR (1969) Evolution of protein molecules. In: Mammalian Protein Metabolism (ed. Munro HN), pp. 21-132. Academic Press, New York.
[49] Keane TM, Creevey CJ, Pentony MM, Naughton TJ, Mclnerney JO (2006) Assessment of methods for amino acid matrix selection and their use on empirical data shows that ad hoc assumptions for choice of matrix are not justified. BMC Evolutionary Biology, 6, 29.
[50] Kimura M (1980) A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences. Journal of Molecular Evolution, 16, 111-120.
[51] Korber B, Muldoon M, Theiler J, Gao F, Gupta R, Lapedes A, Hahn BH, Wolinsky S, Bhattacharya T (2000) Timing the ancestor of the HIV-1 pandemic strains. Science, 288, 1789-1796.
[52] Kumar S (2005) Molecular clocks: Four decades of evolution. Nature Reviews Genetics, 6, 654-662.
[53] Kumar S, Hedges SB (2016) Advances in time estimation methods for molecular data. Molecular Biology and Evolution, 33, 863-869.
[54] Kuo CH, Ochman H (2009) Inferring clocks when lacking rocks: The variable rates of molecular evolution in bacteria. Biology Direct, 4, 35.
[55] Lanfear R, Calcott B, Ho SYW, Guindon S (2012) PartitionFinder: Combined selection of partitioning schemes and substitution models for phylogenetic analyses. Molecular Biology and Evolution, 29, 1695-1701.
[56] Lartillot N, Philippe H (2006) Computing Bayes factors using thermodynamic integration. Systematic Biology, 55, 195-207.
[57] Laws B (2010) Fifty Plants that Changed the Course of History. Firefly Books, Richmond Hill.
[58] Lee MSY (2016) Multiple morphological clocks and total-evidence tip-dating in mammals. Biology Letters, 12, 20160033.
[59] Lepage T, Lawi S, Tupper P, Bryant D (2006) Continuous and tractable models for the variation of evolutionary rates. Mathematical Biosciences, 199, 216-233.
[60] Li KQ (2015) Quantitative analysis of relationship between absolute evolutionary rates and taxa divergence times. Journal of Biology, 32(2), 70-75, 79. (in Chinese with English abstract)
[60] [ 李可群 (2015) 分子绝对进化速率与物种分歧时间之间的定量关系. 生物学杂志, 32(2), 70-75, 79.]
[61] Linder HP, Hardy CR, Rutschmann F (2005) Taxon sampling effects in molecular clock dating: An example from the African Restionaceae. Molecular Phylogenetics and Evolution, 35, 569-582.
[62] Liu XF, Zhang AB (2016) The basic principle and application of the molecular clock hypothesis. Acta Palaeontologica Sinica, 55, 393-402. (in Chinese with English abstract)
[62] [ 刘晓枫, 张爱兵 (2016) 分子钟假说的基本原理及在古生物等学科中的应用. 古生物学报, 55, 393-402.]
[63] Lu LM, Sun M, Zhang JB, Li HL, Lin L, Yang T, Chen M, Chen ZD (2014) Tree of life and its applications. Biodiversity Science, 22, 3-20. (in Chinese with English abstract)
[63] [ 鲁丽敏, 孙苗, 张景博, 李洪雷, 林立, 杨拓, 陈闽, 陈之端 (2014) 生命之树及其应用. 生物多样性, 22, 3-20.]
[64] Magallón S, Castillo A (2009) Angiosperm diversification through time. American Journal of Botany, 96, 349-365.
[65] Makowski D, Ben-Shachar M, Lüdecke D (2019) bayestestR: Describing effects and their uncertainty, existence and significance within the Bayesian framework. Journal of Open Source Software, 4, 1541.
[66] Mao KS, Milne RI, Zhang LB, Peng YL, Liu JQ, Thomas P, Mill RR, Renner SS (2012) Distribution of living Cupressaceae reflects the breakup of Pangea. Proceedings of the National Academy of Sciences, USA, 109, 7793-7798.
[67] Marshall CR (2008) A simple method for bracketing absolute divergence times on molecular phylogenies using multiple fossil calibration points. The American Naturalist, 171, 726-742.
[68] Martin PG, Dowd JM (1993) Using sequences of rbcL to study phylogeny and biogeography of Nothofagus species. Australian Systematic Botany, 6, 441-447.
[69] Miller KB, Bergsten J (2012) Phylogeny and classification of whirligig beetles (Coleoptera: Gyrinidae): Relaxed-clock model outperforms parsimony and time-free Bayesian analyses. Systematic Entomology, 37, 706-746.
[70] Morgan GJ (1998) Emile Zuckerkandl, Linus Pauling, and the molecular evolutionary clock, 1959-1965. Journal of the History of Biology, 31, 155-178.
[71] Newton MA, Raftery AE (1994) Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 56, 3-26.
[72] Nie Y, Foster CSP, Zhu TQ, Yao R, Duchêne DA, Ho SYW, Zhong BJ (2020) Accounting for uncertainty in the evolutionary timescale of green plants through clock-partitioning and fossil calibration strategies. Systematic Biology, 69, 1-16.
[73] O’Reilly JE, Dos Reis M, Donoghue PCJ (2015) Dating tips for divergence-time estimation. Trends in Genetics, 31, 637-650.
[74] O’Reilly JE, Donoghue PCJ (2016) Tips and nodes are complementary not competing approaches to the calibration of molecular clocks. Biology Letters, 12, 20150975.
[75] Parham JF, Donoghue PCJ, Bell CJ, Calway TD, Head JJ, Holroyd PA, Inoue JG, Irmis RB, Joyce WG, Ksepka DT, Patane JSL, Smith ND, Tarver JE, van Tuinen M, Yang ZH, Angielczyk KD, Greenwood JM, Hipsley CA, Jacobs L, Makovicky PJ, Müller J, Smith KT, Theodor JM, Warnock RCM, Benton MJ (2012) Best practices for justifying fossil calibrations. Systematic Biology, 61, 346-359.
[76] Pauling L, Zuckerkandl E (1962) Molecular paleontology. Acta Chemica Scandinavica, 17, S9-S16.
[77] Raftery AE, Newton MA, Satagopan JM, Krivitsky PN (2006) Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Bayesian Statistics, 8, 1-45.
[78] Rector A, Lemey P, Tachezy R, Mostmans S, Ghim SJ, Van Doorslaer K, Roelke M, Bush M, Montali RJ, Joslin J, Burk RD, Jenson AB, Sundberg JP, Shapiro B, van Ranst M (2007) Ancient papillomavirus-host co-speciation in Felidae. Genome Biology, 8, 1-12.
[79] Renner SS (2005) Relaxed molecular clocks for dating historical plant dispersal events. Trends in Plant Science, 10, 550-558.
[80] Reyes A, Pesole G, Saccone C (2000) Long-branch attraction phenomenon and the impact of among-site rate variation on rodent phylogeny. Gene, 259, 177-187.
[81] Ronquist F, Klopfstein S, Vilhelmsen L, Schulmeister S, Murray DL, Rasnitsyn AP (2012) A total-evidence approach to dating with fossils, applied to the early radiation of the Hymenoptera. Systematic Biology, 61, 973-999.
[82] Sanders KL, Lee MSY (2007) Evaluating molecular clock calibrations using Bayesian analyses with soft and hard bounds. Biology Letters, 3, 275-279.
[83] Sauquet H (2013) A practical guide to molecular dating. Comptes Rendus Palevol, 12, 355-367.
[84] Sauquet H, Ho SYW, Gandolfo MA, Jordan GJ, Wilf P, Cantrill DJ, Bayly MJ, Bromham L, Brown GK, Carpenter RJ, Lee DM, Murphy DJ, Sniderman JMK, Udovicic F (2012) Testing the impact of calibration on molecular divergence times using a fossil-rich group: The case of Nothofagus (Fagales). Systematic Biology, 61, 289-313.
[85] Schaefer H, Heibl C, Renner SS (2009) Gourds afloat: A dated phylogeny reveals an Asian origin of the gourd family (Cucurbitaceae) and numerous oversea dispersal events. Proceedings of the Royal Society B: Biological Sciences, 276, 843-851.
[86] Shapiro B, Rambaut A, Drummond AJ (2006) Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences. Molecular Biology and Evolution, 23, 7-9.
[87] Sinsheimer JS, Lake JA, Little RJA (1996) Bayesian hypothesis testing of four-taxon topologies using molecular sequence data. Biometrics, 52, 193-210.
[88] Slack KE, Jones CM, Ando T, Harrison GL, Fordyce RE, Arnason U, Penny D (2006) Early penguin fossils, plus mitochondrial genomes, calibrate avian evolution. Molecular Biology and Evolution, 23, 1144-1155.
[89] Smith SA, Beaulieu JM, Donoghue MJ (2010) An uncorrelated relaxed-clock analysis suggests an earlier origin for flowering plants. Proceedings of the National Academy of Sciences, USA, 107, 5897-5902.
[90] Steel M (2005) Should phylogenetic models be trying to ‘fit an elephant’? Trends in Genetics, 21, 307-309.
[91] Strugnell J, Norman M, Jackson J, Drummond AJ, Cooper A (2005) Molecular phylogeny of coleoid cephalopods (Mollusca: Cephalopoda) using a multigene approach: The effect of data partitioning on resolving phylogenies in a Bayesian framework. Molecular Phylogenetics and Evolution, 37, 426-441.
[92] Suchard MA, Lemey P, Baele G, Ayres DL, Drummond AJ, Rambaut A (2018) Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10. Virus Evolution, 4, vey016.
[93] Suchard MA, Weiss RE, Sinsheimer JS (2001) Bayesian selection of continuous-time Markov chain evolutionary models. Molecular Biology and Evolution, 18, 1001-1013.
[94] Susko E (2015) Bayesian long branch attraction bias and corrections. Systematic Biology, 64, 243-255.
[95] Tavaré S (1986) Some probabilistic and statistical problems in the analysis of DNA sequences. Lectures on Mathematics in the Life Sciences, 17, 57-86.
[96] Thomas JA, Welch JJ, Lanfear R, Bromham L (2010) A generation time effect on the rate of molecular evolution in invertebrates. Molecular Biology and Evolution, 27, 1173-1180.
[97] Thorne JL, Kishino H, Painter IS (1998) Estimating the rate of evolution of the rate of molecular evolution. Molecular Biology and Evolution, 15, 1647-1657.
[98] Van den Bergh D, Haaf JM, Ly A, Rouder JN, Wagenmakers EJ (2021) A cautionary note on estimating effect size. Advances in Methods and Practices in Psychological Science, 4, 1-8.
[99] Vijgen L, Keyaerts E, Mo?s E, Thoelen I, Wollants E, Lemey P, Vandamme AM, Van Ranst M (2005) Complete genomic sequence of human coronavirus OC43: Molecular clock analysis suggests a relatively recent zoonotic coronavirus transmission event. Journal of Virology, 79, 1595-1604.
[100] Wagenmakers EJ, Gronau QF, Dablander F, Etz A (2020) The support interval. Erkenntnis, 10.1007/s10670-019-00209-z.
[101] Wang Q, Mao KS (2016) Puzzling rocks and complicated clocks: How to optimize molecular dating approaches in historical phytogeography. New Phytologist, 209, 1353-1358.
[102] Warnock RCM, Yang ZH, Donoghue PCJ (2017) Testing the molecular clock using mechanistic models of fossil preservation and molecular evolution. Proceedings of the Royal Society B: Biological Sciences, 284, 20170227.
[103] Wasserman L (2004) Bayesian Inference. In: All of Statistics, A Concise Course in Statistical Inference (ed. Wasserman L), pp. 175-190. Springer, New York.
[104] Wertheim JO, Sanderson MJ, Worobey M, Bjork A (2010) Relaxed molecular clocks, the bias-variance trade-off, and the quality of phylogenetic inference. Systematic Biology, 59, 1-8.
[105] Wilf P, Escapa IH (2015) Green Web or megabiased clock? Plant fossils from Gondwanan Patagonia speak on evolutionary radiations. New Phytologist, 207, 283-290.
[106] Wu CH, Suchard MA, Drummond AJ (2013) Bayesian selection of nucleotide substitution models and their site assignments. Molecular Biology and Evolution, 30, 669-688.
[107] Xie WG, Lewis PO, Fan Y, Kuo L, Chen MH (2011) Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Systematic Biology, 60, 150-160.
[108] Yang ZH (2006) Computational Molecular Evolution. Oxford University Press, Oxford.
[109] Yang ZH, Rannala B (1997) Bayesian phylogenetic inference using DNA sequences: A Markov Chain Monte Carlo Method. Molecular Biology and Evolution, 14, 717-724.
[110] Yang ZH (2007) PAML 4: Phylogenetic analysis by maximum likelihood. Molecular Biology and Evolution, 24, 1586-1591.
[111] Yang ZH, 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, 212-226.
[112] Yang ZH, Rannala B (2012) Molecular phylogenetics: Principles and practice. Nature Reviews Genetics, 13, 303-314.
[113] Zhang C (2019) Molecular clock dating using MrBayes. Vertebrata PalaAsiatica, 57, 241-252.
[114] Zhang Y, Chen ZD (2003) Recent progress of sequences analysis methods in molecular evolutionary biology. Chinese Bulletin of Botany, 20, 462-467. (in Chinese with English abstract)
[114] [ 张原, 陈之端 (2003) 分子进化生物学中序列分析方法的新进展. 植物学通报, 20, 462-467.]
[115] Zhu TQ (2019) Bayesian molecular dating with genomic data. Scientia Sinica Vitae, 49, 472-483. (in Chinese with English abstract)
[115] [ 朱天琪 (2019) 使用基因组数据进行贝叶斯物种分化时间估计. 中国科学: 生命科学, 49, 472-483.]
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