The molecular clock of Mycobacterium tuberculosis

Autoři: Fabrizio Menardo aff001;  Sebastian Duchêne aff003;  Daniela Brites aff001;  Sebastien Gagneux aff001
Působiště autorů: Department of Medical Parasitology and Infection Biology, Swiss Tropical and Public Health Institute, Basel, Switzerland aff001;  University of Basel, Basel, Switzerland aff002;  Department of Microbiology and Immunology, Peter Doherty Institute for Infection and Immunity, University of Melbourne, Melbourne, Australia aff003
Vyšlo v časopise: The molecular clock of Mycobacterium tuberculosis. PLoS Pathog 15(9): e1008067. doi:10.1371/journal.ppat.1008067
Kategorie: Research Article


The molecular clock and its phylogenetic applications to genomic data have changed how we study and understand one of the major human pathogens, Mycobacterium tuberculosis (MTB), the etiologic agent of tuberculosis. Genome sequences of MTB strains sampled at different times are increasingly used to infer when a particular outbreak begun, when a drug-resistant clone appeared and expanded, or when a strain was introduced into a specific region. Despite the growing importance of the molecular clock in tuberculosis research, there is a lack of consensus as to whether MTB displays a clocklike behavior and about its rate of evolution. Here we performed a systematic study of the molecular clock of MTB on a large genomic data set (6,285 strains), covering different epidemiological settings and most of the known global diversity. We found that sampling times below 15–20 years were often insufficient to calibrate the clock of MTB. For data sets where such calibration was possible, we obtained a clock rate between 1x10-8 and 5x10-7 nucleotide changes per-site-per-year (0.04–2.2 SNPs per-genome-per-year), with substantial differences between clades. These estimates were not strongly dependent on the time of the calibration points as they changed only marginally when we used epidemiological isolates (sampled in the last 40 years) or three ancient DNA samples (about 1,000 years old) to calibrate the tree. Additionally, the uncertainty and the discrepancies in the results of different methods were sometimes large, highlighting the importance of using different methods, and of considering carefully their assumptions and limitations.

Klíčová slova:

Biology and life sciences – Organisms – Bacteria – Actinobacteria – Mycobacterium tuberculosis – Evolutionary biology – Evolutionary systematics – Phylogenetics – Phylogenetic analysis – Evolutionary processes – Evolutionary rate – Molecular evolution – Taxonomy – Population biology – Population metrics – Population size – Population growth – Computer and information sciences – Data management – Medicine and health sciences – Infectious diseases – Bacterial diseases – Tuberculosis – Extensively drug-resistant tuberculosis – Tropical diseases


1. Zuckerkandl E., & Pauling L. (1962). Molecular disease, evolution and genetic heterogeneity.

2. Morgan G. J. (1998). Emile Zuckerkandl, Linus Pauling, and the molecular evolutionary clock, 1959–1965. Journal of the History of Biology, 31(2), 155–178. 11620303

3. Kimura M. (1968). Evolutionary rate at the molecular level. Nature, 217(5129), 624–626. doi: 10.1038/217624a0 5637732

4. Drummond A. J., Pybus O. G., Rambaut A., Forsberg R., & Rodrigo A. G. (2003). Measurably evolving populations. Trends in ecology & evolution, 18(9), 481–488.

5. Kapur V., Whittam T. S., & Musser J. M. (1994). Is Mycobacterium tuberculosis 15,000 years old?. Journal of Infectious Diseases, 170(5), 1348–1349. doi: 10.1093/infdis/170.5.1348 7963745

6. Cole S., Brosch R., Parkhill J., Garnier T., Churcher C., Harris D., … & Tekaia F. (1998). Deciphering the biology of Mycobacterium tuberculosis from the complete genome sequence. Nature, 393(6685), 537. doi: 10.1038/31159 9634230

7. Comas I., Coscolla M., Luo T., Borrell S., Holt K. E., Kato-Maeda M., … & Gagneu S. (2013). Out-of-Africa migration and Neolithic coexpansion of Mycobacterium tuberculosis with modern humans. Nature genetics, 45(10), 1176. doi: 10.1038/ng.2744 23995134

8. Bos K. I., Harkins K. M., Herbig A., Coscolla M., Weber N., Comas I., … & Campbell T. J. (2014). Pre-Columbian mycobacterial genomes reveal seals as a source of New World human tuberculosis. Nature, 514(7523), 494. doi: 10.1038/nature13591 25141181

9. Merker M., Blin C., Mona S., Duforet-Frebourg N., Lecher S., Willery E., … & Allix-Béguec C. (2015). Evolutionary history and global spread of the Mycobacterium tuberculosis Beijing lineage. Nature genetics, 47(3), 242. doi: 10.1038/ng.3195 25599400

10. Kay G. L., Sergeant M. J., Zhou Z., Chan J. Z. M., Millard A., Quick J., … & Achtman M. (2015). Eighteenth-century genomes show that mixed infections were common at time of peak tuberculosis in Europe. Nature communications, 6, 6717. doi: 10.1038/ncomms7717 25848958

11. Brynildsrud O. B., Pepperell C. S., Suffys P., Grandjean L., Monteserin J., Debech N., … & Fandinho F. (2018). Global expansion of Mycobacterium tuberculosis lineage 4 shaped by colonial migration and local adaptation. Science Advances, 4(10), eaat5869.

12. Liu Q., Ma A., Wei L., Pang Y., Wu B., Luo T., … & Gao Q. (2018). China’s tuberculosis epidemic stems from historical expansion of four strains of Mycobacterium tuberculosis. Nature ecology & evolution, 1.

13. Rutaihwa L. K., Menardo F., Stucki D., Gygli S. M., Ley S. D., Malla B., … & Gagneux S. (2019). Multiple Introductions of the Mycobacterium tuberculosis Lineage 2 Beijing into Africa over centuries. Frontiers in Ecology and Evolution, 7, 112.

14. Eldholm V., Monteserin J., Rieux A., Lopez B., Sobkowiak B., Ritacco V., & Balloux F. (2015). Four decades of transmission of a multidrug-resistant Mycobacterium tuberculosis outbreak strain. Nature communications, 6, 7119. doi: 10.1038/ncomms8119 25960343

15. Lee R. S., Radomski N., Proulx J. F., Levade I., Shapiro B. J., McIntosh F., … & Behr M. A. (2015). Population genomics of Mycobacterium tuberculosis in the Inuit. Proceedings of the National Academy of Sciences, 112(44), 13609–13614.

16. Folkvardsen D. B., Norman A., Andersen Å. B., Michael Rasmussen E., Jelsbak L., & Lillebaek T. (2017). Genomic Epidemiology of a Major Mycobacterium tuberculosis Outbreak: Retrospective Cohort Study in a Low-Incidence Setting Using Sparse Time-Series Sampling. The Journal of infectious diseases, 216(3), 366–374. doi: 10.1093/infdis/jix298 28666374

17. Bainomugisa A., Lavu E., Hiashiri S., Majumdar S., Honjepari A., Moke R., … & Coulter C. (2018). Multi-clonal evolution of multi-drug-resistant/extensively drug-resistant Mycobacterium tuberculosis in a high-prevalence setting of Papua New Guinea for over three decades. Microbial genomics, 4(2).

18. Kühnert D., Coscolla M., Brites D., Stucki D., Metcalfe J., Fenner L., … & Stadler T. (2018). Tuberculosis outbreak investigation using phylodynamic analysis. Epidemics, 25, 47–53. doi: 10.1016/j.epidem.2018.05.004 29880306

19. Cohen K. A., Abeel T., McGuire A. M., Desjardins C. A., Munsamy V., Shea T. P., … & Chapman S. B. (2015). Evolution of extensively drug-resistant tuberculosis over four decades: whole genome sequencing and dating analysis of Mycobacterium tuberculosis isolates from KwaZulu-Natal. PLoS medicine, 12(9), e1001880. doi: 10.1371/journal.pmed.1001880 26418737

20. Eldholm V., Pettersson J. H. O., Brynildsrud O. B., Kitchen A., Rasmussen E. M., Lillebaek T., … & Alfsnes K. (2016). Armed conflict and population displacement as drivers of the evolution and dispersal of Mycobacterium tuberculosis. Proceedings of the National Academy of Sciences, 113(48), 13881–13886.

21. Pepperell C. S., Casto A. M., Kitchen A., Granka J. M., Cornejo O. E., Holmes E. C., … & Feldman M. W. (2013). The role of selection in shaping diversity of natural M. tuberculosis populations. PLoS pathogens, 9(8), e1003543. doi: 10.1371/journal.ppat.1003543 23966858

22. Merker M., Barbier M., Cox H., Rasigade J. P., Feuerriegel S., Kohl T. A., … & Andres S. (2018). Compensatory evolution drives multidrug-resistant tuberculosis in Central Asia. eLife, 7:e38200. doi: 10.7554/eLife.38200 30373719

23. Seo T. K., Thorne J. L., Hasegawa M., & Kishino H. (2002). A viral sampling design for testing the molecular clock and for estimating evolutionary rates and divergence times. Bioinformatics, 18(1), 115–123. doi: 10.1093/bioinformatics/18.1.115 11836219

24. Wirth T., Hildebrand F., Allix-Béguec C., Wölbeling F., Kubica T., Kremer K., … & Meyer A. (2008). Origin, spread and demography of the Mycobacterium tuberculosis complex. PLoS pathogens, 4(9), e1000160. doi: 10.1371/journal.ppat.1000160 18802459

25. Ho S. Y., Phillips M. J., Cooper A., & Drummond A. J. (2005). Time dependency of molecular rate estimates and systematic overestimation of recent divergence times. Molecular biology and evolution, 22(7), 1561–1568. doi: 10.1093/molbev/msi145 15814826

26. Ho S. Y., Lanfear R., Bromham L., Phillips M. J., Soubrier J., Rodrigo A. G., & Cooper A. (2011). Time-dependent rates of molecular evolution. Molecular ecology, 20(15), 3087–3101. doi: 10.1111/j.1365-294X.2011.05178.x 21740474

27. Rieux A., & Balloux F. (2016). Inferences from tip-calibrated phylogenies: a review and a practical guide. Molecular ecology, 25(9), 1911–1924. doi: 10.1111/mec.13586 26880113

28. Rambaut A., Lam T. T., Max Carvalho L., & Pybus O. G. (2016). Exploring the temporal structure of heterochronous sequences using TempEst (formerly Path-O-Gen). Virus evolution, 2(1), vew007.

29. Rambaut A., Lam T. T., Max Carvalho L., & Pybus O. G. (2016). Exploring the temporal structure of heterochronous sequences using TempEst (formerly Path-O-Gen). Virus evolution, 2(1), vew007.

30. Tong K. J., Duchêne D. A., Duchêne S., Geoghegan J. L., & Ho S. Y. (2018). A comparison of methods for estimating substitution rates from ancient DNA sequence data. BMC evolutionary biology, 18(1), 70. doi: 10.1186/s12862-018-1192-3 29769015

31. To T. H., Jung M., Lycett S., & Gascuel O. (2015). Fast dating using least-squares criteria and algorithms. Systematic biology, 65(1), 82–97. doi: 10.1093/sysbio/syv068 26424727

32. Duchêne S., Duchene D. A., Geoghegan J. L., Dyson Z. A., Hawkey J., & Holt K. E. (2018). Inferring demographic parameters in bacterial genomic data using Bayesian and hybrid phylogenetic methods. BMC evolutionary biology, 18(1), 95. doi: 10.1186/s12862-018-1210-5 29914372

33. Duchêne S., Geoghegan J. L., Holmes E. C., & Ho S. Y. (2016a). Estimating evolutionary rates using time-structured data: a general comparison of phylogenetic methods. Bioinformatics, 32(22), 3375–3379.

34. Bouckaert R., Heled J., Kühnert D., Vaughan T., Wu C. H., Xie D., … & Drummond A. J. (2014). BEAST 2: a software platform for Bayesian evolutionary analysis. PLoS computational biology, 10(4), e1003537. doi: 10.1371/journal.pcbi.1003537 24722319

35. Darriba D., Taboada G. L., Doallo R., & Posada D. (2012). jModelTest 2: more models, new heuristics and parallel computing. Nature methods, 9(8), 772.

36. Duchêne S., Holt K. E., Weill F. X., Le Hello S., Hawkey J., Edwards D. J., … & Holmes E. C. (2016b). Genome-scale rates of evolutionary change in bacteria. Microbial Genomics, 2(11).

37. Drummond A. J., Ho S. Y., Phillips M. J., & Rambaut A. (2006). Relaxed phylogenetics and dating with confidence. PLoS biology, 4(5), e88. doi: 10.1371/journal.pbio.0040088 16683862

38. Trewby H., Wright D., Breadon E. L., Lycett S. J., Mallon T. R., McCormick C., … & Herzyk P. (2016). Use of bacterial whole-genome sequencing to investigate local persistence and spread in bovine tuberculosis. Epidemics, 14, 26–35. doi: 10.1016/j.epidem.2015.08.003 26972511

39. Möller S., du Plessis L., & Stadler T. (2018). Impact of the tree prior on estimating clock rates during epidemic outbreaks. Proceedings of the National Academy of Sciences, 115(16), 4200–4205.

40. Bromham L., Duchêne S., Hua X., Ritchie A. M., Duchêne D. A., & Ho S. Y. (2018). Bayesian molecular dating: opening up the black box. Biological Reviews, 93(2), 1165–1191. doi: 10.1111/brv.12390 29243391

41. Duchêne S., Duchêne D., Holmes E. C., & Ho S. Y. (2015). The performance of the date-randomization test in phylogenetic analyses of time-structured virus data. Molecular Biology and Evolution, 32(7), 1895–1906. doi: 10.1093/molbev/msv056 25771196

42. Hatherell H. A., Colijn C., Stagg H. R., Jackson C., Winter J. R., & Abubakar I. (2016). Interpreting whole genome sequencing for investigating tuberculosis transmission: a systematic review. BMC medicine, 14(1), 21.

43. Holt K. E., McAdam P., Thai P. V. K., Thuong N. T. T., Ha D. T. M., Lan N. N., … & Thwaites G. (2018). Frequent transmission of the Mycobacterium tuberculosis Beijing lineage and positive selection for the EsxW Beijing variant in Vietnam. Nature genetics, 1.

44. Glynn J. R., Kremer K., Borgdorff M. W., Rodriguez M. P., & Soolingen D. V. (2006). Beijing/W genotype Mycobacterium tuberculosis and drug resistance.

45. Hanekom M., Mata D., van Pittius N. G., van Helden P. D., Warren R. M., & Hernandez-Pando R. (2010). Mycobacterium tuberculosis strains with the Beijing genotype demonstrate variability in virulence associated with transmission. Tuberculosis, 90(5), 319–325. doi: 10.1016/ 20832364

46. de Steenwinkel J. E., Marian T., de Knegt G. J., Kremer K., Aarnoutse R. E., Boeree M. J., … & Bakker-Woudenberg I. A. (2012). Drug susceptibility of Mycobacterium tuberculosis Beijing genotype and association with MDR TB. Emerging infectious diseases, 18(4), 660. doi: 10.3201/eid1804.110912 22469099

47. Ribeiro S. C., Gomes L. L., Amaral E. P., Andrade M. R., Almeida F. M., Rezende A. L., … & Lasunskaia E. B. (2014). Mycobacterium tuberculosis strains of the modern sublineage of the Beijing family are more likely to display increased virulence than strains of the ancient sublineage. Journal of clinical microbiology, JCM-00498.

48. Wiens K. E., Woyczynski L. P., Ledesma J. R., Ross J. M., Zenteno-Cuevas R., Goodridge A., … & Ray S. E. (2018). Global variation in bacterial strains that cause tuberculosis disease: a systematic review and meta-analysis. BMC medicine, 16(1), 196. doi: 10.1186/s12916-018-1180-x 30373589

49. Ford C. B., Shah R. R., Maeda M. K., Gagneux S., Murray M. B., Cohen T., … & Fortune S. M. (2013). Mycobacterium tuberculosis mutation rate estimates from different lineages predict substantial differences in the emergence of drug-resistant tuberculosis. Nature genetics, 45(7), 784. doi: 10.1038/ng.2656 23749189

50. Stimson J., Gardy J., Mathema B., Crudu V., Cohen T., & Colijn C. (2019). Beyond the SNP threshold: identifying outbreak clusters using inferred transmissions. Molecular biology and evolution, 36(3), 587–603. doi: 10.1093/molbev/msy242 30690464

51. Brosch R., Gordon S. V., Marmiesse M., Brodin P., Buchrieser C., Eiglmeier K., … & Parsons L. M. (2002). A new evolutionary scenario for the Mycobacterium tuberculosis complex. Proceedings of the national academy of Sciences, 99(6), 3684–3689.

52. Mostowy S., Cousins D., Brinkman J., Aranaz A., & Behr M. A. (2002). Genomic deletions suggest a phylogeny for the Mycobacterium tuberculosis complex. The Journal of infectious diseases, 186(1), 74–80. doi: 10.1086/341068 12089664

53. Brites D., Loiseau C., Menardo F., Borrell S., Boniotti M. B., Warren R., … & Fyfe J. A. (2018). A New Phylogenetic Framework for the Animal-adapted Mycobacterium tuberculosis Complex. Frontiers in Microbiology, 9.

54. Ohta T. (1987). Very slightly deleterious mutations and the molecular clock. Journal of Molecular Evolution, 26(1–2), 1–6.

55. Bromham L., & Penny D. (2003). The modern molecular clock. Nature Reviews Genetics, 4(3), 216. doi: 10.1038/nrg1020 12610526

56. Duchêne S., Holmes E. C., & Ho S. Y. (2014). Analyses of evolutionary dynamics in viruses are hindered by a time-dependent bias in rate estimates. Proc. R. Soc. B, 281(1786), 20140732. doi: 10.1098/rspb.2014.0732 24850916

57. Emerson B. C., & Hickerson M. J. (2015). Lack of support for the time-dependent molecular evolution hypothesis. Molecular ecology, 24(4), 702–709. doi: 10.1111/mec.13070 25640964

58. Rieux A., Eriksson A., Li M., Sobkowiak B., Weinert L. A., Warmuth V., … & Balloux F. (2014). Improved calibration of the human mitochondrial clock using ancient genomes. Molecular Biology and Evolution, 31(10), 2780–2792. doi: 10.1093/molbev/msu222 25100861

59. Ford C. B., Lin P. L., Chase M. R., Shah R. R., Iartchouk O., Galagan J., … & Flynn J. L. (2011). Use of whole genome sequencing to estimate the mutation rate of Mycobacterium tuberculosis during latent infection. Nature genetics, 43(5), 482. doi: 10.1038/ng.811 21516081

60. Chan J. Z. M., Sergeant M. J., Lee O. Y. C., Minnikin D. E., Besra G. S., Pap I., … & Pallen M. J. (2013). Metagenomic analysis of tuberculosis in a mummy. New England Journal of Medicine, 369(3), 289–290. doi: 10.1056/NEJMc1302295 23863071

61. Sabin, S., Herbig, A., Vågene, Å. J., Ahlström, T., Bozovic, G., Arcini, C., … & Bos, K. I. (2019). A seventeenth-century Mycobacterium tuberculosis genome supports a Neolithic emergence of the Mycobacterium tuberculosis complex. BioRxiv, 588277.

62. Brites D., & Gagneux S. (2015). Co-evolution of M ycobacterium tuberculosis and H omo sapiens. Immunological reviews, 264(1), 6–24. doi: 10.1111/imr.12264 25703549

63. Rothschild B. M., Martin L. D., Lev G., Bercovier H., Bar-Gal G. K., Greenblatt C., … & Brittain D. (2001). Mycobacterium tuberculosis complex DNA from an extinct bison dated 17,000 years before the present. Clinical Infectious Diseases, 33(3), 305–311. doi: 10.1086/321886 11438894

64. Taylor G. M., Murphy E., Hopkins R., Rutland P., & Chistov Y. (2007). First report of Mycobacterium bovis DNA in human remains from the Iron Age. Microbiology, 153(4), 1243–1249.

65. Hershkovitz I., Donoghue H. D., Minnikin D. E., Besra G. S., Lee O. Y., Gernaey A. M., … & Bar-Gal G. K. (2008). Detection and molecular characterization of 9000-year-old Mycobacterium tuberculosis from a Neolithic settlement in the Eastern Mediterranean. PloS one, 3(10), e3426. doi: 10.1371/journal.pone.0003426 18923677

66. Nicklisch N., Maixner F., Ganslmeier R., Friederich S., Dresely V., Meller H., … & Alt K. W. (2012). Rib lesions in skeletons from early neolithic sites in Central Germany: on the trail of tuberculosis at the onset of agriculture. American journal of physical anthropology, 149(3), 391–404. doi: 10.1002/ajpa.22137 23042554

67. Wilbur A. K., Bouwman A. S., Stone A. C., Roberts C. A., Pfister L. A., Buikstra J. E., & Brown T. A. (2009). Deficiencies and challenges in the study of ancient tuberculosis DNA. Journal of Archaeological Science, 36(9), 1990–1997.

68. Donoghue H. D., Hershkovitz I., Minnikin D. E., Besra G. S., Lee O. Y. C., Galili E., … & Bar-Gal G. K. (2009). Biomolecular archaeology of ancient tuberculosis: response to “Deficiencies and challenges in the study of ancient tuberculosis DNA” by Wilbur et al. (2009). Journal of Archaeological Science, 36(12), 2797–2804.

69. Menardo F., Loiseau C., Brites D., Coscolla M., Gygli S. M., Rutaihwa L. K., … & Gagneux S. (2018). Treemmer: a tool to reduce large phylogenetic datasets with minimal loss of diversity. BMC bioinformatics, 19(1), 164. doi: 10.1186/s12859-018-2164-8 29716518

70. Bolger A. M., Lohse M., & Usadel B. (2014). Trimmomatic: A flexible trimmer for Illumina Sequence Data. Bioinformatics, 30(15), 2114–2120. doi: 10.1093/bioinformatics/btu170 24695404

71. Li H. and Durbin R. (2009) Fast and accurate short read alignment with Burrows-Wheeler Transform. Bioinformatics, 25:1754–60. doi: 10.1093/bioinformatics/btp324 19451168

72. McKenna A, Hanna M, Banks E, Sivachenko A, Cibulskis K, Kernytsky A, Garimella K, Altshuler D, Gabriel S, Daly M, DePristo MA, (2010). The Genome Analysis Toolkit: a MapReduce framework for analyzing next-generation DNA sequencing data. Genome Research, 20:1297–303. doi: 10.1101/gr.107524.110 20644199

73. Li H. (2011). A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data. Bioinformatics, 27(21):2987–93. doi: 10.1093/bioinformatics/btr509 21903627

74. Koboldt D., Zhang Q., Larson D., Shen D., McLellan M., Lin L., Miller C., Mardis E., Ding L., & Wilson R. (2012). VarScan 2: Somatic mutation and copy number alteration discovery in cancer by exome sequencing Genome Research, 22(3), 568–576. doi: 10.1101/gr.129684.111 22300766

75. Steiner A., Stucki D., Coscolla M., Borrell S., & Gagneux S. (2014). KvarQ: targeted and direct variant calling from fastq reads of bacterial genomes. BMC genomics, 15(1), 881.

76. Stucki D., Brites D., Jeljeli L., Coscolla M., Liu Q., Trauner A., … & Gao Q. (2016). Mycobacterium tuberculosis lineage 4 comprises globally distributed and geographically restricted sublineages. Nature genetics, 48(12), 1535. doi: 10.1038/ng.3704 27798628

77. Coll F., McNerney R., Guerra-Assuncao J. A., Glynn J. R., Perdigao J., Viveiros M., … & Clark T. G. (2014). A robust SNP barcode for typing Mycobacterium tuberculosis complex strains. Nature communications, 5, 4812. doi: 10.1038/ncomms5812 25176035

78. Crispell J., Zadoks R. N., Harris S. R., Paterson B., Collins D. M., de-Lisle G. W., … & Kao R. R. (2017). Using whole genome sequencing to investigate transmission in a multi-host system: bovine tuberculosis in New Zealand. BMC genomics, 18(1), 180. doi: 10.1186/s12864-017-3569-x 28209138

79. Stamatakis A. (2014). RAxML version 8: a tool for phylogenetic analysis and post-analysis of large phylogenies. Bioinformatics, 30(9), 1312–1313. doi: 10.1093/bioinformatics/btu033 24451623

80. Paradis E., Schliep K., & Schwartz R. (2018). ape 5.0: an environment for modern phylogenetics and evolutionary analyses in R. Bioinformatics, 1, 3.

81. Ramsden C., Melo F. L., Figueiredo L. M., Holmes E. C., Zanotto P. M., & VGDN Consortium. (2008). High rates of molecular evolution in hantaviruses. Molecular Biology and Evolution, 25(7), 1488–1492. doi: 10.1093/molbev/msn093 18417484

82. Rambaut A., Drummond A. J., Xie D., Baele G., & Suchard M. A. (2018). Posterior summarisation in Bayesian phylogenetics using Tracer 1.7. Syst. Biol, 10.

Hygiena a epidemiologie Infekční lékařství Laboratoř

Článek vyšel v časopise

PLOS Pathogens

2019 Číslo 9
Nejčtenější tento týden
Nejčtenější v tomto čísle

Zvyšte si kvalifikaci online z pohodlí domova

Hypertenze a hypercholesterolémie – synergický efekt léčby
nový kurz
Autoři: prof. MUDr. Hana Rosolová, DrSc.

Multidisciplinární zkušenosti u pacientů s diabetem
Autoři: Prof. MUDr. Martin Haluzík, DrSc., prof. MUDr. Vojtěch Melenovský, CSc., prof. MUDr. Vladimír Tesař, DrSc.

Úloha kombinovaných preparátů v léčbě arteriální hypertenze
Autoři: prof. MUDr. Martin Haluzík, DrSc.

Autoři: MUDr. Ladislav Korábek, CSc., MBA

Terapie roztroušené sklerózy v kostce
Autoři: MUDr. Dominika Šťastná, Ph.D.

Všechny kurzy
Zapomenuté heslo

Zadejte e-mailovou adresu, se kterou jste vytvářel(a) účet, budou Vám na ni zaslány informace k nastavení nového hesla.


Nemáte účet?  Registrujte se