Quasispecies theory in the context of population genetics
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Background: A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory. Results: I review the pertinent literature, and demonstrate for a number of cases that the quasispecies concept is equivalent to the concept of mutation-selection balance developed in population genetics, and that there is no disagreement between the population genetics of haploid, asexually-replicating organisms and quasispecies theory. Conclusion: Since quasispecies theory and mutation-selection balance are two sides of the same medal, the discussion about which is more appropriate to describe virus evolution is moot. In future work on virus evolution, we would do good to focus on the important questions, such as whether we can develop accurate, quantitative models of virus evolution, and to leave aside discussions about the relative merits of perfectly equivalent concepts.
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In many published quasi-species simulations, a quasi-species has one master sequence with superior fitness and all other sequences have inferior fitness.
“But in many published simulations, a quasi-species ‘has one master sequence with superior fitness … and all other sequences have inferior fitness’ [111, p. 2].”
From Systems protobiology: origin of life in lipid catalytic networks (2018) · cites this paper as [111]
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References 84 · Cited by 276
Research works printed but not linked: 72
- Eigen M McCaskill J Schuster P Molecular Quasi-Species J Phys Chem 1988 92 6881 6891 10.1021/j100335a010 · DOI · Paper page
- Moya A Elena SF Bracho A Miralles R Barrio E The evolution of RNA viruses: A population genetics view Proc Natl Acad Sci USA 2000 97 6967 6973 10860958 10.1073/pnas.97.13.6967 PMC34371 · DOI
- Jenkins GM Worobey M Woelk CH Holmes EC Evidence for the non-quasispecies evolution of RNA viruses Mol Biol Evol 2001 18 987 994 11371587
- Holmes EC Moya A Is the Quasispecies Concept Relevant to RNA Viruses? J Virol 2002 76 460 462 11739715 10.1128/JVI.76.1.460-462.2002 PMC135735 · DOI
- Comas I Moya A Gonzalez-Candelas F Validating viral quasispecies with digital organisms: A re-examination of the critical mutation rate BMC Evol Biol 2005 5 5 15651995 10.1186/1471-2148-5-5 PMC546199 · DOI
- Domingo E Quasispecies Theory in Virology J Virol 2002 76 463 465 10.1128/JVI.76.1.463-465.2002 PMC135734 33739796 · DOI
- Eigen M On the nature of virus quasispecies Trends Microbiol 1996 4 216 218 8795155 10.1016/0966-842X(96)20011-3 · DOI
- Eigen M Schuster P The hypercycle, a principle of natural self-organization. Part A: Emergence of the hypercycle Die Naturwissenschaften 1977 64 541 565 593400 10.1007/BF00450633 · DOI · Paper page
- Domingo E Sabo D Taniguchi T Weissmann C Nucleotide sequence heterogeneity of an RNA phage population Cell 1978 13 735 744 657273 10.1016/0092-8674(78)90223-4 · DOI
- Holland J Spindler K Horodyski F Grabau E Nichol S VandePol S Rapid evolution of RNA genomes Science 1982 215 1577 1585 7041255
- Domingo E Holland JJ RNA virus mutations and fitness for survival Annu Rev Microbiol 1997 51 151 178 9343347 10.1146/annurev.micro.51.1.151 · DOI · Paper page
- Swetina J Schuster P Self-replication with errors: a model for polynucleotide replication Biophys Chem 1982 16 329 345 7159681 10.1016/0301-4622(82)87037-3 · DOI
- Galluccio S Exact solution of the quasispecies model in a sharply peaked fitness landscape Phys Rev E 1997 56 4526 4539 10.1103/PhysRevE.56.4526 · DOI
- Alves D Fontanari JF Error threshold in finite populations Phys Rev E 1998 57 7008 7013 10.1103/PhysRevE.57.7008 · DOI
- Campos PRA Fontanari JF Finite-size scaling of the quasispecies model Phys Rev E 1998 58 2664 2667 10.1103/PhysRevE.58.2664 · DOI
- Tannenbaum E Deeds EJ Shakhnovich EI Equilibrium distribution of mutators in the single fitness peak model Phys Rev Lett 2003 91 138105 14525341 10.1103/PhysRevLett.91.138105 · DOI
- Tannenbaum E Deeds EJ Shakhnovich EI Semiconservative replication in the quasispecies model Phys Rev E 2004 69 061916 10.1103/PhysRevE.69.061916 15244626 · DOI
- Demetrius L Selection and evolution in macromolecular systems J Theor Biol 1983 103 619 643 6195487 10.1016/0022-5193(83)90286-2 · DOI
- Demetrius L Schuster P Sigmund K Polynucleotide evolution and branching processes Bull Math Biol 1985 47 239 262 4027436 10.1016/S0092-8240(85)90051-5 · DOI
- Wilke CO Ronnewinkel C Martinetz T Dynamic Fitness Landscapes in Molecular Evolution Phys Rep 2001 349 395 446 10.1016/S0370-1573(00)00118-6 · DOI
- Kimura M Maruyama T The mutational load with epistatic gene interactions in fitness Genetics 1966 54 1337 1351 17248359 PMC1211299
- Burger R The Mathematical Theory of Selection, Recombination, and Mutation 2000 Chichester: Wiley
- van Nimwegen E Crutchfield JP Huynen M Neutral Evolution of Mutational Robustness Proc Natl Acad Sci USA 1999 96 9716 9720 10449760 10.1073/pnas.96.17.9716 PMC22276 · DOI
- Wilke CO Adami C Evolution of mutational robustness Mut Res 2003 522 3 11 12517406
- Thompson CJ McBride JL On Eigen's Theory of Self-Organization of Matter and the Evolution of Biological Macromolecules Math Biosci 1974 21 127 142 10.1016/0025-5564(74)90110-2 · DOI
- Jones BL Enns RH Rangnekar SS On the theory of selection of coupled macromolecular systems Bull Math Biol 1976 38 15 28 10.1016/S0092-8240(76)80040-7 · DOI
- Schuster P Swetina J Stationary mutant distributions and evolutionary optimization Bull Math Biol 1988 50 635 660 3219448 10.1016/S0092-8240(88)80059-4 · DOI
- Wilke CO Wang JL Ofria C Lenski RE Adami C Evolution of digital organisms at high mutation rate leads to survival of the flattest Nature 2001 412 331 333 11460163 10.1038/35085569 · DOI
- McCaskill JS A stochastic theory of macromolecular evolution Biological Cybernetics 1984 50 63 73 10.1007/BF00317940 · DOI
- Nowak M Schuster P Error Thresholds of Replication in Finite Populations–Mutation Frequencies and the Onset of Muller's Ratchet J Theor Biol 1989 137 375 395 2626057
- Woodcock G Higgs PG Population evolution on a multiplicative single-peak fitness landscape J Theor Biol 1996 179 61 73 8733432 10.1006/jtbi.1996.0049 · DOI
- van Nimwegen E Crutchfield JP Mitchell M Statistical Dynamics of the Royal Road Genetic Algorithm Theoretical Computer Science 1999 229 41 102 10.1016/S0304-3975(99)00119-X · DOI
- Rouzine IM Wakeley J Coffin JM The solitary wave of asexual evolution Proc Natl Acad Sci USA 2003 100 587 592 12525686 10.1073/pnas.242719299 PMC141040 · DOI
- Bornberg-Bauer E Chan HS Modeling evolutionary landscapes: Mutational stability, topology, and superfunnels in sequence space Proc Natl Acad Sci USA 1999 96 10689 10694 10485887 10.1073/pnas.96.19.10689 PMC17944 · DOI
- Wilke CO Adaptive Evolution on Neutral Networks Bull Math Biol 2001 63 715 730 11497165 10.1006/bulm.2001.0244 · DOI
- Wilke CO Molecular clock in neutral protein evolution BMC Genetics 2004 5 25 15333142 10.1186/1471-2156-5-25 PMC517495 · DOI
- Iwasa Y Michor F Nowak MA Evolutionary dynamics of invasion and escape J Theor Biol 2003 226 205 214 14643190 10.1016/j.jtbi.2003.08.014 · DOI
- Wilke CO Probability of Fixation of an Advantageous Mutant in a Viral Quasispecies Genetics 2003 163 467 474 12618386 PMC1462447
- Barton NH Linkage and the limits to natural selection Genetics 1995 140 821 841 7498757 PMC1206655
- Johnson T Barton NH The Effect of Deleterious Alleles on Adaptation in Asexual Populations Genetics 2002 162 395 411 12242249 PMC1462245
- Price DA Goulder PJR Klenerman P Sewell AK Easterbrook PJ Troop M Bangham CRM Phillips RE Positive selection of HIV-1 cytotoxic T lymphocyte escape variants during primary infection Proc Natl Acad Sci USA 1997 94 1890 1895 9050875 10.1073/pnas.94.5.1890 PMC20013 · DOI
- Drake JW Rates of spontaneous mutation among RNA viruses Proc Natl Acad Sci USA 1993 90 4171 4175 8387212 PMC46468
- Haigh J Accumulation of deleterious mutations: Muller's ratchet Theor Popul Biol 1978 14 251 267 746491 10.1016/0040-5809(78)90027-8 · DOI
- Charlesworth B Mutation-selection balance and the evolutionary advantage of sex and recombination Genet Res 1990 55 199 221 2394378
- Wagner GP Krall P What is the difference between models of error thresholds and Muller's ratchet? J Math Biol 1993 32 33 44 10.1007/BF00160372 · DOI
- Wiehe T Model dependency of error thresholds: the role of fitness functions and contrasts between the finite and infinite sites models Genet Res 1997 69 127 136 10.1017/S0016672397002619 · DOI
- Baake E Wagner H Mutation-selection models solved exactly with methods of statistical mechanic Genet Res 2001 78 93 117 11556140 10.1017/S0016672301005110 · DOI
- Malpica JM Fraile A Moreno I Obies C Drake JW García-Arenal F The Rate and Character of Spontaneous Mutation in an RNA Virus Genetics 2002 162 1505 1511 12524327 PMC1462378
- Sanjuán R Moya A Elena SF The distribution of fitness effects caused by single-nucleotide substitutions in an RNA virus Proc Natl Acad Sci USA 2004 101 8396 8401 15159545 10.1073/pnas.0400146101 PMC420405 · DOI · Paper page
- Pariente N Sierra S Lowenstein PR Domingo E Efficient virus extinction by combinations of a mutagen and antiviral inhibitors J Virol 2001 75 9723 9730 11559805 10.1128/JVI.75.20.9723-9730.2001 PMC114544 · DOI
- Crotty S Cameron CE Andino R RNA virus error catastrophe: Direct molecular test by using ribavirin Proc Natl Acad Sci USA 2001 98 6895 6900 11371613 10.1073/pnas.111085598 PMC34449 · DOI
- Grande-Perez A Sierra S Castro MG Domingo E Lowenstein PR Molecular indetermination in the transition to error catastrophe: Systematic elimination of lymphocytic choriomeningitis virus through mutagenesis does not correlate linearly with large increases in mutant spectrum complexity Proc Natl Acad Sci USA 2002 99 12938 12943 12215495 10.1073/pnas.182426999 PMC130564 · DOI
- Anderson JP Daifuku R Loeb LA Viral error catastrophe by mutagenic nucleosides Annu Rev Microbiol 2004 58 183 205 15487935 10.1146/annurev.micro.58.030603.123649 · DOI · Paper page
- Gabriel W Lynch M Burger R Muller's ratchet and mutational meltdowns Evolution 1993 47 1744 1757 28567994
- Lynch M Burger R Butcher D Gabriel W The mutational meltdown in asexual populations J Hered 1993 84 339 344 8409355
- Lynch M Conery J Burger R Mutation accumulation and the extinction of small populations Am Nat 1995 146 489 518 10.1086/285812 · DOI
- Tannenbaum E Shakhnovich EI Solution of the quasispecies model for an arbitrary gene network Phys Rev E 2004 70 021903 10.1103/PhysRevE.70.021903 15447511 · DOI
- Nee S Maynard Smith J The evolutionary biology of molecular parasites Parasitology 1990 100 S5 S18 2172893
- Bangham CRM Kirkwood TBL Defective interfering particles: effects in modulating virus growth and persistence Virology 1990 179 821 826 2238471 10.1016/0042-6822(90)90150-P · DOI
- Kirkwood TBL Bangham CRM Cycles, chaos, and evolution in virus cultures: A model of defective interfering particles Proc Natl Acad Sci USA 1994 91 8685 8689 8078942 PMC44671
- Szathmáry E Natural selection and dynamical coexistence of defective and complementing virus segments J theor Biol 1992 157 383 406 1465021
- Szathmáry E Co-operation and defection: playing the field in virus dynamics J theor Biol 1993 165 341 356 8114502 10.1006/jtbi.1993.1193 · DOI
- Turner PE Burch CL Hanley KA Chao L Hybrid frequencies confirm limit to coinfection in the RNA bacteriophage Φ6 J Virol 1999 73 2420 2424 9971826 PMC104488
- Turner PE Chao L Prisoner's dilemma in an RNA virus Nature 1999 398 441 443 10201376 10.1038/18913 · DOI
- Brown SP Collective action in an RNA virus J Evol Biol 2001 14 821 828 10.1046/j.1420-9101.2001.00317.x · DOI
- Frank SA Within-host spatial dynamics of viruses and defective interfering particles J theor Biol 2000 206 279 290 10966764 10.1006/jtbi.2000.2120 · DOI
- Frank SA Multiplicity of infection and the evolution of hybrid incompatibility in segmented viruses Heredity 2001 87 522 529 11869342 10.1046/j.1365-2540.2001.00911.x · DOI
- Wilke CO Novella IS Phenotypic mixing and hiding may contribute to memory in viral quasispecies BMC Microbiology 2003 3 11 12795816 10.1186/1471-2180-3-11 PMC165440 · DOI
- Novella IS Reissig DD Wilke CO Density-dependent selection in vesicular stomatitis virus J Virol 2004 78 5799 5804 15140977 10.1128/JVI.78.11.5799-5804.2004 PMC415817 · DOI
- Wilke CO Reissig DD Novella IS Replication at periodically changing multiplicity of infection promotes stable coexistence of competing viral populations Evolution 2004 58 900 905 15154565
- Froissart R Wilke CO Montville R Remold SK Chao L Turner PE Co-infection weakens selection against epistatic mutations in RNA viruses Genetics 2004 168 9 19 15454523 10.1534/genetics.104.030205 PMC1448111 · DOI
- Bretscher MT Althaus CL Müller V Bonhoeffer S Recombination in HIV and the evolution of drug resistance: for better or for worse? BioEssays 2004 26 180 188 14745836 10.1002/bies.10386 · DOI
- Authors
- Wilke, C. O.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Wilke, Claus O
- ORCID
- Wilke, Claus O
- Venue
- BMC Evolutionary Biology
- Published
- 2005-08-17
- Volume
- 5
- Issue
- 1
- Pages
- 44-44
- ISSN
- 1471-2148 (ISSN-L)
- PMC
- PMC1208876
- OpenAlex
- W2144625133
- Cited by
- 276
- References
- 84
- Citations by year
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- FWCI
- 8.84
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- BMC Evolutionary Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Institutes of Health
- National Institute of Allergy and Infectious Diseases (R01AI065960, AI 065960)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy and History of Science
- Keywords
- quasispecies theory, mutation-selection balance, viral evolution, population genetics, viral quasispecies, asexual replication, haploid organisms
- MeSH terms
- Data Interpretation, Statistical, Biological Evolution, Gene Frequency, Genes, Viral, Genetics, Population, Models, Biological, Models, Theoretical, Mutation, Phenotype, Ploidies, Research Design, RNA Viruses, Selection, Genetic, Species Specificity, Genetic Variation, Reproducibility of Results, Models, Statistical, Mutagenesis, Genome, Viral, Evolution, Molecular, Genetic Drift
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