Quasispecies Made Simple
Publication Date
November 25, 2005
Journal
PLOS Computational Biology
Authors
J. J Bull, Lauren Ancel Meyers & Michael Lachmann
Volume
1
Issue
6
Pages
e61
DOI
https://dx.plos.org/10.1371/journal.pcbi.0010061
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.0010061
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/16322763
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1289388
Europe PMC
http://europepmc.org/abstract/MED/16322763
Web of Science
000234713300003
Scopus
34547553128
Mendeley
http://www.mendeley.com/research/quasispecies-made-simple
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{"title"=>"Quasispecies made simple", "type"=>"generic", "authors"=>[{"first_name"=>"J. J.", "last_name"=>"Bull", "scopus_author_id"=>"7202139148"}, {"first_name"=>"Lauren Ancel", "last_name"=>"Meyers", "scopus_author_id"=>"7005055717"}, {"first_name"=>"Michael", "last_name"=>"Lachmann", "scopus_author_id"=>"6603915382"}], "year"=>2005, "source"=>"PLoS Computational Biology", "identifiers"=>{"pmid"=>"16322763", "doi"=>"10.1371/journal.pcbi.0010061", "sgr"=>"34547553128", "isbn"=>"1553-7358 (Electronic) 1553-734X (Linking)", "scopus"=>"2-s2.0-34547553128", "issn"=>"1553734X", "pui"=>"135774944"}, "id"=>"84555458-39d4-396a-ada3-54bae2818b04", "abstract"=>"Quasispecies are clouds of genotypes that appear in a population at mutation-selection balance. This concept has recently attracted the attention of virologists, because many RNA viruses appear to generate high levels of genetic variation that may enhance the evolution of drug resistance and immune escape. The literature on these important evolutionary processes is, however, quite challenging. Here we use simple models to link mutation-selection balance theory to the most novel property of quasispecies: the error threshold-a mutation rate below which populations equilibrate in a traditional mutation-selection balance and above which the population experiences an error catastrophe, that is, the loss of the favored genotype through frequent deleterious mutations. These models show that a single fitness landscape may contain multiple, hierarchically organized error thresholds and that an error threshold is affected by the extent of back mutation and redundancy in the genotype-to-phenotype map. Importantly, an error threshold is distinct from an extinction threshold, which is the complete loss of the population through lethal mutations. Based on this framework, we argue that the lethal mutagenesis of a viral infection by mutation-inducing drugs is not a true error catastophe, but is an extinction catastrophe.", "link"=>"http://www.mendeley.com/research/quasispecies-made-simple", "reader_count"=>221, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>24, "Student > Doctoral Student"=>10, "Researcher"=>57, "Student > Ph. D. Student"=>61, "Student > Postgraduate"=>7, "Student > Master"=>22, "Other"=>6, "Student > Bachelor"=>10, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>16}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>24, "Student > Doctoral Student"=>10, "Researcher"=>57, "Student > Ph. D. Student"=>61, "Student > Postgraduate"=>7, "Student > Master"=>22, "Other"=>6, "Student > Bachelor"=>10, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>16}, "reader_count_by_subject_area"=>{"Unspecified"=>11, "Agricultural and Biological Sciences"=>140, "Veterinary Science and Veterinary Medicine"=>1, "Chemistry"=>1, "Computer Science"=>8, "Economics, Econometrics and Finance"=>1, "Engineering"=>3, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>23, "Mathematics"=>4, "Medicine and Dentistry"=>8, "Neuroscience"=>1, "Physics and Astronomy"=>13, "Social Sciences"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>8}, "Social Sciences"=>{"Social Sciences"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>13}, "Mathematics"=>{"Mathematics"=>4}, "Unspecified"=>{"Unspecified"=>11}, "Environmental Science"=>{"Environmental Science"=>4}, "Engineering"=>{"Engineering"=>3}, "Chemistry"=>{"Chemistry"=>1}, "Neuroscience"=>{"Neuroscience"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>140}, "Computer Science"=>{"Computer Science"=>8}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>23}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>1}}, "reader_count_by_country"=>{"Colombia"=>2, "Argentina"=>1, "United States"=>13, "Japan"=>2, "Kenya"=>1, "Switzerland"=>2, "India"=>1, "Canada"=>1, "Turkey"=>1, "Belgium"=>1, "China"=>1, "Brazil"=>7, "Mexico"=>2, "Israel"=>1, "France"=>1, "Peru"=>1, "Germany"=>2}, "group_count"=>4}

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Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/960650"], "description"=>"<div><p>Left: replacement rates of the two genotypes in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g001\" target=\"_blank\">Figure 1</a>, <i>w</i><sub>1</sub>(1 − μ<sub>1</sub>) for <i>A</i><sub>1</sub> (solid black line extending to dashes) and <i>w</i><sub>2</sub>(1 − μ<sub>2</sub>) for <i>A</i><sub>2</sub> (gray line). Here we let μ<sub>1</sub> = <i>k</i>μ and μ<sub>2</sub> = μ, with <i>k</i> > 1 so the two replacement rates can be plotted as lines in the same plane. Since <i>w</i><sub>1</sub> > <i>w</i><sub>2</sub>, the constraint on <i>k</i> ensures a higher replacement rate of <i>A</i><sub>1</sub> than of <i>A</i><sub>2</sub> at low mutation rates and the reverse at higher mutation rates. The point at which the lines intersect is the error threshold, beyond which <i>A</i><sub>1</sub> is absent, hence the use of dashes for this part of its replacement rate function. If replacement rate drops below unity, the population goes extinct, so the functions are not extended below one on the vertical axis.</p><p>Right: the frequency of <i>A</i><sub>1</sub> declines as the mutation rate increases until the error threshold is reached. At higher mutation rates, only <i>A</i><sub>2</sub> is present. The decline in the frequency of <i>A</i><sub>1</sub> with μ toward the error threshold may be linear (as shown here), concave, or convex, depending on parameter values. (Right side drawn for <i>w</i><sub>1</sub> = 3.0, <i>w</i><sub>2</sub> = 2, and <i>k</i> = 2.)</p></div>", "links"=>[], "tags"=>["Computational biology", "Evolutionary biology", "Virology"], "article_id"=>630659, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g003", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Error_Threshold_and_Error_Catastrophe_/630659", "title"=>"The Error Threshold and Error Catastrophe", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:51:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/961176"], "description"=>"<div><p>Top: effect of back mutation (μ<sub>3</sub>) between the pair of <i>A</i><sub>2</sub> genotypes in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g008\" target=\"_blank\">Figure 8</a>. The vertical axis gives the replacement rate of the <i>A</i><sub>2</sub> network. Since all <i>A</i><sub>2</sub> genotypes are mutationally interconnected, they ultimately grow at the same rate in the limit. In the absence of back mutation, the neutral network has the replacement rate <i>w</i><sub>2</sub> (1 − μ<sub>2</sub>), and replacement rate increases as back mutation is increased up to its maximum of μ<sub>3,max</sub> = 1 − μ<sub>2</sub>. (The replacement rate function is\n\t\t\t\t\t\tobtained as the eigenvalue associated with <i>A</i><sub>2</sub> in the transition matrix.)\n\t\t\t\t\t</p><p>Bottom: the replacement rate of the neutral network also increases with the number of genotypes in it. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g008\" target=\"_blank\">Figure 8</a> shows the network with two genotypes; third and additional genotypes would be added so that each is mutationally balanced: each additional genotype loses μ<sub>2</sub> of its progeny to become the genotype to its right and loses μ<sub>3</sub> of its progeny to become the genotype to its left, but it receives μ<sub>2</sub> mutants from the genotype to its left and receives μ<sub>3</sub> mutants from the genotype to its right. The benefit of increasing the network size is shown for three different combinations of forward and back mutation rates.</p></div>", "links"=>[], "tags"=>["mutational", "connectivity"], "article_id"=>631174, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g009", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Network_Size_and_Mutational_Connectivity_Affects_Replacement_Rate_/631174", "title"=>"Network Size and Mutational Connectivity Affects Replacement Rate", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/960914"], "description"=>"<p>As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g001\" target=\"_blank\">Figure 1</a>, except that some of the mutations away from <i>A</i><sub>2</sub> recreate genotype <i>A</i><sub>1</sub>. The total mutation rate of <i>A</i><sub>2</sub> is still μ<sub>2</sub>, so the back mutation rate cannot exceed this value (i.e., μ<sub>3</sub> ≤ μ<sub>2</sub>).</p>", "links"=>[], "tags"=>["genotypes"], "article_id"=>630919, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g006", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_of_Two_Genotypes_with_Back_Mutation_3_/630919", "title"=>"Model of Two Genotypes with Back Mutation, μ<sub>3</sub>", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:53:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/960852"], "description"=>"<p>Each genotype <i>A<sub>i</sub></i> has its own fitness <i>w<sub>i</sub></i> and mutational loss μ<i><sub>i</sub></i> so that error thresholds can exist between each pair of genotypes.</p>", "links"=>[], "tags"=>["genotypes"], "article_id"=>630859, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g005", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_of_Several_Genotypes_with_Forward_Mutation_/630859", "title"=>"Model of Several Genotypes with Forward Mutation", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:53:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/960477"], "description"=>"<p>Each genotype <i>A<sub>i</sub></i> has its own fitness <i>w<sub>i</sub></i> and mutational loss μ<sub>i</sub>. Mutation is asymmetric, so that <i>A</i><sub>1</sub> gives rise to <i>A</i><sub>2</sub>, but not vice versa.</p>", "links"=>[], "tags"=>["genotypes"], "article_id"=>630483, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g001", "stats"=>{"downloads"=>2, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_of_Two_Genotypes_with_Forward_Mutation_/630483", "title"=>"Model of Two Genotypes with Forward Mutation", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:50:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/960990"], "description"=>"<p>In contrast to the case of no back mutation in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g003\" target=\"_blank\">Figure 3</a>, the eigenvalues here do not cross but change slope as they approach each other. The dark curves (upper) correspond to the maximum eigenvalue (λ<sub>1</sub>) and the light curves (lower) to the smaller eigenvalue. The thick, outer curves are drawn for a back mutation rate of μ<sub>3</sub> = 0.05, and the thin, inner curves for μ<sub>3</sub> = 0.001. The effect of increasing back mutation is clearly seen as increasing the minimum distance between the eigenvalue functions. Other parameters are the same as for the right side of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g003\" target=\"_blank\">Figure 3</a>: <i>w</i><sub>1</sub> = 3.0, <i>w</i><sub>2</sub> = 2, and <i>k</i> = 2.</p>", "links"=>[], "tags"=>["mutation"], "article_id"=>630995, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g007", "stats"=>{"downloads"=>3, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Eigenvalues_When_a_Small_Level_of_Back_Mutation_Occurs_/630995", "title"=>"Eigenvalues When a Small Level of Back Mutation Occurs", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:54:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/961254"], "description"=>"<div><p>Each allele has two states—wild-type and mutant. The per base mutation rate from wild-type to mutant is identical for all loci. Back mutation from mutant to wild-type is not allowed. As mutant alleles fix in the population, the proportion of the sequence that can still mutate decreases. Multiple error thresholds exist because the effective mutation rate per genome drops as mutations accumulate. The model is otherwise as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g001\" target=\"_blank\">Figure 1</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-box001\" target=\"_blank\">Box 1</a>, and as specified below.</p><p>Top: the fitness landscape. The <i>x</i>-axis shows the mutation distance from the “perfect” genotype consisting of all wild-type (zero mutant) alleles. The <i>y</i>-axis shows the fitness.</p><p>Lower left: equilibrium distributions of genotypes in the population for seven mutation rates from 0.0001 to 0.045. In all plots the <i>x</i>-axis indicates the number of mutations in the genome and the <i>y</i>-axis indicates frequency in the steady-state population; the shortest bars merely indicate the presence of genotypes at some (low) frequency, and the absence of a bar indicates absence of that genotype from the equilibrium population. Plots 1–5 show equilibria before the first error catastrophe, that is, for mutation rates that are less than the first error threshold. Plot 6 shows an equilibrium after the first error catastrophe and before the second error catastrophe, and plot 7 shows an equilibrium after the second catastrophe. The vertical dashed green lines indicate the stable networks that can attract error catastrophes. These correspond to the first (wild-type), third (5–14 mutations), and fourth (15–31 mutations) networks, starting from the left. The second network, with 1–4 mutations (represented by a red line), is never stable as the fittest type in the population, and is skipped.</p><p>Lower right: replacement rates of the various fitness plateaus. Numbers correspond to panels in the figure to the left. The <i>x</i>-axis shows the mutation rate; the <i>y</i>-axis shows the growth rate (with a log scale). One can see two error thresholds. The red dashed line represents the replacement rate of the second network, with 1–4 mutations, and shows why this plateau never stabilizes—it is too narrow relative to its fitness advantage.</p></div>", "links"=>[], "tags"=>["thresholds", "binary"], "article_id"=>631253, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g010", "stats"=>{"downloads"=>4, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Multiple_Error_Thresholds_on_a_Binary_Sequence_of_Length_40_/631253", "title"=>"Multiple Error Thresholds on a Binary Sequence of Length 40", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:56:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/961095"], "description"=>"<p>Both <i>A</i><sub>2</sub> genotypes have the same fitness and the same forward mutation rates μ<sub>2</sub>. The error threshold with μ<sub>3</sub> = 0 is the same as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g001\" target=\"_blank\">Figure 1</a>. As μ<sub>3</sub> increases, the <i>A</i><sub>2</sub> network becomes more competitive against <i>A</i><sub>1</sub>, and thus the error threshold value of μ<sub>1</sub> decreases. Equations for this system can be derived and analyzed with similar methods as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-box001\" target=\"_blank\">Box 1</a>.</p>", "links"=>[], "tags"=>["genotypes"], "article_id"=>631095, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g008", "stats"=>{"downloads"=>2, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_of_Three_Genotypes_with_a_Simple_Neutral_Network_/631095", "title"=>"Model of Three Genotypes with a Simple Neutral Network", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:54:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/960554"], "description"=>"<p>Drawn for <i>w</i><sub>1</sub> = 1.5, <i>w</i><sub>2</sub> = 1.0, μ<sub>1</sub> = 0.7, and μ<sub>2</sub> = 0.6. The upper, black curve represents a different starting condition than the lower, gray curve, but they both equilibrate to the same value.</p>", "links"=>[], "tags"=>["quasispecies", "genotypes", "illustrated"], "article_id"=>630563, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g002", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamic_Approach_to_the_Quasispecies_Equilibrium_for_the_Genotypes_Illustrated_in_Figure_1_/630563", "title"=>"Dynamic Approach to the Quasispecies Equilibrium, for the Genotypes Illustrated in Figure 1", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:51:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/960736"], "description"=>"<div><p>Left: the error threshold is crossed at a lower mutation rate (μ) than the extinction threshold.</p><p>Right: the extinction threshold is crossed before the error threshold.</p><p>Otherwise as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010061#pcbi-0010061-g003\" target=\"_blank\">Figure 3</a>.</p></div>", "links"=>[], "tags"=>["Computational biology", "Evolutionary biology", "Virology"], "article_id"=>630739, "categories"=>["Virology", "Biological Sciences", "Evolutionary Biology"], "users"=>["J. J Bull", "Lauren Ancel Meyers", "Michael Lachmann"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0010061.g004", "stats"=>{"downloads"=>2, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Extinction_versus_Error_Catastrophe_/630739", "title"=>"Extinction versus Error Catastrophe", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:52:18"}

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  • {"unique-ip"=>"6", "full-text"=>"3", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"12"}
  • {"unique-ip"=>"10", "full-text"=>"6", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"1"}
  • {"unique-ip"=>"2", "full-text"=>"3", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"2"}
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  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"5"}
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  • {"unique-ip"=>"5", "full-text"=>"5", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"8"}
  • {"unique-ip"=>"22", "full-text"=>"13", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"10", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2016", "month"=>"9"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"10"}
  • {"unique-ip"=>"3", "full-text"=>"4", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"11"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"12"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"1"}
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  • {"unique-ip"=>"7", "full-text"=>"9", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"5"}
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  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"8"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"9"}
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  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"12"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"1"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"3"}
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  • {"unique-ip"=>"8", "full-text"=>"11", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"4"}
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  • {"unique-ip"=>"8", "full-text"=>"8", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"6"}
  • {"unique-ip"=>"21", "full-text"=>"26", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"8"}
  • {"unique-ip"=>"17", "full-text"=>"18", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
  • {"unique-ip"=>"6", "full-text"=>"6", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"7"}
  • {"unique-ip"=>"31", "full-text"=>"36", "pdf"=>"10", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
  • {"unique-ip"=>"10", "full-text"=>"12", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"12"}
  • {"unique-ip"=>"15", "full-text"=>"17", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"11"}
  • {"unique-ip"=>"25", "full-text"=>"37", "pdf"=>"9", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"27", "full-text"=>"37", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"32", "full-text"=>"33", "pdf"=>"7", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"23", "full-text"=>"29", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"30", "full-text"=>"33", "pdf"=>"6", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
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Relative Metric

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