elife01914.xml

<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1d1 20130915//EN"  "JATS-archivearticle1.dtd"><article article-type="research-article" dtd-version="1.1d1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="hwp">eLife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">01914</article-id><article-id pub-id-type="doi">10.7554/eLife.01914</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research article</subject></subj-group><subj-group subj-group-type="heading"><subject>Genomics and evolutionary biology</subject></subj-group><subj-group subj-group-type="heading"><subject>Microbiology and infectious disease</subject></subj-group></article-categories><title-group><article-title>Integrating influenza antigenic dynamics with molecular evolution</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes" id="author-9070"><name><surname>Bedford</surname><given-names>Trevor</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="corresp" rid="cor1">*</xref><xref ref-type="fn" rid="pa1">†</xref><xref ref-type="other" rid="par-1"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4087"><name><surname>Suchard</surname><given-names>Marc A</given-names></name><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff3"/><xref ref-type="aff" rid="aff4"/><xref ref-type="other" rid="par-2"/><xref ref-type="other" rid="par-3"/><xref ref-type="other" rid="par-4"/><xref ref-type="other" rid="par-5"/><xref ref-type="other" rid="par-6"/><xref ref-type="other" rid="par-7"/><xref ref-type="other" rid="par-8"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4914"><name><surname>Lemey</surname><given-names>Philippe</given-names></name><xref ref-type="aff" rid="aff5"/><xref ref-type="other" rid="par-6"/><xref ref-type="other" rid="par-7"/><xref ref-type="other" rid="par-8"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4915"><name><surname>Dudas</surname><given-names>Gytis</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4916"><name><surname>Gregory</surname><given-names>Victoria</given-names></name><xref ref-type="aff" rid="aff6"/><xref ref-type="other" rid="par-9"/><xref ref-type="fn" rid="con7"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4917"><name><surname>Hay</surname><given-names>Alan J</given-names></name><xref ref-type="aff" rid="aff6"/><xref ref-type="other" rid="par-9"/><xref ref-type="fn" rid="con8"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4918"><name><surname>McCauley</surname><given-names>John W</given-names></name><xref ref-type="aff" rid="aff6"/><xref ref-type="other" rid="par-9"/><xref ref-type="fn" rid="con9"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4919"><name><surname>Russell</surname><given-names>Colin A</given-names></name><xref ref-type="aff" rid="aff7"/><xref ref-type="aff" rid="aff8"/><xref ref-type="other" rid="par-11"/><xref ref-type="other" rid="par-12"/><xref ref-type="other" rid="par-13"/><xref ref-type="other" rid="par-14"/><xref ref-type="other" rid="par-15"/><xref ref-type="other" rid="par-16"/><xref ref-type="other" rid="par-17"/><xref ref-type="fn" rid="con10"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4920"><name><surname>Smith</surname><given-names>Derek J</given-names></name><xref ref-type="aff" rid="aff7"/><xref ref-type="aff" rid="aff9"/><xref ref-type="aff" rid="aff10"/><xref ref-type="other" rid="par-11"/><xref ref-type="other" rid="par-12"/><xref ref-type="other" rid="par-13"/><xref ref-type="other" rid="par-14"/><xref ref-type="other" rid="par-15"/><xref ref-type="other" rid="par-16"/><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><contrib contrib-type="author" id="author-4769"><name><surname>Rambaut</surname><given-names>Andrew</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff11"/><xref ref-type="aff" rid="aff12"/><xref ref-type="other" rid="par-6"/><xref ref-type="other" rid="par-7"/><xref ref-type="other" rid="par-8"/><xref ref-type="other" rid="par-10"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/><xref ref-type="other" rid="dataro1"/></contrib><aff id="aff1"><institution content-type="dept">Institute of Evolutionary Biology</institution>, <institution>University of Edinburgh</institution>, <addr-line><named-content content-type="city">Edinburgh</named-content></addr-line>, <country>United Kingdom</country></aff><aff id="aff2"><institution content-type="dept">Department of Biomathematics</institution>, <institution>David Geffen School of Medicine, University of California, Los Angeles</institution>, <addr-line><named-content content-type="city">Los Angeles</named-content></addr-line>, <country>United States</country></aff><aff id="aff3"><institution content-type="dept">Department of Human Genetics</institution>, <institution>David Geffen School of Medicine, University of California, Los Angeles</institution>, <addr-line><named-content content-type="city">Los Angeles</named-content></addr-line>, <country>United States</country></aff><aff id="aff4"><institution content-type="dept">Department of Biostatistics</institution>, <institution>UCLA Fielding School of Public Health, University of California, Los Angeles</institution>, <addr-line><named-content content-type="city">Los Angeles</named-content></addr-line>, <country>United States</country></aff><aff id="aff5"><institution content-type="dept">Department of Microbiology and Immunology</institution>, <institution>Rega Institute, Katholieke Universiteit Leuven</institution>, <addr-line><named-content content-type="city">Leuven</named-content></addr-line>, <country>Belgium</country></aff><aff id="aff6"><institution content-type="dept">Division of Virology</institution>, <institution>MRC National Institute for Medical Research</institution>, <addr-line><named-content content-type="city">London</named-content></addr-line>, <country>United Kingdom</country></aff><aff id="aff7"><institution content-type="dept">WHO Collaborating Centre for Modeling, Evolution and Control of Emerging Infectious Diseases</institution>, <institution>University of Cambridge</institution>, <addr-line><named-content content-type="city">Cambridge</named-content></addr-line>, <country>United Kingdom</country></aff><aff id="aff8"><institution content-type="dept">Department of Veterinary Medicine</institution>, <institution>University of Cambridge</institution>, <addr-line><named-content content-type="city">Cambridge</named-content></addr-line>, <country>United Kingdom</country></aff><aff id="aff9"><institution content-type="dept">Centre for Pathogen Evolution, Department of Zoology</institution>, <institution>University of Cambridge</institution>, <addr-line><named-content content-type="city">Cambridge</named-content></addr-line>, <country>United Kingdom</country></aff><aff id="aff10"><institution content-type="dept">Department of Virology</institution>, <institution>Erasmus Medical Centre</institution>, <addr-line><named-content content-type="city">Rotterdam</named-content></addr-line>, <country>Netherlands</country></aff><aff id="aff11"><institution content-type="dept">Fogarty International Center</institution>, <institution>National Institutes of Health</institution>, <addr-line><named-content content-type="city">Bethesda</named-content></addr-line>, <country>United States</country></aff><aff id="aff12"><institution content-type="dept">Centre for Immunity, Infection and Evolution</institution>, <institution>University of Edinburgh</institution>, <addr-line><named-content content-type="city">Edinburgh</named-content></addr-line>, <country>United Kingdom</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Losick</surname><given-names>Richard</given-names></name><role>Reviewing editor</role><aff><institution>Harvard University</institution>, <country>United States</country></aff></contrib></contrib-group><author-notes><corresp id="cor1"><label>*</label>For correspondence: <email>tbedford@fhcrc.org</email></corresp><fn fn-type="present-address" id="pa1"><label>†</label><p>Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, United States</p></fn></author-notes><pub-date date-type="pub" publication-format="electronic"><day>04</day><month>02</month><year>2014</year></pub-date><pub-date pub-type="collection"><year>2014</year></pub-date><volume>3</volume><elocation-id>e01914</elocation-id><history><date date-type="received"><day>19</day><month>11</month><year>2013</year></date><date date-type="accepted"><day>18</day><month>12</month><year>2013</year></date></history><permissions><copyright-statement>© 2013, Bedford et al</copyright-statement><copyright-year>2013</copyright-year><copyright-holder>Bedford et al</copyright-holder><license xlink:href="http://creativecommons.org/licenses/by/3.0/"><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife01914.pdf"/><abstract><object-id pub-id-type="doi">10.7554/eLife.01914.001</object-id><p>Influenza viruses undergo continual antigenic evolution allowing mutant viruses to evade host immunity acquired to previous virus strains. Antigenic phenotype is often assessed through pairwise measurement of cross-reactivity between influenza strains using the hemagglutination inhibition (HI) assay. Here, we extend previous approaches to antigenic cartography, and simultaneously characterize antigenic and genetic evolution by modeling the diffusion of antigenic phenotype over a shared virus phylogeny. Using HI data from influenza lineages A/H3N2, A/H1N1, B/Victoria and B/Yamagata, we determine patterns of antigenic drift across viral lineages, showing that A/H3N2 evolves faster and in a more punctuated fashion than other influenza lineages. We also show that year-to-year antigenic drift appears to drive incidence patterns within each influenza lineage. This work makes possible substantial future advances in investigating the dynamics of influenza and other antigenically-variable pathogens by providing a model that intimately combines molecular and antigenic evolution.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.001">http://dx.doi.org/10.7554/eLife.01914.001</ext-link></p></abstract><abstract abstract-type="executive-summary"><object-id pub-id-type="doi">10.7554/eLife.01914.002</object-id><title>eLife digest</title><p>Every year, seasonal influenza, commonly called flu, infects up to one in five people around the world, and causes up to half a million deaths. Even though the human immune system can detect and destroy the virus that causes influenza, people can catch flu many times throughout their lifetimes because the virus keeps evolving in an effort to avoid the immune system. This antigenic drift—so-called because the antigens displayed by the virus keep changing—also explains why influenza vaccines become less effective over time and need to be reformulated every year.</p><p>It is possible to determine which antigens are displayed by a new strain of the virus by observing how blood samples that respond to known strains respond to the new strain. This information about the “antigenic phenotype” of the virus can be plotted on an antigenic map in which strains with similar antigens cluster together. Gene sequencing has shown that there are four subtypes of the flu virus that commonly infect people; but the relationship between changes in antigenic phenotype and changes in gene sequences of the influenza virus is poorly understood.</p><p>Bedford et al. have now developed an approach to combine antigenic maps with genetic information about the four subtypes of the human flu virus. This revealed that the antigenic phenotype of H3N2—a subtype that is becoming increasingly common—evolved faster than the other three subtypes. Further, a correlation was observed between antigenic drift and the number of new influenza cases per year for each flu strain. This suggests that knowing which antigenic phenotypes are present at the start of flu season could help predict which strains of the virus will predominate later on.</p><p>The work of Bedford et al. provides a useful framework to study influenza, and could help to pinpoint which changes in viral genes cause the changes in antigens. This information could potentially speed up the development of new flu vaccines for each flu season.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.002">http://dx.doi.org/10.7554/eLife.01914.002</ext-link></p></abstract><kwd-group kwd-group-type="author-keywords"><title>Author keywords</title><kwd>influenza</kwd><kwd>evolution</kwd><kwd>antigenic cartography</kwd><kwd>phylogenetics</kwd><kwd>Bayesian inference</kwd><kwd>multidimensional scaling</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>viruses</kwd></kwd-group><funding-group><award-group id="par-1"><funding-source><institution-wrap><institution>Royal Society</institution></institution-wrap></funding-source><award-id>Newton International Fellowship</award-id><principal-award-recipient><name><surname>Bedford</surname><given-names>Trevor</given-names></name></principal-award-recipient></award-group><award-group id="par-2"><funding-source><institution-wrap><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01 HG006139</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name></principal-award-recipient></award-group><award-group id="par-3"><funding-source><institution-wrap><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01 AI107034</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name></principal-award-recipient></award-group><award-group id="par-4"><funding-source><institution-wrap><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>DMS126153</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name></principal-award-recipient></award-group><award-group id="par-5"><funding-source><institution-wrap><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>IIS1251151</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name></principal-award-recipient></award-group><award-group id="par-6"><funding-source><institution-wrap><institution>European Commission</institution></institution-wrap></funding-source><award-id>278433-PREDEMICS</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name><name><surname>Lemey</surname><given-names>Philippe</given-names></name><name><surname>Rambaut</surname><given-names>Andrew</given-names></name></principal-award-recipient></award-group><award-group id="par-7"><funding-source><institution-wrap><institution>European Commission</institution></institution-wrap></funding-source><award-id>260864</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name><name><surname>Lemey</surname><given-names>Philippe</given-names></name><name><surname>Rambaut</surname><given-names>Andrew</given-names></name></principal-award-recipient></award-group><award-group id="par-8"><funding-source><institution-wrap><institution>National Science Foundation</institution></institution-wrap></funding-source><award-id>EF-0423641</award-id><principal-award-recipient><name><surname>Suchard</surname><given-names>Marc A</given-names></name><name><surname>Lemey</surname><given-names>Philippe</given-names></name><name><surname>Rambaut</surname><given-names>Andrew</given-names></name></principal-award-recipient></award-group><award-group id="par-9"><funding-source><institution-wrap><institution>Medical Research Council</institution></institution-wrap></funding-source><award-id>U117512723</award-id><principal-award-recipient><name><surname>Gregory</surname><given-names>Victoria</given-names></name><name><surname>Hay</surname><given-names>Alan J</given-names></name><name><surname>McCauley</surname><given-names>John W</given-names></name></principal-award-recipient></award-group><award-group id="par-10"><funding-source><institution-wrap><institution>Wellcome Trust</institution></institution-wrap></funding-source><award-id>092807</award-id><principal-award-recipient><name><surname>Rambaut</surname><given-names>Andrew</given-names></name></principal-award-recipient></award-group><award-group id="par-11"><funding-source><institution-wrap><institution>European Commission</institution></institution-wrap></funding-source><award-id>223498-EMPERIE</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-12"><funding-source><institution-wrap><institution>European Commission</institution></institution-wrap></funding-source><award-id>278976-ANTIGONE</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-13"><funding-source><institution-wrap><institution>Human Frontier Science Program</institution></institution-wrap></funding-source><award-id>P0050/2008</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-14"><funding-source><institution-wrap><institution>Wellcome Trust</institution></institution-wrap></funding-source><award-id>087982AIA</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-15"><funding-source><institution-wrap><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>DP1-OD000490-01</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-16"><funding-source><institution-wrap><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>HHSN266200700010C</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name><name><surname>Smith</surname><given-names>Derek J</given-names></name></principal-award-recipient></award-group><award-group id="par-17"><funding-source><institution-wrap><institution>Royal Society</institution></institution-wrap></funding-source><award-id>University Research Fellowship</award-id><principal-award-recipient><name><surname>Russell</surname><given-names>Colin A</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta><meta-name>elife-xml-version</meta-name><meta-value>2</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Combined antigenic and genetic analysis shows that different strains of the human influenza virus display dramatically different rates of antigenic drift, and that these differences have a significant impact on the number of new infections in each flu season.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Seasonal influenza infects between 10% and 20% of the human population every year, causing an estimated 250,000 to 500,000 deaths annually (<xref ref-type="bibr" rid="bib43">Influenza Fact sheet, 2009</xref>). Although individuals develop long-lasting immunity to particular influenza strains after infection, antigenic mutations to the influenza virus genome result in proteins that are recognized to a lesser degree by the human immune system, leaving individuals susceptible to future infection. The influenza virus population continually evolves in antigenic phenotype in a process known as antigenic drift. A large proportion of the disease burden of influenza stems from antigenic drift, which allows individuals to be infected multiple times throughout their lives. Although influenza vaccines may lack efficacy for a variety of reasons (<xref ref-type="bibr" rid="bib69">Osterholm et al., 2012</xref>), antigenic drift causes efficacy of a fixed vaccine formulation against circulating viruses to decline over time. A thorough understanding of the process of antigenic drift is essential to public health efforts to control mortality and morbidity through the use of a seasonal influenza vaccine.</p><p>Before 2009, there were four major lineages of influenza circulating within the human population: the H3N2 and H1N1 subtypes of influenza A, and the Victoria and Yamagata lineages of influenza B. In the case of influenza A, subtypes A/H3N2 and A/H1N1 refer to the genes, hemagglutinin (H or HA) and neuraminidase (N or NA), that are primarily responsible for the antigenic character of a strain. In the case of influenza B, Victoria (B/Vic) and Yamagata (B/Yam) refer to antigenically distinct lineages which diverged from a single lineage prior to 1980 (<xref ref-type="bibr" rid="bib75">Rota et al., 1990</xref>). Mutations to the HA1 region of the hemagglutinin protein are thought to drive the majority of antigenic drift in the influenza virus (<xref ref-type="bibr" rid="bib83">Wiley et al., 1981</xref>; <xref ref-type="bibr" rid="bib66">Nelson and Holmes, 2007</xref>). Experimental characterization of antigenic phenotype is possible through the hemagglutination inhibition (HI) assay (<xref ref-type="bibr" rid="bib42">Hirst, 1943</xref>), which measures the cross-reactivity of one virus strain to serum raised against another strain through challenge or vaccination. Sera raised against older strains react poorly to more recent viruses resulting in new strains having a selective advantage over previously established strains.</p><p>The results of many HI assays across a multitude of viruses of a single subtype can be combined to yield a two-dimensional map, quantifying antigenic similarity and distance (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>). The antigenic map of influenza A/H3N2 has shown substantial evolution of the influenza virus population since its emergence in 1968. Evolution of antigenic phenotype appears punctuated with episodes of more rapid innovation interspersed by periods of relative stasis, whereas genetic evolution appears more continuous (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>), suggesting that a relatively small number of genetic changes or combinations of genetic changes may drive changes in antigenic phenotype (<xref ref-type="bibr" rid="bib47">Koel et al., 2013</xref>). The process of antigenic drift results in the rapid turnover of the virus population, so that despite mutation, genetic diversity among contemporaneous viruses remains low. Such population turnover is supported by phylogenetic analysis that shows a characteristically ‘spindly’ tree with a single predominant trunk lineage and transitory side branches that persist for only 1–5 years (<xref ref-type="bibr" rid="bib23">Fitch et al., 1997</xref>).</p><p>Previously, the antigenic and genetic patterns of influenza evolution have been analyzed essentially in isolation. An antigenic map is constructed from a panel of HI measurements, and a phylogenetic tree is constructed from sequence data. However, the opportunity for a combined approach exists as both the antigenic map and the phylogenetic tree often contain many of the same isolates. Here, we implement a flexible Bayesian approach to jointly characterize the antigenic and genetic evolution of the influenza virus population. We apply this approach to investigate the dynamics of A/H3N2, A/H1N1, B/Vic and B/Yam viruses, and, for the first time, present detailed reconstructions of the antigenic dynamics of all four circulating influenza lineages.</p></sec><sec id="s2" sec-type="results|discussion"><title>Results and discussion</title><sec id="s2-1"><title>Antigenic and evolutionary cartography</title><p>To assess patterns of antigenic evolution among influenza strains, we implemented a Bayesian probabilistic analog of multidimensional scaling (MDS), referred to here as BMDS (see ‘Materials and methods’). In this model, viruses and sera are given <italic>N</italic>-dimensional locations, thus specifying an ‘antigenic map’, such that distances between viruses and sera in this space are inversely proportional to cross-reactivity. In the BMDS model, a map distance of one antigenic unit translates to an expectation of a twofold drop in HI titer between virus and sera. Maps that produce pairwise distances most congruent with the observed titers will have a high likelihood and will be favored by the BMDS model. We integrate over sources of uncertainty, such as antigenic locations, in a flexible Bayesian fashion. We apply this model to HI measurements of virus isolates against post-infection ferret antisera for influenza A/H3N2, A/H1N1, B/Vic and B/Yam.</p><p>We begin with Bayesian analogs of the models used by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, in which viruses and sera are represented as <italic>N</italic>-dimensional locations as described in the ‘Antigenic cartography’ section of ‘Materials and methods’. In this case, ‘serum potencies’ are fixed to the maximum titers exhibited by particular ferret sera and give the baseline expectation for titer when virus and serum are antigenically identical. Potency differs between serum isolates due to experimental noise (e.g., variation in serum concentration), but also due to differential ferret immune responses, causing some serum isolates to inhibit hemagglutination at generally higher titers than other isolates. In this model, virus and serum locations follow an uninformative diffuse normal prior. After comparing models of differing dimensions, <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> arrive at a 2D model as the preferred model for their data. <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> implement a form of MDS, seeking to optimize virus and serum locations such that the sum of squared errors between expected and observed titers is minimized (<xref ref-type="disp-formula" rid="equ3">Equation 3</xref> of ‘Materials and methods’). Here, in implementing BMDS, we provide a likelihood function for the probability of observing HI data given virus and serum locations (<xref ref-type="disp-formula" rid="equ8">Equation 8</xref> of ‘Materials and methods’) and seek to estimate model parameters through Bayesian inference using Markov Chain Monte Carlo (MCMC). However, the basic antigenic model describing drop in HI titer as proportional to Euclidean distance between virus and serum locations is identical between these methods.</p><p>We test model performance by constructing training datasets representing 90% of the HI measurements for each of the four influenza lineages and test datasets representing the remaining 10% of the measurements for each lineage. By fitting the BMDS model to the training dataset, we are able to predict HI titers in the test dataset and compare these predicted titers to observed titers. We find that a two-dimensional model has better predictive power than models of lower or higher dimension in all four influenza lineages (models 1–5; <xref ref-type="table" rid="tbl1">Table 1</xref>). We find that this 2D model performs well, yielding an average absolute predictive error of between 0.78 and 0.91 log<sub>2</sub> HI titers across influenza lineages (model 2; <xref ref-type="table" rid="tbl1">Table 1</xref>), in line with the results of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. Consequently, we specify a two-dimensional model in all subsequent analyses. The finding of a low-dimensional map across influenza lineages extends previous studies in A/H3N2 (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>) and remains an interesting and fundamental empirical observation.<table-wrap id="tbl1" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.003</object-id><label>Table 1.</label><caption><p>Average absolute prediction error of log<sub>2</sub> HI titer for test data across models and datasets</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.003">http://dx.doi.org/10.7554/eLife.01914.003</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th/><th/><th/><th/><th/><th colspan="5">Test error</th></tr><tr><th>Model</th><th>Data</th><th>Dimen</th><th>Location prior</th><th>Serum potency</th><th>Virus avidity</th><th>A/H3N2</th><th>A/H1N1</th><th>B/Vic</th><th>B/Yam</th></tr></thead><tbody><tr><td align="char" char=".">1</td><td>HI</td><td>1D</td><td>Uninformed</td><td>Fixed</td><td>None</td><td align="char" char=".">1.35</td><td align="char" char=".">0.94</td><td align="char" char=".">0.90</td><td align="char" char=".">1.08</td></tr><tr><td align="char" char=".">2</td><td>HI</td><td>2D</td><td>Uninformed</td><td>Fixed</td><td>None</td><td align="char" char=".">0.91</td><td align="char" char=".">0.78</td><td align="char" char=".">0.82</td><td align="char" char=".">0.90</td></tr><tr><td align="char" char=".">3</td><td>HI</td><td>3D</td><td>Uninformed</td><td>Fixed</td><td>None</td><td align="char" char=".">0.93</td><td align="char" char=".">0.80</td><td align="char" char=".">0.85</td><td align="char" char=".">0.92</td></tr><tr><td align="char" char=".">4</td><td>HI</td><td>4D</td><td>Uninformed</td><td>Fixed</td><td>None</td><td align="char" char=".">0.98</td><td align="char" char=".">0.84</td><td align="char" char=".">0.90</td><td align="char" char=".">0.97</td></tr><tr><td align="char" char=".">5</td><td>HI</td><td>5D</td><td>Uninformed</td><td>Fixed</td><td>None</td><td align="char" char=".">1.04</td><td align="char" char=".">0.89</td><td align="char" char=".">0.98</td><td align="char" char=".">1.04</td></tr><tr><td align="char" char=".">6</td><td>HI/year</td><td>2D</td><td>Drift</td><td>Fixed</td><td>None</td><td align="char" char=".">0.91</td><td align="char" char=".">0.75</td><td align="char" char=".">0.77</td><td align="char" char=".">0.83</td></tr><tr><td align="char" char=".">7</td><td>HI/year/seq</td><td>2D</td><td>Diffusion/Drift</td><td>Fixed</td><td>None</td><td align="char" char=".">0.89</td><td align="char" char=".">0.74</td><td align="char" char=".">0.74</td><td align="char" char=".">0.83</td></tr><tr><td align="char" char=".">8</td><td>HI/year/seq</td><td>2D</td><td>Diffusion/Drift</td><td>Estimated</td><td>None</td><td align="char" char=".">0.77</td><td align="char" char=".">0.73</td><td align="char" char=".">0.66</td><td align="char" char=".">0.75</td></tr><tr><td align="char" char=".">9</td><td>HI/year/seq</td><td>2D</td><td>Diffusion/Drift</td><td>Fixed</td><td>Estimated</td><td align="char" char=".">0.80</td><td align="char" char=".">0.72</td><td align="char" char=".">0.69</td><td align="char" char=".">0.75</td></tr><tr><td align="char" char=".">10</td><td>HI/year/seq</td><td>2D</td><td>Diffusion/Drift</td><td>Estimated</td><td>Estimated</td><td align="char" char=".">0.76</td><td align="char" char=".">0.71</td><td align="char" char=".">0.64</td><td align="char" char=".">0.72</td></tr></tbody></table></table-wrap></p><p>Previous work on influenza antigenic and genetic evolution has shown that antigenic distance accumulates with increasing genetic distance (<xref ref-type="bibr" rid="bib27">Hay and Gregory, 2001</xref>; <xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>; <xref ref-type="bibr" rid="bib76">Russell et al., 2008</xref>). Here, we examine pairwise relationships between viruses and observe a correlation between amino acid mutations and antigenic distance (<xref ref-type="fig" rid="fig1">Figure 1</xref>) and a similar correlation between phylogenetic distance, measured in years, and antigenic distance (<xref ref-type="fig" rid="fig1">Figure 1</xref>). Thus, genetic relationships between viruses provide some predictive power to estimate antigenic distances in the absence of HI data. However, the magnitudes of the coefficients of determination <italic>R</italic><sup>2</sup>are low (<xref ref-type="fig" rid="fig1">Figure 1</xref>), suggesting that genetic relationships alone will not completely resolve antigenic distances.<fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.004</object-id><label>Figure 1.</label><caption><title>Pairwise correlations between genetic distance, measured as amino acid mutations or as phylogenetic distance, and antigenic distance for influenza A/H3N2, A/H1N1, B/Vic, and B/Yam.</title><p>The top row shows correlations between number of amino acid mutations in HA1 and average antigenic distance between 10,000 random pairs of viruses. The bottom row shows correlations between average phylogenetic distance, measured in terms of years, and average antigenic distance between 10,000 random pairs of viruses. Dashed lines show linear model fits, with <italic>R</italic><sup>2</sup> and slope noted, while solid lines show LOESS fits. Antigenic distances derive from model 2 of <xref ref-type="table" rid="tbl1">Table 1</xref>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.004">http://dx.doi.org/10.7554/eLife.01914.004</ext-link></p></caption><graphic xlink:href="elife01914f001"/></fig></p><p>Consequently, we seek to flexibly incorporate genetic data by modeling antigenic phenotype as an evolutionary diffusion (<xref ref-type="bibr" rid="bib48">Lemey et al., 2010</xref>), wherein a virus’s antigenic character state evolves along branches of the phylogenetic tree according to a Brownian motion process (see ‘Materials and methods’). The phylogenetic diffusion process acts as a prior on virus locations, so that genetically similar viruses are expected to share similar antigenic locations. The antigenic diffusion process includes both systematic drift with time and covariance induced by phylogenetic proximity. We examine the effects of including only systematic drift (model 6; <xref ref-type="table" rid="tbl1">Table 1</xref>) and systematic drift plus phylogenetic diffusion (model 7; <xref ref-type="table" rid="tbl1">Table 1</xref>), finding a small increase in predictive accuracy of between 0.02 and 0.08 log<sub>2</sub> HI titers when both processes are included. The systematic drift process informs virus and serum locations by dates of isolation and the phylogenetic diffusion process informs virus locations by genetic sequences. Thus, in these models, antigenic locations are inferred using both genetic data and HI data and will differ from locations inferred from HI data alone. If HI data is rich, then we expect minor differences in antigenic locations with the inclusion of genetic data (as may be the case for A/H3N2), while if HI data is spare, then we expect genetic data to play a larger role in determining antigenic locations (as may be the case for B/Vic and B/Yam).</p><p>We further extend the model by estimating serum potencies, rather than fixing serum potencies at maximum titers. Serum potencies differ across isolates due to experimental variation in serum extraction and processing or due to variation in ferret immune response. Serum potency determines the baseline expectation of titer when virus and serum have identical antigenic locations. However, if serum potency is fixed to the serum’s maximum titer, this will often not be the case, as the virus giving the maximum titer may be antigenically distinct from the serum. Thus, fixing serum potencies will tend to under-estimate effect size; we observe a mean effect of 10.42 log<sub>2</sub> HI titers for A/H3N2 when fixing serum potencies and a mean of 10.94 when estimating serum potencies. We find that estimating serum potencies improves test error further (model 8, <xref ref-type="table" rid="tbl1">Table 1</xref>), with improvements of between 0.01 and 0.12 log<sub>2</sub> HI titers.</p><p>Additionally, we include and estimate ‘virus avidity’ in an analogous fashion, which is intended to represent differences in overall HI reactivity between viruses. Experimental work has demonstrated that influenza variants exist that differ in HA binding activity for cell surface glycan receptors, and that these high-avidity variants may arise in the presence of antibody pressure (<xref ref-type="bibr" rid="bib41">Hensley et al., 2009</xref>). The presence of differential virus avidity has been previously shown to distort antigenic maps constructed from a model that disregards avidity effects (<xref ref-type="bibr" rid="bib49">Li et al., 2013</xref>). Here, with virus avidities estimated, baseline titer derives from both the virus and the serum used in the HI reaction. We find that including virus avidities further improves test error, either with fixed serum potencies (model 9, <xref ref-type="table" rid="tbl1">Table 1</xref>) or with estimated serum potencies (model 10, <xref ref-type="table" rid="tbl1">Table 1</xref>). With fixed serum potencies, the inclusion of virus avidities results in improvements of between 0.02 and 0.09 log<sub>2</sub> HI titers and with estimated serum potencies, the inclusion of virus avidities results in improvements of between 0.01 and 0.05 log<sub>2</sub> HI titers.</p><p>We find that the average absolute error in predicted log<sub>2</sub> HI titer is nearly constant with antigenic distance (Pearson correlation, <italic>r</italic> = 0.098), thus supporting our model assumption that the drop in log<sub>2</sub> titer is proportional to the Euclidean distance separating viruses and sera on the antigenic map. Additionally, we find that the absolute error in predicted titer is nearly constant with time (Pearson correlation, <italic>r</italic> = −0.007). Antigenic locations inferred by the model are well resolved; estimates of antigenic distance between pairs of viruses show relatively little variation across the posterior. We estimate that virus distances have, on average, a 50% credible interval of ±0.45 antigenic units for A/H3N2, ±0.57 units for A/H1N1, ±0.76 units for B/Vic, and ±0.65 units for B/Yam.</p><p>We find strong correspondence between our results and previous results by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, with equivalent models producing globally consistent antigenic maps and other models producing locally consistent maps with a small degree of global inconsistency (see ‘Methods’). When implementing the same underlying model, differences in the MDS and BMDS approaches reflect greater philosophical differences between maximum-likelihood and Bayesian statistical approaches, with the former seeking the single most likely explanation for the data, and the latter seeking to fully characterize model uncertainty. Additionally, the BMDS method improves flexibility, allowing extensions to the basic cartographic model, such as the incorporation of virus avidities and evolutionary priors, that improve fit and add biological interpretability.</p></sec><sec id="s2-2"><title>Antigenic evolution across influenza lineages</title><p>Through our analysis, we reveal the antigenic, as well as evolutionary, relationships among viruses in influenza A/H3N2, A/H1N1, B/Vic and B/Yam, quantifying both antigenic and evolutionary distances between strains (<xref ref-type="fig" rid="fig2">Figure 2</xref>, <xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). Over the time period of 1968 to 2011, influenza A/H3N2 shows substantially more antigenic evolution than is exhibited by A/H1N1 over the course of 1977 to 2009 or B/Vic and B/Yam over the course of 1986 to 2011. We observe prominent antigenic clusters in A/H3N2 and A/H1N1, but less prominent, though still apparent, clustering in B/Vic and B/Yam. Antigenic clusters show high genetic similarity, so that we observe very few mutation events leading to each cluster, rather than the repeated emergence of clusters. This analysis makes the fate of antigenic clusters obvious, with two clusters in A/H3N2 (Victoria/75 and Beijing/89) appearing to be evolutionary dead-ends. Labeling of prominent antigenic clusters in <xref ref-type="fig" rid="fig2">Figure 2</xref> is intended as a rough guide for orientation and not as exhaustive catalog of antigenic variation.<fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.005</object-id><label>Figure 2.</label><caption><title>Antigenic locations of A/H3N2, A/H1N1, B/Vic, and B/Yam viruses showing evolutionary relationships between virus samples.</title><p>Circles represent a posterior sample of virus locations and have been shaded based on year of isolation. Antigenic units represent twofold dilutions of the HI assay. Absolute positioning of lineages, for example A/H3N2 and A/H1N1, is arbitrary. Lines represent mean posterior diffusion paths when virus locations are fixed. Prominent antigenic clusters are labeled after vaccine strains present within clusters, and are abbreviated from Hong Kong/68, England/72, Victoria/75, Bangkok/79, Sichuan/87, Beijing/89, Beijing/92, Wuhan/95, Sydney/97, Fujian/02, California/04, Wisconsin/05, Brisbane/07, Perth/09 (A/H3N2), USSR/77, Singapore/86, Beijing/95, New Caledonia/99, Solomon Islands/06 (H1N1), Victoria/87, Hong Kong/01, Malaysia/04, Brisbane/08 (Vic), Yamagata/88, Shanghai/02, Florida/06, Wisconsin/10 (Yam).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.005">http://dx.doi.org/10.7554/eLife.01914.005</ext-link></p><p><supplementary-material id="SD1-data"><object-id pub-id-type="doi">10.7554/eLife.01914.006</object-id><label>Figure 2—source data 1.</label><caption><title>This tab-delimited text file lists every virus in <xref ref-type="fig" rid="fig2 fig3">Figures 2 and 3</xref>, including lineage, strain name, year of isolation, and coordinates in antigenic dimensions 1 and 2.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.006">http://dx.doi.org/10.7554/eLife.01914.006</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s001.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f002"/></fig></p><p>HI assays lack sensitivity beyond a certain point, so that for A/H3N2, cross-reactive measurements only exist between strains sampled at most 14 years apart, leaving only threshold titers, for example ‘&lt;40’, in more temporally distant comparisons. Because of the threshold of sensitivity of the HI assay, it is difficult to distinguish a linear trajectory in 2D antigenic space from a slightly curved trajectory (see ‘Materials and Methods’). To solve this problem of identifiability, we assumed a weak prior that favors linear movement in the 2D antigenic space (present in models 6 through 9; <xref ref-type="table" rid="tbl1">Table 1</xref>), with the slope of the linear relationship and the precision of the relationship incorporated into the Bayesian model (see ‘Materials and methods’). Because of this, we interpret map locations locally rather than globally, and assess rates of antigenic movement without making strong statements about the larger configuration under which the movement occurs.</p><p>We find that influenza A/H3N2 evolved along antigenic dimension 1 at an estimated rate of 1.01 antigenic units per year (<xref ref-type="fig" rid="fig3">Figure 3</xref>, <xref ref-type="supplementary-material" rid="SD2-data">Figure 3—source data 1</xref>; <xref ref-type="table" rid="tbl2">Table 2</xref>). However, we observe occasional large jumps in antigenic phenotype (<xref ref-type="fig" rid="fig3">Figure 3</xref>), corresponding to cluster transitions identified by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. Most variation is contained within the first antigenic dimension, but dimension 2 occasionally shows variation when two antigenically distinct lineages emerge and transiently coexist (<xref ref-type="fig" rid="fig2">Figure 2</xref>), as is the case with the previously identified Beijing/89 and Beijing/92 clusters.<fig id="fig3" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.007</object-id><label>Figure 3.</label><caption><title>Antigenic drift of A/H3N2, A/H1N1, B/Vic and B/Yam viruses showing evolutionary relationships between virus samples.</title><p>Antigenic drift is shown in terms of change of location in the first antigenic dimension through time. Circles represent a posterior sample of virus locations and have been shaded based on year of isolation. Antigenic units represent twofold dilutions of the HI assay. Relative positioning of lineages, for example A/H3N2 and A/H1N1, in the vertical axis is arbitrary. Lines represent mean posterior diffusion paths when virus locations are fixed. Prominent antigenic clusters are labeled after vaccine strains present within clusters, and are abbreviated from Hong Kong/68, England/72, Victoria/75, Bangkok/79, Sichuan/87, Beijing/89, Beijing/92, Wuhan/95, Sydney/97, Fujian/02, California/04, Wisconsin/05, Brisbane/07, Perth/09 (A/H3N2), USSR/77, Singapore/86, Beijing/95, New Caledonia/99, Solomon Islands/06 (H1N1), Victoria/87, Hong Kong/01, Malaysia/04, Brisbane/08 (Vic), Yamagata/88, Shanghai/02, Florida/06, Wisconsin/10 (Yam).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.007">http://dx.doi.org/10.7554/eLife.01914.007</ext-link></p><p><supplementary-material id="SD2-data"><object-id pub-id-type="doi">10.7554/eLife.01914.008</object-id><label>Figure 3—source data 1.</label><caption><title>This tab-delimited text file lists every virus in <xref ref-type="fig" rid="fig2 fig3">Figures 2 and 3</xref>, including lineage, strain name, year of isolation, and coordinates in antigenic dimensions 1 and 2.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.008">http://dx.doi.org/10.7554/eLife.01914.008</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s002.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f003"/></fig><table-wrap id="tbl2" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.009</object-id><label>Table 2.</label><caption><p>Estimates of drift rate <italic>μ</italic> (in units per year), diffusion volatility <inline-formula><mml:math id="inf1"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> (in units<sup>2</sup> per year) and scaled effective population size <inline-formula><mml:math id="inf2"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mi>τ</mml:mi></mml:mrow></mml:math></inline-formula> (in years) for influenza A/H3N2, A/H1N1, B/Vic and B/Yam including posterior means and 95% highest posterior density intervals</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.009">http://dx.doi.org/10.7554/eLife.01914.009</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th>Lineage</th><th>Drift <italic>μ</italic></th><th>Volatility <inline-formula><mml:math id="inf3"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula></th><th>Effective pop size <inline-formula><mml:math id="inf4"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mi>τ</mml:mi></mml:mrow></mml:math></inline-formula></th></tr></thead><tbody><tr><td>A/H3N2</td><td>1.01 (0.98–1.04)</td><td>1.25 (0.98–2.35)</td><td>5.03 (4.42–5.73)</td></tr><tr><td>A/H1N1</td><td>0.62 (0.56–0.67)</td><td>0.92 (0.65–1.56)</td><td>6.38 (4.99–8.12)</td></tr><tr><td>B/Vic</td><td>0.42 (0.32–0.51)</td><td>1.22 (0.85–2.25)</td><td>10.40 (8.42–12.80)</td></tr><tr><td>B/Yam</td><td>0.32 (0.25–0.39)</td><td>0.71 (0.46–1.36)</td><td>9.48 (7.76–11.50)</td></tr></tbody></table></table-wrap></p><p>We find that other lineages of influenza evolved in antigenic phenotype substantially slower than A/H3N2 (<xref ref-type="fig" rid="fig3">Figure 3</xref>, <xref ref-type="table" rid="tbl2">Table 2</xref>). Influenza A/H1N1 evolved at a rate of 0.62 units per year, but showed a similar pattern of punctuated antigenic evolution with occasional larger jumps in phenotype, such as the emergence of the Solomon Islands/06 cluster. Influenza B/Victoria and B/Yamagata evolved slower still, with mean estimated rates 0.42 units per year and 0.32 units per year, respectively. Punctuated evolution is less obvious in B/Yam and B/Vic compared to A/H3N2 and A/H1N1, but antigenic clusters are still apparent, with recent transitions to the Brisbane/08 cluster in B/Vic (<xref ref-type="bibr" rid="bib5">Barr et al., 2010</xref>) and to the Wisconsin/10 cluster in B/Yam (<xref ref-type="bibr" rid="bib46">Klimov et al., 2012</xref>). Interestingly, a minor lineage of B/Vic, denoted B/Hubei-Songzi/51/2008 (<xref ref-type="bibr" rid="bib5">Barr et al., 2010</xref>), has persisted through 2011, while remaining antigenically distinct from B/Brisbane/60/2008 viruses (<xref ref-type="fig" rid="fig3">Figure 3</xref>). Although we observe significantly different drift rates between lineages, we observe less variation in diffusion volatility (<xref ref-type="table" rid="tbl2">Table 2</xref>). This is reflected in <xref ref-type="fig" rid="fig3">Figure 3</xref>, where all four lineages exhibit similar levels of standing antigenic variation, despite A/H3N2 drifting more quickly in antigenic phenotype.</p><p>These patterns of antigenic drift influence the corresponding virus phylogenies (<xref ref-type="fig" rid="fig4">Figure 4</xref>). Influenza A/H3N2 has a characteristically spindly tree showing rapid turnover of the virus population, while A/H1N1 and B have trees that show greater degrees of viral coexistance (<xref ref-type="fig" rid="fig4">Figure 4</xref>). The scaled effective population size <italic>N<sub>e</sub>τ</italic> measures the timescale of coalescence of a phylogeny and quantifies the visual distinction between a ‘spindly’ tree and a ‘bushy’ tree (<xref ref-type="bibr" rid="bib6">Bedford et al., 2011</xref>). In this case, <italic>N<sub>e</sub></italic> represents the number of concurrent infections in a panmictic population with generation interval <italic>τ</italic> (time separating infections up the genealogical tree), so that <italic>N<sub>e</sub>τ</italic> is measured in terms of years and gives the expected waiting time for two randomly chosen lineages to coalesce in the genealogical tree. We see that <italic>N<sub>e</sub>τ</italic> broadly correlates with the rate of antigenic drift (<xref ref-type="table" rid="tbl2">Table 2</xref>), with A/H3N2 showing fast drift and reduced effective population size as expected from basic epidemiological models (<xref ref-type="bibr" rid="bib7">Bedford et al., 2012</xref>). Antigenic drift results in the replacement of antigenically primitive lineages by antigenically advanced lineages, thereby reducing genealogical diversity.<fig id="fig4" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.010</object-id><label>Figure 4.</label><caption><title>Time-resolved phylogenetic trees of A/H3N2, A/H1N1, B/Vic and B/Yam viruses.</title><p>The maximium-clade credibility (MCC) tree is shown for each virus. These trees show genealogical relationships, so that branches are measured in terms of years rather than substitutions.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.010">http://dx.doi.org/10.7554/eLife.01914.010</ext-link></p></caption><graphic xlink:href="elife01914f004"/></fig></p><p>Thus, we observe a faster rate of antigenic drift in influenza A/H3N2 than in A/H1N1 or either lineage of influenza B. Previous work using general epidemiological models has suggested that rates of antigenic drift may be influenced by both the fundamental reproductive number <italic>R</italic><sub>0</sub> and the rate at which mutation decreases cross-immunity (<xref ref-type="bibr" rid="bib24">Gog and Grenfell, 2002</xref>; <xref ref-type="bibr" rid="bib50">Lin et al., 2003</xref>). Correspondingly, models specific to influenza evolution ascribe differences in the rate of antigenic drift of A/H3N2 relative to A/H1N1 and influenza B to either greater <italic>R</italic><sub>0</sub> or greater mutation rate (<xref ref-type="bibr" rid="bib22">Ferguson et al., 2003</xref>; <xref ref-type="bibr" rid="bib7">Bedford et al., 2012</xref>). Without more detailed epidemiological modeling, the present study cannot conclusively distinguish between these causal possibilities.</p></sec><sec id="s2-3"><title>Punctuated evolution and its epidemiological consequences</title><p>We sought to summarize year-to-year patterns of antigenic drift by calculating the difference in mean virus location between consecutive years (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). We estimate year-to-year antigenic drift for years 1992 to 2011 by calculating the average location along dimension 1 of phylogenetic lineages present in the tree at year <italic>i</italic> and comparing this location to the average location of phylogenetic lineages present in the tree at year <italic>i</italic> − 1. There may often be large discontinuities in virus locations across the population; our use of difference in mean location is meant to capture both the distance between antigenic clusters and also the change in cluster frequency over consecutive years. We observe greater heterogeneity in year-to-year antigenic drift in type A than in type B lineages (<xref ref-type="fig" rid="fig5">Figure 5B</xref>), with standard deviation of year-to-year antigenic drift equal to 0.97 units in A/H3N2, 0.66 units in A/H1N1, 0.46 units in B/Vic and 0.26 units in B/Yam. This analysis classifies drift only to the level of consecutive years; some coarse-graining of the timings of transition events will necessarily occur.<fig id="fig5" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.011</object-id><label>Figure 5.</label><caption><title>Year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses.</title><p>(<bold>A</bold>) Timeseries of year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses. Colored lines represent year-to-year antigenic drift, where drift for year <italic>i</italic> is measured as the mean of antigenic dimension 1 of phylogenetic lineages in year <italic>i</italic> compared to the mean of antigenic dimension 1 of phylogenetic lineages from the previous year <italic>i</italic> − 1. For example, 2000 represents difference in antigenic dimension 1 between viruses from 1999 to 2000. Error bars represent 50% Bayesian credible intervals of year-to-year drift. Gray dotted lines represent lineage-specific seasonal incidence in the USA taken as average influenza-like illness (ILI) multiplied by proportion of viruses attributable to a lineage for each season. Here, 2000 represents the 2000/2001 influenza season. (<bold>B</bold>) Distribution of year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.011">http://dx.doi.org/10.7554/eLife.01914.011</ext-link></p></caption><graphic xlink:href="elife01914f005"/></fig></p><p>We investigate the relationship between rates of antigenic drift and seasonal incidence in the USA in A/H3N2, A/H1N1, B/Vic and B/Yam. We measure seasonal incidence from USA CDC influenza surveillance reports for each virus lineage (A/H3N2, A/H1N1, B/Vic, B/Yam) by taking the average influenza-like (ILI) percentage in a season and multiplying this by the relative proportion of virus isolations attributable to a particular influenza lineage in a season (see ‘Materials and methods’). This measure of incidence has previously been shown to have have predictive power in the analysis of seasonal influenza trends (<xref ref-type="bibr" rid="bib25">Goldstein et al., 2011</xref>). We analyze incidence from the 1998/1999 to the 2008/2009 seasons to avoid possible complications from the 2009 pandemic. We begin by comparing overall rates of antigenic drift (<xref ref-type="fig" rid="fig3">Figure 3</xref>, <xref ref-type="table" rid="tbl2">Table 2</xref>) to overall levels of seasonal incidence across influenza lineages, finding a significant correlation between rate of antigenic drift and relative incidence across the four lineages (Pearson correlation, r = 0.97, <italic>p</italic> = 0.041).</p><p>We follow-up this analysis with a more detailed analysis of year-to-year variation in antigenic drift and lineage-specific incidence, comparing incidence in a season to antigenic drift of viruses coming into this season (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). For example, we compare antigenic drift of viruses from 2000 to 2001 to incidence in the 2001/2002 season. Within each virus lineage, we find that years with pronounced antigenic drift tend to show increased incidence (<xref ref-type="fig" rid="fig6">Figure 6</xref>), finding Pearson correlation coefficients of 0.51, 0.29, 0.44 and 0.14 for A/H3N2, A/H1N1, B/Vic and B/Yam respectively. We calculated significance using bootstrap permutation tests finding <italic>p</italic>-values of 0.056, 0.201, 0.097, and 0.341 respectively. We applied a similar bootstrap permutation test to calculate the significance of finding the observed degree of correlation across all four lineages, arriving at a <italic>p</italic>-value of 0.018. The fact that we observe periods of pronounced antigenic drift preceding increased incidence in each of the four influenza lineages suggests a causal relationship, in which antigenic evolution drives increased incidence.<fig id="fig6" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.012</object-id><label>Figure 6.</label><caption><title>Relationship between antigenic drift and seasonal incidence for years 1998 to 2009 in influenza A/H3N2, A/H1N1, B/Vic and B/Yam.</title><p>Antigenic drift from year <italic>i</italic> − 1 to year <italic>i</italic> is compared to incidence in the season <italic>i</italic>/<italic>i</italic> + 1. For example, year-to-year antigenic drift from 2000 to 2001 is measured against incidence in the 2001/2002 season.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.012">http://dx.doi.org/10.7554/eLife.01914.012</ext-link></p></caption><graphic xlink:href="elife01914f006"/></fig></p><p>However, it is possible that if sampling count influences cartographic estimates then a spurious correlation could arise in which years with greater incidence have higher sample counts and artifactually high estimates of drift. We controlled for this possibility by testing to see if viral isolate count influences estimates of year-to-year drift by correlating drift between years <italic>i</italic> and <italic>i</italic> − 1 against the ratio of the number of isolates from year <italic>i</italic> to the number of isolates from year <italic>i</italic> − 1. We found little correlation when combining data across lineages (<xref ref-type="fig" rid="fig7">Figure 7</xref>, Pearson’s <italic>r</italic> = −0.01). We tested significance following the same bootstrap procedure we used to assess the correlation between drift and incidence, finding a <italic>p</italic>-value of 0.514. Separating lineages gave <italic>p</italic>-values of 0.717, 0.246, 0.337, 0.504 for A/H3N2, A/H1N1, B/Vic and B/Yam, respectively. These findings suggest our results to be unbiased with regard to sample count.<fig id="fig7" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.013</object-id><label>Figure 7.</label><caption><title>Relationship between antigenic drift and sample counts for years 1998 to 2011 in influenza A/H3N2, A/H1N1, B/Vic and B/Yam.</title><p>Antigenic drift from year <italic>i</italic> − 1 to year <italic>i</italic> is compared to the ratio of sample counts in year <italic>i</italic> to counts in year <italic>i</italic> − 1. Only comparisons which had one or more samples in years <italic>i</italic> − 1 and <italic>i</italic> were retained, leaving 11 A/H3N2, 7 A/H1N1, 9 B/Vic and 10 B/Yam comparisons. Points are colored according to influenza lineage based on the color scheme in <xref ref-type="fig" rid="fig6">Figure 6</xref>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.013">http://dx.doi.org/10.7554/eLife.01914.013</ext-link></p></caption><graphic xlink:href="elife01914f007"/></fig></p></sec><sec id="s2-4"><title>Conclusions</title><p>Understanding antigenic evolution in seasonal influenza is crucial to our efforts of surveillance and control. Cartographic methods allow complex HI datasets to be compressed to more approachable location-based summaries that quantify antigenic relationships between strains, including relationships not directly measured via HI. In this study, we provide a foundation for evolutionary antigenic cartography, which seeks to simultaneously assess antigenic phenotype and antigenic evolution. We use this approach to characterize competitive dynamics across influenza lineages A/H3N2, A/H1N1, B/Vic and B/Yam and show that antigenic evolution within each lineage drives strain replacement and contributes to seasonal incidence patterns. We find that influenza A/H3N2 evolves faster in antigenic phenotype than A/H1N1, which in turn evolves faster than B/Vic or B/Yam. Consequently, the influenza A/H3N2 virus population turns over more quickly than A/H1N1 or influenza B, exhibiting a smaller effective population size and a ‘spindlier’ phylogenetic tree. Furthermore, we observe a correlation between antigenic drift and viral incidence both across and within influenza lineages. The finding that antigenic evolution correlates with subsequent increased incidence within a lineage suggests a causal role for antigenic drift driving influenza incidence patterns. The correlation between incidence and drift further suggests the possibility of using HI data at the start of an influenza season to predict which lineage will subsequently predominate.</p><p>The statistical framework presented here represents a baseline to which further advancements in modeling antigenic phenotype and evolution may be made. For example, our likelihood-based model facilitates the inclusion of possible covariates affecting immunological titer, which could include experimental factors such as red blood cell type used in the HI assay (<xref ref-type="bibr" rid="bib53">Lin et al., 2012</xref>) and whether oseltamivir is included in the HI reaction (<xref ref-type="bibr" rid="bib52">Lin et al., 2010</xref>). Additionally, this framework should be ideally suited to uncovering genetic determinants of antigenic change, as both the sequence state and antigenic location of internal nodes in the phylogeny may be estimated. In this fashion, it should be possible to correlate sequence substitutions directly to antigenic diffusion. Identifying viruses that will come to predominate in the global virus population while they are still at low frequency remains an enormous challenge. However, combining evolutionary and antigenic information may eventually prove useful in identifying low-frequency, but expanding, lineages of antigenically novel viruses that represent ideal targets for vaccine strain selection.</p></sec></sec><sec id="s3" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Antigenic cartography</title><p>Antigenic characteristics of viral strains are often assessed through immunological assays such as the hemagglutination inhibition (HI) assay (<xref ref-type="bibr" rid="bib42">Hirst, 1943</xref>). At heart, these assays compare the reactivity of one virus strain to antibodies raised against another virus strain via challenge or vaccination. In the case of HI, the measurement of cross-reactivity takes the form of a titer representing the dilution factor at which serum raised against a particular virus ceases to be effective at inhibiting the binding of another virus to red blood cells. These factors are commonly assessed by serial dilution, so that HI titers will form a log series, 40, 80, 160, etc…. Because experimental HI titers typically differ by factors of two, we find it convenient to work in log<sub>2</sub> space and represent the titer of virus <italic>i</italic> against serum <italic>j</italic> as <inline-formula><mml:math id="inf5"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mtext>log</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mtext>HI titer</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, that is a titer of 160 has <italic>H</italic><sub><italic>ij</italic></sub> = 7.32. Due to experimental constraints, most comparisons cannot be made, leading to a sparse observation matrix <inline-formula><mml:math id="inf6"><mml:mrow><mml:mi mathvariant="bold">H</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. Further, measurements are usually interval and truncated, for example inhibition may cease somewhere between the serial titers of 160 and 320, or inhibition may be absent at all titers assayed, suggesting a threshold somewhere between 0 and 40.</p><p>Previous work (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>; <xref ref-type="bibr" rid="bib10">Cai et al., 2010</xref>) has used multidimensional scaling (MDS) to place viruses and sera on an ‘antigenic map’. These methods heuristically optimize locations of viruses and sera by seeking to minimize the sum of squared errors between titers predicted by map locations and observed titers. Antigenic maps produced by these methods have proven useful in categorizing virus phenotypes (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>), but the extension of these methods to integrate genetic data remains notably lacking.</p><p>Here, we follow previous models in representing antigenic locations as points in a low <italic>P</italic>-dimensional antigenic map. One of our initial goals is to find an optimal projection of the high-dimensional distance matrix <bold>H</bold> into this lower dimensional space. We conduct this projection using Bayesian multidimensional scaling (BMDS) (<xref ref-type="bibr" rid="bib68">Oh and Raftery, 2001</xref>) in which we construct a probabilistic model to quantify the fit of a particular configuration of cartographic locations to the observed matrix of serological measurements. Typically, <italic>P</italic> = 2, but higher or lower dimensions may better reflect the data.</p><p>Let <inline-formula><mml:math id="inf7"><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mi mathvariant="script">R</mml:mi><mml:mi>P</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> represent the cartographic location of virus <italic>i</italic> for <italic>i</italic> = 1,…, n, so that <inline-formula><mml:math id="inf8"><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula> for <italic>P</italic> = 2. Similarly, let <bold>y</bold><sub><italic>j</italic></sub> represent the cartographic location of serum <italic>j</italic> for <italic>j</italic> = 1,…, <italic>k</italic>, so that <inline-formula><mml:math id="inf9"><mml:mrow><mml:msub><mml:mi mathvariant="bold">y</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula> for <italic>P</italic> = 2. For notational compactness, we collect together all virus coordinates into an <italic>n</italic> × <italic>P</italic> matrix <inline-formula><mml:math id="inf10"><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula> and all serum coordinates into an <italic>k</italic> × <italic>P</italic> matrix <inline-formula><mml:math id="inf11"><mml:mrow><mml:mi mathvariant="bold">y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="bold">y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="bold">y</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula>. Virus and serum may be isolated from/raised against the same strain and have different cartographic locations, and separate serum isolates raised against the same strain may also have different cartographic locations. This gives a set of distances between virus and serum cartographic locations.<disp-formula id="equ1"><label>(1)</label><mml:math id="m1"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>|</mml:mo><mml:mo>|</mml:mo><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="bold">y</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mo>|</mml:mo><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <inline-formula><mml:math id="inf12"><mml:mrow><mml:mo>|</mml:mo><mml:mo>|</mml:mo><mml:mo>⋅</mml:mo><mml:mo>|</mml:mo><mml:msub><mml:mo>|</mml:mo><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is an <italic>L</italic><sub>2</sub> norm.</p><p>Traditional approaches to antigenic cartography (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>) begin by defining immunological distance as<disp-formula id="equ2"><label>(2)</label><mml:math id="m2"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <italic>H</italic><sub><italic>ij</italic></sub> is the log<sub>2</sub> titer of virus <italic>i</italic> against serum <italic>j</italic> and serum potency <inline-formula><mml:math id="inf13"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>max</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> is fixed. In following multidimensional scaling, these approaches attempt to optimize over unknown <bold>X</bold> and <bold>Y</bold> such that<disp-formula id="equ3"><label>(3)</label><mml:math id="m3"><mml:mrow><mml:munder><mml:mstyle displaystyle="true"><mml:mo>∑</mml:mo></mml:mstyle><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mi mathvariant="script">I</mml:mi></mml:mrow></mml:munder><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></disp-formula>is minimized, where, <inline-formula><mml:math id="inf14"><mml:mrow><mml:mi mathvariant="script">I</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>:</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mtext> is measured</mml:mtext></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. In the case of threshold measurements, this error function is modified slightly; see <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> for further details.</p><p>Here, we instead assume a probabilistic interpretation in which an observed titer is normally distributed around its cartographic expectation with variance <inline-formula><mml:math id="inf15"><mml:mrow><mml:msup><mml:mi>φ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>,<disp-formula id="equ4"><label>(4)</label><mml:math id="m4"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:msup><mml:mi>φ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Consequently, the likelihood of observing an exact titer given the placement of antigenic locations is<disp-formula id="equ5"><label>(5)</label><mml:math id="m5"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>|</mml:mo></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mi>φ</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <inline-formula><mml:math id="inf16"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> represents the standard normal probability density function (PDF). Previous BMDS has employed a sampling density truncated to strictly positive quantities since <italic>d</italic><sub><italic>ij</italic></sub> are directly observed, non-negative quantities. In the antigenic setting, these remain random and can be negative since neither <italic>s</italic><sub><italic>j</italic></sub> is known nor is <italic>H</italic><sub><italic>ij</italic></sub> observed with much precision.</p><p>HI assays sometimes show no inhibition at all measured titrations, for example a measurement can be reported as ‘&lt;40’. In this case, the likelihood of observing the threshold measurement follows the cumulative density of the lower tail of the normal distribution.<disp-formula id="equ6"><label>(6)</label><mml:math id="m6"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⌟</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mtext>Φ</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mi>φ</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <inline-formula><mml:math id="inf17"><mml:mrow><mml:mtext>Φ</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> represents the standard normal cumulative distribution function (CDF). Although it is simplest to assume that immunological measurements represent point estimates, it seems more natural to assume that the threshold for inhibition occurs between two titers, for example we observe inhibition at 1:160 dilution and no inhibition at 1:320 dilution. Rather than taking the HI titer as 160, we can instead treat this as an interval measurement, assuming that the exact titer for inhibition would occur somewhere between 160 and 320. HI titers are usually reported as the highest titer that successfully inhibits virus binding, so that in this case, we calculate the likelihood of an interval measurement as<disp-formula id="equ7"><label>(7)</label><mml:math id="m7"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⊔</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mtext>Φ</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>φ</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:mtext>Φ</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mi>φ</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>These likelihoods are illustrated in <xref ref-type="fig" rid="fig8">Figure 8</xref>. Throughout our analyses, we use interval likelihoods <inline-formula><mml:math id="inf18"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⊔</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> rather than point likelihoods <inline-formula><mml:math id="inf19"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>|</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> unless otherwise noted.<fig id="fig8" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.014</object-id><label>Figure 8.</label><caption><title>Likelihood of HI titers in the BMDS model.</title><p>Here, we show the likelihoods of observing three different outcomes given <inline-formula><mml:math id="inf20"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf21"><mml:mrow><mml:mi>φ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.95</mml:mn></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf22"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mtext>log</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1280</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>10.32</mml:mn></mml:mrow></mml:math></inline-formula>. The likelihood of observing a threshold titer of ‘&lt;40’ is equal to the lower tail of the probability density function <inline-formula><mml:math id="inf23"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⌟</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>5.32</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.146</mml:mn></mml:mrow></mml:math></inline-formula>. The likelihood of observing a point measurement with an exact inhibiting titer of ‘90.5’ is equal to the density function <inline-formula><mml:math id="inf24"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>|</mml:mo></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>6.5</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.413</mml:mn></mml:mrow></mml:math></inline-formula>. The likelihood of observing an interval measurement with an inhibiting titer somewhere between ‘160’ and ‘320’ is equal to <inline-formula><mml:math id="inf25"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⊔</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>7.32</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.129.</mml:mn></mml:mrow></mml:math></inline-formula></p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.014">http://dx.doi.org/10.7554/eLife.01914.014</ext-link></p></caption><graphic xlink:href="elife01914f008"/></fig></p><p>We calculate the overall likelihood by multiplying probabilities of individual measurements<disp-formula id="equ8"><label>(8)</label><mml:math id="m8"><mml:mrow><mml:mi>L</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mstyle displaystyle="true"><mml:mo>∏</mml:mo></mml:mstyle><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mi mathvariant="script">I</mml:mi></mml:mrow></mml:munder><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>using probability functions <inline-formula><mml:math id="inf26"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>|</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf27"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⌟</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf28"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">⊔</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as appropriate. We begin by assuming independent, diffuse normal priors on virus and serum locations.<disp-formula id="equ9"><mml:math id="m9"><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">m</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">Σ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula><disp-formula id="equ10"><label>(9)</label><mml:math id="m10"><mml:mrow><mml:msub><mml:mi mathvariant="bold">y</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">m</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">Σ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <inline-formula><mml:math id="inf29"><mml:mrow><mml:mi mathvariant="bold">m</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf30"><mml:mi mathvariant="bold">Σ</mml:mi></mml:math></inline-formula> is a diagonal matrix with diagonal elements all equal to 10,000.</p></sec><sec id="s4-2"><title>Virus avidity and serum potency</title><p>The preceding model represents immunological distance as a drop in titer against the most reactive comparison for a particular serum. However, this model may be biased in some circumstances. In one example, if a particular serum <italic>j</italic> is only measured against distant viruses, its maximum titer will be artificially low and the likelihoods concerning this serum will appear poor. To address this issue, we relax the assumption of fixed <italic>s</italic><sub><italic>j</italic></sub> values and treat the expected log<sub>2</sub> titer when <inline-formula><mml:math id="inf31"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></inline-formula> as a random variable. In this case, <italic>H</italic><sub><italic>ij</italic></sub> still follows <xref ref-type="disp-formula" rid="equ4">Equation 4</xref> with expectation <inline-formula><mml:math id="inf32"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, but the vector of ‘serum potencies’ s = (<italic>s</italic><sub>1</sub>,…, <italic>s</italic><sub><italic>k</italic></sub>) is random and estimated rather than fixed. We assume that <italic>s</italic><sub><italic>j</italic></sub> values are hierarchically distributed according to a normal distribution. We take an Empirical Bayesian approach in specifying the mean and variance of this distribution, set to the empirical mean and empirical variance of the set of maximum titers across sera <inline-formula><mml:math id="inf33"><mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtext>max</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>:</mml:mo><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. This formulation assumes that particular sera are more reactive in general than other sera.</p><p>Additionally, we follow the same logic and assume that some virus isolates are more reactive than other virus isolates and include a parameter for ‘virus avidity’ <italic>v</italic><sub><italic>i</italic></sub> representing the general level of reactivity across HI assays. With virus avidity included, observed titers follow<disp-formula id="equ11"><label>(10)</label><mml:math id="m11"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo>−</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:msup><mml:mi>φ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>and the vector of virus avidities <italic>v</italic><sub><italic>i</italic></sub> for <italic>i</italic> = 1,…, <italic>n</italic> is estimated in an analogous hierarchical fashion, with <bold>v</bold> normally distributed with mean and variance equal to the empirical mean and variance of the set of maximum titers across viruses <inline-formula><mml:math id="inf34"><mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtext>max</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>:</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>.</p></sec><sec id="s4-3"><title>Drift model of antigenic evolution</title><p>As presented, multiple configurations of virus and serum locations <bold>X</bold> and <bold>Y</bold> will give the same likelihood of an observed data matrix <bold>H</bold>. An example of this phenomenon is shown in <xref ref-type="fig" rid="fig9">Figure 9</xref>. In this case, it is impossible to determine from the HI data at hand whether the blue and yellow viruses are antigenically similar (<xref ref-type="fig" rid="fig9">Figure 9A</xref>) or antigenically divergent (<xref ref-type="fig" rid="fig9">Figure 9B</xref>). This presents an issue of model identifiability, where absolute, as opposed to relative, antigenic locations cannot be determined from observing the serological data alone. Thus, in order to achieve a more interpretable model we impose a weak prior on global locations. In influenza, it’s clear that antigenic distance between strains increases with time (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>; <xref ref-type="bibr" rid="bib10">Cai et al., 2010</xref>). To capture this, we replace our previous diffuse prior with an informed prior in which the expected location of viruses and sera increases with date of sampling along dimension one, and each virus and serum location follows an independent normal distribution centered around this temporal expectation, so that<disp-formula id="equ12"><mml:math id="m12"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula><disp-formula id="equ13"><label>(11)</label><mml:math id="m13"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>t</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <italic>t</italic> is the difference between the date of the indexed virus or serum and the date of the earliest sampled virus or serum, and other dimensions follow <inline-formula><mml:math id="inf35"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf36"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> for <italic>m</italic> ≥ 2. Thus, this model assumes that virus and serum locations drift in a line across the antigenic map at rate <italic>μ</italic>. The parameter <inline-formula><mml:math id="inf37"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> determines the breadth of the cloud of virus locations at each point in time, while <inline-formula><mml:math id="inf38"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> determines the breadth of the cloud of serum locations.<fig id="fig9" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.015</object-id><label>Figure 9.</label><caption><title>Schematic antigenic map with three viruses and two sera.</title><p>(<bold>A</bold>) Map with virus 1 and virus 3 antigenically similar. (<bold>B</bold>) Map with virus 1 and virus 3 antigenically divergent. Virus 1 is shown in blue, virus 2 is shown in red and virus 3 is shown in yellow. Virus isolates are represented by filled circles, sera raised against viruses are shown as open circles and map distances <inline-formula><mml:math id="inf39"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are shown as solid lines connecting viruses and sera. Sera from virus 1 is compared against viruses 1 and 2, while sera from virus 2 is compared against viruses 2 and 3. Configurations (<bold>A</bold>) and (<bold>B</bold>) represent cartographic models that would give equal likelihoods to a set of serological data <inline-formula><mml:math id="inf40"><mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>22</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mn>32</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.015">http://dx.doi.org/10.7554/eLife.01914.015</ext-link></p></caption><graphic xlink:href="elife01914f009"/></fig></p></sec><sec id="s4-4"><title>Phylogenetic diffusion model of antigenic evolution</title><p>We simultaneously model antigenic locations and genetic relatedness by assuming that virus locations are influenced by evolution following a Brownian motion process (<xref ref-type="bibr" rid="bib48">Lemey et al., 2010</xref>). To do this, we replace the previous prior specifying independent virus locations with a prior that incorporates covariance based on shared evolutionary history.<disp-formula id="equ14"><label>(12)</label><mml:math id="m14"><mml:mrow><mml:mi mathvariant="bold">X</mml:mi><mml:mo>∼</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>t</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>⋮</mml:mo></mml:mtd><mml:mtd><mml:mo>⋮</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>t</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mtext> </mml:mtext><mml:mtext>Evolutionary Brownian Process</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>for <italic>P</italic> = 2, where, <inline-formula><mml:math id="inf41"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volatility parameter of the Brownian motion over virus locations and <italic>τ</italic> is a phylogeny specifying tree topology and branch lengths. Thus, viruses that are genetically similar are induced to have prior locations close to one another on the antigenic map. In the evolutionary Brownian process, the tips of the phylogeny <italic>τ</italic> correspond to the set of virus locations (<bold>x</bold><sub>1</sub>,…, <bold>x</bold><sub><italic>n</italic></sub>), and the probability of observing tip locations depends on the locations of internal nodes (<bold>x</bold><sub><italic>n</italic>+1</sub>,…, <bold>x</bold><sub>2<italic>n−</italic>2</sub>) and on the location of the root node <bold>x</bold><sub>2<italic>n−</italic>2</sub>. This process assumes that a virus location <bold>x</bold><sub><italic>i</italic></sub> follows from the location of its parent virus <bold>x</bold><sub><italic>f</italic><bold>(</bold><italic>i</italic>)</sub>, and with the addition of drift along dimension 1, is distributed as<disp-formula id="equ15"><label>(13)</label><mml:math id="m15"><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mn>0</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo><mml:mo>+</mml:mo><mml:mi mathvariant="script">N</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="bold">x</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mtext> </mml:mtext><mml:mi mathvariant="bold">Σ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>for <italic>P</italic> = 2, where, <italic>f</italic><bold>(</bold><italic>i</italic>) is a function that maps nodes to parental nodes, <italic>d</italic><sub><italic>i</italic></sub> is the length of the branch connecting virus <italic>i</italic> to parent virus <italic>f</italic><bold>(</bold><italic>i</italic>), and <inline-formula><mml:math id="inf42"><mml:mi mathvariant="bold">Σ</mml:mi></mml:math></inline-formula> is a diagonal matrix with diagonal elements all equal to <inline-formula><mml:math id="inf43"><mml:mrow><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>. The root virus location <bold>x</bold><sub>2<italic>n−</italic>1</sub> is assumed to follow a normal distribution with expectation <inline-formula><mml:math id="inf44"><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mtext> </mml:mtext><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:math></inline-formula> for <italic>P</italic> = 2 and variance determined by the diffusion volatility <inline-formula><mml:math id="inf45"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib48">Lemey et al., 2010</xref>). The probability of virus locations <inline-formula><mml:math id="inf46"><mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>|</mml:mo><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> is determined through analytical integration across internal states following the methods introduced in (<xref ref-type="bibr" rid="bib48">Lemey et al., 2010</xref>). This formulation corresponds to a Wiener process with drift, in which the drift term <italic>μ</italic> only influences the expected states of nodes along the phylogeny, but does not influence the covariance structure among these nodes, which remains the same as it does in a standard Wiener process (<xref ref-type="bibr" rid="bib9">Borodin and Salminen, 2002</xref>). This allows the separation in <xref ref-type="disp-formula" rid="equ14">Equation 12</xref> between drift terms affecting only expectations and the evolutionary Brownian process that includes covariance among virus locations (<bold>x</bold><sub>1</sub>,…, <bold>x</bold><sub><italic>n</italic></sub>).</p><p>In this study, the phylogenetic tree <italic>τ</italic> is estimated using sequence data for viruses 1,…, <italic>n</italic> according to well-established methods implemented in the software package BEAST (<xref ref-type="bibr" rid="bib20">Drummond et al., 2012</xref>).</p></sec><sec id="s4-5"><title>Posterior inference</title><p>Top-level priors for <inline-formula><mml:math id="inf47"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>φ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, <italic>μ</italic>, <inline-formula><mml:math id="inf48"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf49"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> are assumed to follow diffuse Gamma(<italic>a</italic>, <italic>b</italic>) distributions with <italic>a</italic> = 0.001 and <italic>b</italic> = 0.001. These diffuse priors were chosen to be non-informative and provide little-to-no weight on the resulting posterior distributions. Under the full model, the posterior probability of observing virus and serum locations given immunological data is factored.<disp-formula id="equ16"><label>(14)</label><mml:math id="m16"><mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">y</mml:mi><mml:mo>|</mml:mo><mml:mi mathvariant="bold">H</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∝</mml:mo><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">H</mml:mi><mml:mo>|</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">v</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext> </mml:mtext><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>|</mml:mo><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext> </mml:mtext><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">y</mml:mi><mml:mo>|</mml:mo><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext> </mml:mtext><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="bold">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">v</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>We sample from this posterior distribution using the MCMC procedures implemented in the software package BEAST (<xref ref-type="bibr" rid="bib20">Drummond et al., 2012</xref>). Metropolis–Hastings proposals include transition kernels that translate individual virus and serum locations <bold>x</bold><sub><italic>i</italic></sub> and <bold>y</bold><sub><italic>j</italic></sub> and individual virus avidities <italic>v</italic><sub><italic>i</italic></sub> and serum potencies s<sub><italic>j</italic></sub>, and other transition kernels that scale the entire set of virus and serum locations <bold>X</bold> and <bold>Y</bold> and that scale parameters <italic>φ</italic>, <italic>μ</italic>, <inline-formula><mml:math id="inf50"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf51"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. For the present analysis, a two-step approach was taken to sample phylogenies, where a posterior sample of phylogenies was gathered using sequence data and then, in the cartographic analysis, trees from this set were randomly proposed and accepted following the Metropolis–Hastings algorithm (<xref ref-type="bibr" rid="bib70">Pagel et al., 2004</xref>).</p></sec><sec id="s4-6"><title>Genetic, antigenic and surveillance data</title><p>We compiled an antigenic dataset of hemagglutination inhibition (HI) measurements of virus isolates against post-infection ferret sera for influenza A/H3N2 by collecting data from previous publications (<xref ref-type="bibr" rid="bib27">Hay and Gregory, 2001</xref>; <xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>; <xref ref-type="bibr" rid="bib76">Russell et al., 2008</xref>; <xref ref-type="bibr" rid="bib5">Barr et al., 2010</xref>), NIMR vaccine strain selection reports for 2002 and 2008–2012 (<xref ref-type="bibr" rid="bib28">Hay et al., 2002</xref>; <xref ref-type="bibr" rid="bib35">2008a</xref>, <xref ref-type="bibr" rid="bib32">2009a</xref>; <xref ref-type="bibr" rid="bib55">McCauley et al., 2010a</xref>; <xref ref-type="bibr" rid="bib58">2010b</xref>, <xref ref-type="bibr" rid="bib59">2011b</xref>, <xref ref-type="bibr" rid="bib57">2012</xref>) and the February 2011 VRBPAC report (<xref ref-type="bibr" rid="bib15">Cox, 2011</xref>). We queried the Influenza Research Database (<xref ref-type="bibr" rid="bib80">Squires et al., 2012</xref>) and the EpiFlu Database (<xref ref-type="bibr" rid="bib8">Bogner et al., 2006</xref>) for HA nucleotide sequences by matching strain names, for example A/HongKong/1/1968, and only strains for which sequence was present were retained. If a strain had multiple sequences in the databases, we preferentially kept the IRD sequence and preferentially kept the longest sequence in IRD. Many strains had full length HA sequences, while other strains only possessed HA1 sequences. Sequences were aligned using MUSCLE v3.7 under default parameters (<xref ref-type="bibr" rid="bib21">Edgar, 2004</xref>). This dataset had 2051 influenza isolates (present as either virus or serum in HI comparisons) dating from 1968 to 2011. However, the majority of isolates were present from 2002 to 2007. Because we are interested in longer-term antigenic evolution, we subsampled the data to have at most 20 virus isolates per year, preferentially keeping those isolates with more antigenic comparisons. We then kept only those serum isolates that are relatively informative to the antigenic placement of viruses, dropping serum isolates that are compared to four or fewer different virus isolates. This censoring left 402 virus isolates, 519 serum isolates and 10,059 HI measurements. Each virus isolate was compared to an average of 21.9 serum isolates, and each serum isolate was compared to an average of 18.0 virus isolates.</p><p>Antigenic data for influenza A/H1N1 was collected from previous publications (<xref ref-type="bibr" rid="bib45">Kendal et al., 1978</xref>; <xref ref-type="bibr" rid="bib63">Nakajima et al., 1979</xref>; <xref ref-type="bibr" rid="bib82">Webster et al., 1979</xref>; <xref ref-type="bibr" rid="bib64">Nakajima et al., 1981</xref>; <xref ref-type="bibr" rid="bib12">Chakraverty et al., 1982</xref>; <xref ref-type="bibr" rid="bib71">Pereira and Chakraverty, 1982</xref>; <xref ref-type="bibr" rid="bib14">Cox et al., 1983</xref>; <xref ref-type="bibr" rid="bib16">Daniels et al., 1985</xref>; <xref ref-type="bibr" rid="bib13">Chakraverty et al., 1986</xref>; <xref ref-type="bibr" rid="bib74">Raymond et al., 1986</xref>; <xref ref-type="bibr" rid="bib81">Stevens et al., 1987</xref>; <xref ref-type="bibr" rid="bib19">Donatelli et al., 1993</xref>; <xref ref-type="bibr" rid="bib27">Hay and Gregory, 2001</xref>; <xref ref-type="bibr" rid="bib17">Daum et al., 2002</xref>; <xref ref-type="bibr" rid="bib60">McDonald et al., 2007</xref>; <xref ref-type="bibr" rid="bib5">Barr et al., 2010</xref>) and NIMR vaccine strain selection reports for 2002–2010 (<xref ref-type="bibr" rid="bib28">Hay et al., 2002</xref>, <xref ref-type="bibr" rid="bib35">2008a</xref>, <xref ref-type="bibr" rid="bib32">2009a</xref>; <xref ref-type="bibr" rid="bib55">McCauley et al., 2010</xref>; <xref ref-type="bibr" rid="bib29">Hay et al., 2003</xref>, <xref ref-type="bibr" rid="bib30">2004</xref>, <xref ref-type="bibr" rid="bib31">2005a</xref>, <xref ref-type="bibr" rid="bib36">2005b</xref>, <xref ref-type="bibr" rid="bib33">2006a</xref>, <xref ref-type="bibr" rid="bib37">2006b</xref>, <xref ref-type="bibr" rid="bib34">2007a</xref>, <xref ref-type="bibr" rid="bib38">2007b</xref>, <xref ref-type="bibr" rid="bib39">2008b</xref>). The same procedure that was followed for A/H3N2 was repeated to match sequence data and to subsample antigenic comparisons. This procedure yielded 115 virus isolates, 77 serum isolates, and 1882 HI measurements over the course of 1977–2009. Each virus isolate was compared to an average of 10.0 serum isolates, and each serum isolate was compared to an average of 16.2 virus isolates.</p><p>Antigenic comparisons for influenza B/Victoria were collated from previous publications (<xref ref-type="bibr" rid="bib75">Rota et al., 1990</xref>; <xref ref-type="bibr" rid="bib27">Hay and Gregory, 2001</xref>; <xref ref-type="bibr" rid="bib61">Muyanga et al., 2001</xref>; <xref ref-type="bibr" rid="bib78">Shaw et al., 2002</xref>; <xref ref-type="bibr" rid="bib3">Ansaldi et al., 2004</xref>; <xref ref-type="bibr" rid="bib72">Puzelli et al., 2004</xref>; <xref ref-type="bibr" rid="bib84">Xu et al., 2004</xref>; <xref ref-type="bibr" rid="bib4">Barr et al., 2006</xref>; <xref ref-type="bibr" rid="bib18">Daum et al., 2006</xref>; <xref ref-type="bibr" rid="bib51">Lin et al., 2007</xref>) and vaccine strain selection reports for 2002–2012 (<xref ref-type="bibr" rid="bib28">Hay et al., 2002</xref>, <xref ref-type="bibr" rid="bib35">2008a</xref>, <xref ref-type="bibr" rid="bib32">2009a</xref>; <xref ref-type="bibr" rid="bib55">McCauley et al., 2010a</xref>; <xref ref-type="bibr" rid="bib58">2010b</xref>, <xref ref-type="bibr" rid="bib59">2011b</xref>, <xref ref-type="bibr" rid="bib57">2012</xref>; <xref ref-type="bibr" rid="bib29">Hay et al., 2003</xref>, <xref ref-type="bibr" rid="bib30">2004</xref>, <xref ref-type="bibr" rid="bib31">2005a</xref>, <xref ref-type="bibr" rid="bib36">2005b</xref>, <xref ref-type="bibr" rid="bib33">2006a</xref>, <xref ref-type="bibr" rid="bib37">2006b</xref>, <xref ref-type="bibr" rid="bib34">2007a</xref>, <xref ref-type="bibr" rid="bib38">2007b</xref>; <xref ref-type="bibr" rid="bib26">Gust et al., 2006</xref>; <xref ref-type="bibr" rid="bib40">Hay et al., 2009a</xref>; <xref ref-type="bibr" rid="bib56">McCauley et al., 2011b</xref>). Here, the sequence matching and subsampling procedure yielded 179 virus isolates, 70 serum isolates and 2003 HI measurements over the course of 1986–2011. Each virus isolate was compared to an average of 6.5 serum isolates, and each serum isolate was compared to an average of 16.7 virus isolates.</p><p>Antigenic comparisons for influenza B/Yamagata were collected from previous publications (<xref ref-type="bibr" rid="bib44">Kanegae et al., 1990</xref>; <xref ref-type="bibr" rid="bib75">Rota et al., 1990</xref>; <xref ref-type="bibr" rid="bib65">Nakajima et al., 1992</xref>; <xref ref-type="bibr" rid="bib67">Nerome et al., 1998</xref>; <xref ref-type="bibr" rid="bib27">Hay and Gregory, 2001</xref>; <xref ref-type="bibr" rid="bib61">Muyanga et al., 2001</xref>; <xref ref-type="bibr" rid="bib62">Nakagawa et al., 2002</xref>; <xref ref-type="bibr" rid="bib78">Shaw et al., 2002</xref>; <xref ref-type="bibr" rid="bib1">Abed et al., 2003</xref>; <xref ref-type="bibr" rid="bib2">Ansaldi et al., 2003</xref>, <xref ref-type="bibr" rid="bib3">2004</xref>; <xref ref-type="bibr" rid="bib54">Matsuzaki et al., 2004</xref>; <xref ref-type="bibr" rid="bib72">Puzelli et al., 2004</xref>; <xref ref-type="bibr" rid="bib84">Xu et al., 2004</xref>; <xref ref-type="bibr" rid="bib4">Barr et al., 2006</xref>; <xref ref-type="bibr" rid="bib18">Daum et al., 2006</xref>; <xref ref-type="bibr" rid="bib51">Lin et al., 2007</xref>) and vaccine strain selection reports for 2002–2012 (<xref ref-type="bibr" rid="bib28">Hay et al., 2002</xref>, <xref ref-type="bibr" rid="bib35">2008a</xref>, <xref ref-type="bibr" rid="bib32">2009a</xref>; <xref ref-type="bibr" rid="bib55">McCauley et al., 2010a</xref>; <xref ref-type="bibr" rid="bib58">2010b</xref>, <xref ref-type="bibr" rid="bib59">2011b</xref>, <xref ref-type="bibr" rid="bib57">2012</xref>; <xref ref-type="bibr" rid="bib29">Hay et al., 2003</xref>, <xref ref-type="bibr" rid="bib30">2004</xref>, <xref ref-type="bibr" rid="bib31">2005a</xref>, <xref ref-type="bibr" rid="bib36">2005b</xref>, <xref ref-type="bibr" rid="bib33">2006a</xref>, <xref ref-type="bibr" rid="bib37">2006b</xref>, <xref ref-type="bibr" rid="bib34">2007a</xref>, <xref ref-type="bibr" rid="bib38">2007b</xref>; <xref ref-type="bibr" rid="bib26">Gust et al., 2006</xref>; <xref ref-type="bibr" rid="bib40">Hay et al., 2009a</xref>; <xref ref-type="bibr" rid="bib56">McCauley et al., 2011b</xref>). For B/Yamagata, the matching and subsampling procedure resulted in 174 virus isolates, 69 serum isolates and 1962 HI measurements over the course of 1987–2011. Each virus isolate was compared to an average of 6.9 serum isolates, and each serum isolate was compared to an average of 17.3 virus isolates.</p><p>Surveillance data was obtained from the Centers of Disease Control and Prevention FluView Influenza Reports from the yearly summaries of influenza seasons 1997–1998 to 2010–2011 (<xref ref-type="bibr" rid="bib11">Centers for Disease Control and Prevention, 2012</xref>). As an example, one report states ‘collaborating laboratories in the United States tested 195,744 respiratory specimens for influenza viruses, 27,682 (14%) of which were positive. Of these, 18,175 (66%) were positive for influenza A viruses, and 9507 (34%) were positive for influenza B viruses. Of the 18,175 specimens positive for influenza A viruses, 7631 (42%) were subtyped; 6762 (87%) of these were seasonal influenza A (H1N1) viruses, and 869 (13%) were influenza A (H3N2) viruses’. In this case, we estimate the relative proportion of A/H3N2 of the four lineages as 0.66 × 0.13 = 0.09. Similar calculations were performed for A/H1N1, B/Vic and B/Yam.</p></sec><sec id="s4-7"><title>Implementation</title><p>Phylogenetic trees were estimated for A/H3N2, A/H1N1, B/Vic, and B/Yam using BEAST (<xref ref-type="bibr" rid="bib20">Drummond et al., 2012</xref>) and incorporated the SRD06 nucleotide substitution model (<xref ref-type="bibr" rid="bib77">Shapiro et al., 2006</xref>), a coalescent demographic model with constant effective population size and a strict molecular clock across branches. MCMC was run for 60 million steps and trees were sampled every 50,000 steps after allowing a burn-in of 10 million steps, yielding a total sample of 2000 trees. These trees were treated as a discrete set of possibilities when subsequently sampled in the BMDS analysis (<xref ref-type="bibr" rid="bib70">Pagel et al., 2004</xref>). However, it would be possible to jointly sample from sequence data and serological data using these methods.</p><p>MCMC was used to sample virus locations <bold>X</bold>, serum locations <bold>Y</bold>, virus avidities <bold>v</bold>, serum potencies <bold>s</bold>, MDS precision <inline-formula><mml:math id="inf52"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>φ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, antigenic drift rate <italic>μ</italic>, virus location precision <inline-formula><mml:math id="inf53"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, serum location precision <inline-formula><mml:math id="inf54"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msubsup><mml:mi>σ</mml:mi><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, and phylogenetic tree <italic>τ</italic>. MCMC chains were run for 500 million steps and parameter values sampled every 200,000 steps after a burn-in of 100 million steps, yielding a total of 2000 MCMC samples. In all cases, when drift parameter <italic>μ</italic> was included the MCMC chain mixed well and arrived at the same estimated posterior distribution from different starting points. However, without drift parameter <italic>μ</italic>, maps for A/H3N2 showed some degree of metastability, where some chains would converge on one solution and other chains would converge on a different solution. We favor models that include <italic>μ</italic>, because its inclusion, in addition to correcting most identifiability issues, yields much improved mixing of antigenic locations.</p><p>There is some difficulty in summarizing posterior cartographic samples, as sampled virus and serum locations represent only relative quantities, and because of this, over the course of the MCMC, virus locations may shift. Our prior on virus and serum locations remove much of this issue, orienting the antigenic map along dimension 1 and fixing it to begin at the origin. However, local isometries are often still a problem. For example, in A/H3N2 the HK/68, EN/72 and VI/75 clusters may rotate in relation to other clusters. Consequently, it may be difficult to fully align MCMC samples using Procrustes analysis. For the present study, we take a simple approach and sample a single MCMC step and visualize the antigenic locations at this state (<xref ref-type="fig" rid="fig2">Figure 2</xref>, <xref ref-type="fig" rid="fig3">Figure 3</xref>). Then, for specific quantities of interest, like rate of antigenic drift and rate of diffusion at different points along the phylogeny, we calculate the quantity across MCMC samples to yield an expectation and a credible interval. This approach accurately characterizes uncertainty that may be hidden in an analysis of a single antigenic map.</p><p>We summarize diffusion paths of viral lineages (<xref ref-type="fig" rid="fig2">Figure 2</xref>, <xref ref-type="fig" rid="fig3">Figure 3</xref>) by taking each virus and reconstructing <italic>x</italic> and <italic>y</italic> locations along antigenic dimensions 1 and 2 backward through time. We use MCMC to sample tip locations, but when outputting trees sample internal node locations using a peeling algorithm as described in <xref ref-type="bibr" rid="bib73">Pybus et al. (2012)</xref>. Thus, after the MCMC is finished, we have a posterior sample of 2000 trees each tagged with estimated tip locations and internal node locations. We post-processed each posterior tree by conducting a linear interpolation between parent–child node locations to arrive at <italic>x</italic> and <italic>y</italic> values at intervals of 0.05 years for each virus. Then, for each interval, <italic>x</italic> and <italic>y</italic> values are averaged across the sample of posterior trees. We draw lines between these locations to approximate mean posterior diffusion paths. As virus lineages coalesce backwards through time down the phylogeny these diffusion paths will also coalesce.</p></sec><sec id="s4-8"><title>Comparison with previous results</title><p>Here, we attempt to compare antigenic locations inferred by our BMDS model to antigenic locations previously inferred by the error minimization methods of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, referred to here as antigenic cartography by MDS. For this comparison, we use exactly the same HI data used to produce the results in <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, consisting of 273 virus isolates, 79 serum isolates and a total of 4252 HI measurements taken between 1968 and 2003. We begin with a BMDS analog of the antigenic model used in <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, where serum potencies are taken as the maximum titer of a particular ferret serum and the expected log<sub>2</sub> drop in HI titer is proportional to Euclidean distance between virus and serum locations. To bring models into further alignment, we use a Uniform (−100, 100) distribution over virus locations and serum locations. Unsurprisingly, we find that this BMDS model produces results that are strongly congruent with MDS results (<xref ref-type="fig" rid="fig10">Figure 10</xref>, <xref ref-type="supplementary-material" rid="SD3-data">Figure 10—source data 1</xref>). Antigenic cluster locations are consistent between methods (<xref ref-type="fig" rid="fig10">Figure 10A–B</xref>) and antigenic distances between pairs of viruses are consistent between temporally similar and temporally divergent viruses (<xref ref-type="fig" rid="fig10">Figure 10C–E</xref>), suggesting that the resulting maps are consistent at both local and global scales. Credible intervals of antigenic distances for the BMDS model remain narrow across the temporal spectrum (<xref ref-type="fig" rid="fig10">Figure 10C–E</xref>), implying a fair degree of rigidity to the map.<fig id="fig10" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.016</object-id><label>Figure 10.</label><caption><title>Comparison of A/H3N2 antigenic locations estimated by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> using MDS and an equivalent BMDS model.</title><p>(<bold>A</bold>) MDS antigenic locations, reoriented so that the primary dimension lies on the <italic>x</italic>-axis rather than on the <italic>y</italic>-axis as in Figure 1 of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. (<bold>B</bold>) A posterior sample of antigenic locations from an equivalent BMDS model. In (<bold>A</bold>) and (<bold>B</bold>), viruses are shown as colored circles, with color denoting antigenic cluster inferred by (<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>), and sera are shown as gray points. (<bold>C</bold>) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (<bold>D</bold>) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (<bold>E</bold>) Antigenic distances between 750 random pairs of viruses determined for both methods. In (<bold>C</bold>), (<bold>D</bold>) and (<bold>E</bold>) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and serum potencies fixed at maximum titer values.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.016">http://dx.doi.org/10.7554/eLife.01914.016</ext-link></p><p><supplementary-material id="SD3-data"><object-id pub-id-type="doi">10.7554/eLife.01914.017</object-id><label>Figure 10—source data 1.</label><caption><title>This tab-delimited text file lists every virus and serum in <xref ref-type="fig" rid="fig10">Figure 10</xref>, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.017">http://dx.doi.org/10.7554/eLife.01914.017</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s003.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f010"/></fig></p><p><xref ref-type="bibr" rid="bib79">Smith et al. 2004</xref> show that there exist at least two solutions in their assignment of antigenic locations, involving the rotation of clusters HK/68, EN/72 and VI/75 (shown in Figure S2 of [<xref ref-type="bibr" rid="bib79">Smith et al., 2004</xref>]). We observe the same metastable behavior in our analysis; some MCMC chains converge on the solution shown in <xref ref-type="fig" rid="fig10">Figure 10B</xref>, while other MCMC chains converge on the alternative solution shown in <xref ref-type="fig" rid="fig11">Figure 11B</xref>. The distribution of likelihood values appears highly similar between these two solutions, suggesting that they represent global optima. The rotation of the HK/68, EN/72, and VI/75 clusters creates a map that bends slightly, so that temporally distant viruses appear closer in the rotated solution than in the original solution (<xref ref-type="fig" rid="fig11">Figure 11C–E</xref>, <xref ref-type="supplementary-material" rid="SD4-data">Figure 11—source data 1</xref>). In this case, it is clear that the solutions are locally consistent between viruses up to ∼15 years divergent, even if there is some degree of global flexibility. <fig id="fig11" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.018</object-id><label>Figure 11.</label><caption><title>Comparison of A/H3N2 antigenic locations estimated by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> using MDS and an equivalent BMDS model under an alternative solution.</title><p>(<bold>A</bold>) MDS antigenic locations, reoriented so that the primary dimension lies on the <italic>x</italic>-axis rather than on the <italic>y</italic>-axis as in Figure 1 of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. (<bold>B</bold>) A posterior sample of antigenic locations from an equivalent BMDS model that has converged on the alternative solution. In (<bold>A</bold>) and (<bold>B</bold>), viruses are shown as colored circles, with color denoting antigenic cluster inferred by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, and sera are shown as gray points. (<bold>C</bold>) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (<bold>D</bold>) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (<bold>E</bold>) Antigenic distances between 750 random pairs of viruses determined for both methods. In (<bold>C</bold>), (<bold>D</bold>) and (<bold>E</bold>) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and serum potencies fixed at maximum titer values.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.018">http://dx.doi.org/10.7554/eLife.01914.018</ext-link></p><p><supplementary-material id="SD4-data"><object-id pub-id-type="doi">10.7554/eLife.01914.019</object-id><label>Figure 11—source data 1.</label><caption><title>This tab-delimited text file lists every virus and serum in <xref ref-type="fig" rid="fig11">Figure 11</xref>, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.019">http://dx.doi.org/10.7554/eLife.01914.019</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s004.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f011"/></fig></p><p>As discussed in the main text, the presence of multiple optima with different degrees of 2D curvature implies an issue of identifiability; the HI likelihood model alone cannot distinguish between these possibilities. Because of this issue, and to more easily estimate rates of antigenic drift, we include a model of systematic drift in antigenic location that favors linear movement in the antigenic map. We find that including this drift prior on antigenic locations removes the problem of identifiability. Antigenic locations produced by this model remain locally consistent with MDS results between viruses ∼15 years divergent, but global comparisons show that this BMDS model has partitioned more variance to the first antigenic dimension (<xref ref-type="fig" rid="fig12">Figure 12</xref>, <xref ref-type="supplementary-material" rid="SD5-data">Figure 12—source data 1</xref>). We additionally find that including the drift prior on antigenic locations often results in greater predictive power, with a slight improvement of test error for the A/H1N1, B/Vic, and B/Yam datasets (<xref ref-type="table" rid="tbl1">Table 1</xref>).<fig id="fig12" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.020</object-id><label>Figure 12.</label><caption><title>Comparison of A/H3N2 antigenic locations estimated by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> using MDS and an extended BMDS model that includes date-informed priors on antigenic locations.</title><p>(<bold>A</bold>) MDS antigenic locations, reoriented so that the primary dimension lies on the <italic>x</italic>-axis rather than on the <italic>y</italic>-axis as in Figure 1 of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. (<bold>B</bold>) A posterior sample of antigenic locations from a BMDS model that includes date-informed priors on antigenic locations. In (<bold>A</bold>) and (<bold>B</bold>), viruses are shown as colored circles, with color denoting antigenic cluster inferred by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, and sera are shown as gray points. (<bold>C</bold>) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (<bold>D</bold>) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (<bold>E</bold>) Antigenic distances between 750 random pairs of viruses determined for both methods. In (<bold>C</bold>), (<bold>D</bold>) and (<bold>E</bold>) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a date-informed prior on antigenic locations and serum potencies fixed at maximum titer values.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.020">http://dx.doi.org/10.7554/eLife.01914.020</ext-link></p><p><supplementary-material id="SD5-data"><object-id pub-id-type="doi">10.7554/eLife.01914.021</object-id><label>Figure 12—source data 1.</label><caption><title>This tab-delimited text file lists every virus and serum in <xref ref-type="fig" rid="fig12">Figure 12</xref>, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.021">http://dx.doi.org/10.7554/eLife.01914.021</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s005.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f012"/></fig></p><p>Our final BMDS model (model 9, <xref ref-type="table" rid="tbl1">Table 1</xref>) differs from antigenic model used by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> in including temporally- and phylogenetically-informed priors on antigenic locations and also in estimating serum and virus avidities. Here, we investigate the impact on antigenic locations of estimating virus avidity and serum potency in the BMDS model. To isolate this difference, we use a Uniform (−100, 100) prior on antigenic locations. Surprisingly, estimating virus avidity and serum potency results in a more linear antigenic map (<xref ref-type="fig" rid="fig13">Figure 13</xref>, <xref ref-type="supplementary-material" rid="SD6-data">Figure 13—source data 1</xref>), resembling the appearance of the map incorporating the antigenic drift prior, while preserving local consistency. We generally observe congruence between MDS and BMDS antigenic locations for viruses less than ∼10 years divergent (<xref ref-type="fig" rid="fig13">Figure 13E</xref>). However, specific viruses may be affected, for instance A/Bilthoven/16,190/1968 (<xref ref-type="fig" rid="fig13">Figure 13C</xref>), which appears more distant from all other viruses when serum and virus avidities are included.<fig id="fig13" position="float"><object-id pub-id-type="doi">10.7554/eLife.01914.022</object-id><label>Figure 13.</label><caption><title>Comparison of A/H3N2 antigenic locations estimated by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref> using MDS and an extended BMDS model that estimates serum and virus avidities.</title><p>(<bold>A</bold>) MDS antigenic locations, reoriented so that the primary dimension lies on the <italic>x</italic>-axis rather than on the <italic>y</italic>-axis as in Figure 1 of <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>. (<bold>B</bold>) A posterior sample of antigenic locations from a BMDS model that estimates virus avidity and serum potency. In (<bold>A</bold>) and (<bold>B</bold>), viruses are shown as colored circles, with color denoting antigenic cluster inferred by <xref ref-type="bibr" rid="bib79">Smith et al. (2004)</xref>, and sera are shown as gray points. (<bold>C</bold>) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (<bold>D</bold>) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (<bold>E</bold>) Antigenic distances between 750 random pairs of viruses determined for both methods. In (<bold>C</bold>), (<bold>D</bold>), and (<bold>E</bold>) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and virus avidities and serum potencies estimated in a hierarchical Bayesian fashion.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.022">http://dx.doi.org/10.7554/eLife.01914.022</ext-link></p><p><supplementary-material id="SD6-data"><object-id pub-id-type="doi">10.7554/eLife.01914.023</object-id><label>Figure 13—source data 1.</label><caption><title>This tab-delimited text file lists every virus and serum in <xref ref-type="fig" rid="fig13">Figure 13</xref>, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, potency for sera and avidity for viruses.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.01914.023">http://dx.doi.org/10.7554/eLife.01914.023</ext-link></p></caption><media mime-subtype="tsv" mimetype="application" xlink:href="elife01914s006.tsv"/></supplementary-material></p></caption><graphic xlink:href="elife01914f013"/></fig></p><p>In this dataset, viruses 15 or more years divergent always yield threshold titers, and hence, their relative locations must be indirectly inferred rather than through direct comparison. This may explain why we observe local consistency between models at scales less than ∼15 years, but some degree of global inconsistency. Still, these results suggest that, when making local comparisons, such as those used to calculate year-to-year antigenic drift (<xref ref-type="fig" rid="fig3">Figure 3</xref>), outcomes are expected to be robust to many model particulars.</p></sec><sec id="s4-9"><title>Availability</title><p>Source code implementing the cartographic models has been made fully available as part of the software package BEAST (<xref ref-type="bibr" rid="bib20">Drummond et al., 2012</xref>), and can be downloaded from its Google code repository (<ext-link ext-link-type="uri" xlink:href="http://code.google.com/p/beast-mcmc/">http://code.google.com/p/beast-mcmc/</ext-link>). More details on implementing these models can be found at <ext-link ext-link-type="uri" xlink:href="https://github.com/trvrb/flux/tree/master/example-xmls">https://github.com/trvrb/flux/tree/master/example-xmls</ext-link>. Incidence data and HI data used in this analysis is archived with Dryad (doi: <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.5061/dryad.rc515">10.5061/dryad.rc515</ext-link>).</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We thank Richard Reeve, Dan Haydon, and Simon Frost for insights on antigenic modeling and MDS. We acknowledge the laboratories that provided sequences to EpiFlu database: Centers for Disease Control and Prevention (USA), Chinese Center of Disease Prevention and Control, Hospital Clinic of Barcelona, National Institute of Hygiene of Morocco, National Institute of Infectious Diseases (Japan), National Institute for Medical Research (UK), Norwegian Institute of Public Health, Swedish Institute for Infectious Disease Control, Victorian Infectious Diseases Reference Laboratory (Australia).</p></ack><sec sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="conflict" id="conf1"><p>The authors declare that no competing interests exist.</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>TB, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con2"><p>DJS, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con3"><p>AR, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con4"><p>MAS, Conception and design, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con5"><p>PL, Conception and design, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con6"><p>GD, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con7"><p>VG, Acquisition of data, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con8"><p>AJH, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con9"><p>JWMC, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con10"><p>CAR, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn></fn-group></sec><sec sec-type="supplementary-material"><title>Additional files</title><sec sec-type="datasets"><title>Major dataset</title><p>The following dataset was generated:</p><p><related-object content-type="generated-dataset" document-id="Dataset ID and/or url" document-id-type="dataset" document-type="data" id="dataro1"><name><surname>Bedford</surname><given-names>T</given-names></name>, <name><surname>Suchard</surname><given-names>MA</given-names></name>, <name><surname>Lemey</surname><given-names>P</given-names></name>, <name><surname>Dudas</surname><given-names>G</given-names></name>, <name><surname>Gregory</surname><given-names>V</given-names></name>, <name><surname>Hay</surname><given-names>AJ</given-names></name>, <name><surname>McCauley</surname><given-names>JW</given-names></name>, <name><surname>Russell</surname><given-names>CA</given-names></name>, <name><surname>Smith</surname><given-names>DJ</given-names></name>, <name><surname>Rambaut</surname><given-names>A</given-names></name>, <year>2013</year><x>, </x><source>Data from: Integrating influenza antigenic dynamics with molecular evolution</source><x>, </x><ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.5061/dryad.rc515">http://dx.doi.org/10.5061/dryad.rc515</ext-link><x>, </x><comment>Available at Dryad Digital Repository under a CC0 Public Domain Dedication.</comment></related-object></p></sec></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Abed</surname><given-names>Y</given-names></name><name><surname>Coulthart</surname><given-names>MB</given-names></name><name><surname>Li</surname><given-names>Y</given-names></name><name><surname>Boivin</surname><given-names>G</given-names></name></person-group><year>2003</year><article-title>Evolution of surface and nonstructural-1 genes of influenza B viruses isolated in the province of Quebec, Canada, during the 1998–2001 period</article-title><source>Virus Genes</source><volume>27</volume><fpage>125</fpage><lpage>135</lpage><pub-id pub-id-type="doi">10.1023/A:1025768308631</pub-id></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ansaldi</surname><given-names>F</given-names></name><name><surname>D’Agaro</surname><given-names>P</given-names></name><name><surname>de Florentiis</surname><given-names>D</given-names></name><name><surname>Puzelli</surname><given-names>S</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennett</surname><given-names>M</given-names></name><name><surname>Donatelli</surname><given-names>I</given-names></name><name><surname>Gasparini</surname><given-names>R</given-names></name><name><surname>Crovari</surname><given-names>P</given-names></name><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Campello</surname><given-names>C</given-names></name></person-group><year>2003</year><article-title>Molecular characterization of influenza B viruses circulating in northern Italy during the 2001–2002 epidemic season</article-title><source>Journal of Medical Virology</source><volume>70</volume><fpage>463</fpage><lpage>469</lpage><pub-id pub-id-type="doi">10.1002/jmv.10418</pub-id></element-citation></ref><ref id="bib3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ansaldi</surname><given-names>F</given-names></name><name><surname>Bacilieri</surname><given-names>S</given-names></name><name><surname>Amicizia</surname><given-names>D</given-names></name><name><surname>Valle</surname><given-names>L</given-names></name><name><surname>Banfi</surname><given-names>F</given-names></name><name><surname>Durando</surname><given-names>P</given-names></name><name><surname>Sticchi</surname><given-names>L</given-names></name><name><surname>Gasparini</surname><given-names>R</given-names></name><name><surname>Icardi</surname><given-names>G</given-names></name><name><surname>Crovari</surname><given-names>P</given-names></name></person-group><year>2004</year><article-title>Antigenic characterisation of influenza B virus with a new microneutralisation assay: comparison to haemagglutination and sequence analysis</article-title><source>Journal of Medical Virology</source><volume>74</volume><fpage>141</fpage><lpage>146</lpage><pub-id pub-id-type="doi">10.1002/jmv.20157</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Barr</surname><given-names>I</given-names></name><name><surname>Komadina</surname><given-names>N</given-names></name><name><surname>Durrant</surname><given-names>C</given-names></name><name><surname>Sjogren</surname><given-names>H</given-names></name><name><surname>Hurt</surname><given-names>A</given-names></name><name><surname>Shaw</surname><given-names>RP</given-names></name></person-group><year>2006</year><article-title>Circulation and antigenic drift in human influenza B viruses in SE Asia and Oceania since 2000</article-title><source>Communicable diseases intelligence</source><volume>30</volume><fpage>350</fpage><lpage>357</lpage></element-citation></ref><ref id="bib5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Barr</surname><given-names>I</given-names></name><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Cox</surname><given-names>N</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Engelhardt</surname><given-names>O</given-names></name><name><surname>Fukuda</surname><given-names>K</given-names></name><name><surname>Grohmann</surname><given-names>G</given-names></name><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Kelso</surname><given-names>A</given-names></name><name><surname>Klimov</surname><given-names>A</given-names></name><name><surname>Odagiri</surname><given-names>T</given-names></name><name><surname>Smith</surname><given-names>D</given-names></name><name><surname>Russell</surname><given-names>C</given-names></name><name><surname>Tashiro</surname><given-names>M</given-names></name><name><surname>Webby</surname><given-names>R</given-names></name><name><surname>Wood</surname><given-names>J</given-names></name><name><surname>Ye</surname><given-names>Z</given-names></name><name><surname>Zhang</surname><given-names>W</given-names></name>, <collab>Writing Committee of the World Health Organization Consultation on Northern Hemisphere Influenza Vaccine Composition for 2009-2010</collab></person-group><year>2010</year><article-title>Epidemiological, antigenic and genetic characteristics of seasonal influenza A (H1N1), A (H3N2) and B influenza viruses: basis for the WHO recommendation on the composition of influenza vaccines for use in the 2009-2010 Northern Hemisphere season</article-title><source>Vaccine</source><volume>28</volume><fpage>1156</fpage><lpage>1167</lpage><pub-id pub-id-type="doi">10.1016/j.vaccine.2009.11.043</pub-id></element-citation></ref><ref id="bib6"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bedford</surname><given-names>T</given-names></name><name><surname>Cobey</surname><given-names>S</given-names></name><name><surname>Pascual</surname><given-names>M</given-names></name></person-group><year>2011</year><article-title>Strength and tempo of selection revealed in viral gene genealogies</article-title><source>BMC Evolutionary Biology</source><volume>11</volume><fpage>220</fpage><pub-id pub-id-type="doi">10.1186/1471-2148-11-220</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bedford</surname><given-names>T</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name><name><surname>Pascual</surname><given-names>M</given-names></name></person-group><year>2012</year><article-title>Canalization of the evolutionary trajectory of the human influenza virus</article-title><source>BMC Biology</source><volume>10</volume><fpage>38</fpage><pub-id pub-id-type="doi">10.1186/1741-7007-10-38</pub-id></element-citation></ref><ref id="bib8"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bogner</surname><given-names>P</given-names></name><name><surname>Capua</surname><given-names>I</given-names></name><name><surname>Lipman</surname><given-names>D</given-names></name><name><surname>Cox</surname><given-names>N</given-names></name><name><surname>Lipman</surname><given-names>DJ</given-names></name></person-group><year>2006</year><article-title>A global initiative on sharing avian flu data</article-title><source>Nature</source><volume>442</volume><fpage>981</fpage><lpage>981</lpage><pub-id pub-id-type="doi">10.1038/442981a</pub-id></element-citation></ref><ref id="bib9"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Borodin</surname><given-names>AN</given-names></name><name><surname>Salminen</surname><given-names>P</given-names></name></person-group><year>2002</year><article-title>Handbook of Brownian motion – facts and formulae</article-title><publisher-loc>Basel</publisher-loc><publisher-name>Birkhäuser Verlag</publisher-name></element-citation></ref><ref id="bib10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cai</surname><given-names>Z</given-names></name><name><surname>Zhang</surname><given-names>T</given-names></name><name><surname>Wan</surname><given-names>XF</given-names></name></person-group><year>2010</year><article-title>A computational framework for influenza antigenic cartography</article-title><source>PLOS Computational Biol</source><volume>6</volume><fpage>e1000949</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000949</pub-id></element-citation></ref><ref id="bib11"><element-citation publication-type="web"><collab>Centers for Disease Control and Prevention</collab><year>2012</year><article-title>FluView weekly influenza reports</article-title><comment>Available at <ext-link ext-link-type="uri" xlink:href="http://www.cdc.gov/flu/weekly/">http://www.cdc.gov/flu/weekly/</ext-link></comment></element-citation></ref><ref id="bib12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chakraverty</surname><given-names>P</given-names></name><name><surname>Cunningham</surname><given-names>P</given-names></name><name><surname>Pereira</surname><given-names>MS</given-names></name></person-group><year>1982</year><article-title>The return of the historic influenza A H1N1 virus and its impact on the population of the United Kingdom</article-title><source>The Journal of Hygiene</source><volume>89</volume><fpage>89</fpage><lpage>100</lpage><pub-id pub-id-type="doi">10.1017/S0022172400070571</pub-id></element-citation></ref><ref id="bib13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chakraverty</surname><given-names>P</given-names></name><name><surname>Cunningham</surname><given-names>P</given-names></name><name><surname>Shen</surname><given-names>GZ</given-names></name><name><surname>Pereira</surname><given-names>MS</given-names></name></person-group><year>1986</year><article-title>Influenza in the United Kingdom 1982–85</article-title><source>The Journal of Hygiene</source><volume>97</volume><fpage>347</fpage><lpage>358</lpage><pub-id pub-id-type="doi">10.1017/S0022172400065438</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cox</surname><given-names>NJ</given-names></name><name><surname>Bai</surname><given-names>ZS</given-names></name><name><surname>Kendal</surname><given-names>AP</given-names></name></person-group><year>1983</year><article-title>Laboratory-based surveillance of influenza A(H1N1) and A(H3N2) viruses in 1980–81: antigenic and genomic analyses</article-title><source>Bulletin of the World Health Organization</source><volume>61</volume><fpage>143</fpage><lpage>152</lpage></element-citation></ref><ref id="bib15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cox</surname><given-names>NJ</given-names></name></person-group><year>2011</year><article-title>Information for the vaccines and related biological products advisory committee. Seasonal influenza vaccines</article-title><comment>Technical report, WHO Collaborating Centre for Surveillance, Epidemiology and Control of Influenza, Centers for Disease Control and Prevention, USA</comment></element-citation></ref><ref id="bib16"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Daniels</surname><given-names>RS</given-names></name><name><surname>Douglas</surname><given-names>AR</given-names></name><name><surname>Skehel</surname><given-names>JJ</given-names></name><name><surname>Wiley</surname><given-names>DC</given-names></name></person-group><year>1985</year><article-title>Antigenic and amino acid sequence analyses of influenza viruses of the H1N1 subtype isolated between 1982 and 1984</article-title><source>Bulletin of the World Health Organization</source><volume>63</volume><fpage>273</fpage><lpage>277</lpage></element-citation></ref><ref id="bib17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Daum</surname><given-names>LT</given-names></name><name><surname>Canas</surname><given-names>LC</given-names></name><name><surname>Smith</surname><given-names>CB</given-names></name><name><surname>Klimov</surname><given-names>A</given-names></name><name><surname>Huff</surname><given-names>W</given-names></name><name><surname>Barnes</surname><given-names>W</given-names></name><name><surname>Lohman</surname><given-names>KL</given-names></name></person-group><year>2002</year><article-title>Genetic and antigenic analysis of the first A/New Caledonia/20/99-like H1N1 influenza isolates reported in the Americas</article-title><source>Emerging Infectious Diseases</source><volume>8</volume><fpage>408</fpage><lpage>412</lpage><pub-id pub-id-type="doi">10.3201/eid0804.010311</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Daum</surname><given-names>LT</given-names></name><name><surname>Canas</surname><given-names>LC</given-names></name><name><surname>Klimov</surname><given-names>AI</given-names></name><name><surname>Shaw</surname><given-names>MW</given-names></name><name><surname>Gibbons</surname><given-names>RV</given-names></name><name><surname>Shrestha</surname><given-names>SK</given-names></name><name><surname>Myint</surname><given-names>KS</given-names></name><name><surname>Acharya</surname><given-names>RP</given-names></name><name><surname>Rimal</surname><given-names>N</given-names></name><name><surname>Reese</surname><given-names>F</given-names></name><name><surname>Niemeyer</surname><given-names>DM</given-names></name><name><surname>Arulanandam</surname><given-names>BP</given-names></name><name><surname>Chambers</surname><given-names>JP</given-names></name></person-group><year>2006</year><article-title>Molecular analysis of isolates from influenza B outbreaks in the U.S. and Nepal, 2005</article-title><source>Archives of Virology</source><volume>151</volume><fpage>1863</fpage><lpage>1874</lpage><pub-id pub-id-type="doi">10.1007/s00705-006-0777-0</pub-id></element-citation></ref><ref id="bib19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Donatelli</surname><given-names>I</given-names></name><name><surname>Campitelli</surname><given-names>L</given-names></name><name><surname>Ruggieri</surname><given-names>A</given-names></name><name><surname>Castrucci</surname><given-names>MR</given-names></name><name><surname>Calzoletti</surname><given-names>L</given-names></name><name><surname>Oxford</surname><given-names>JS</given-names></name></person-group><year>1993</year><article-title>Concurrent antigenic analysis of recent epidemic influenza A and B viruses and quantitation of antibodies in population serosurveys in Italy</article-title><source>European Journal of Epidemiology</source><volume>9</volume><fpage>241</fpage><lpage>250</lpage><pub-id pub-id-type="doi">10.1007/BF00146258</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Drummond</surname><given-names>AJ</given-names></name><name><surname>Suchard</surname><given-names>MA</given-names></name><name><surname>Xie</surname><given-names>D</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name></person-group><year>2012</year><article-title>Bayesian phylogenetics with BEAUti and the BEAST 1.7</article-title><source>Molecular Biology and Evolution</source><volume>29</volume><fpage>1969</fpage><lpage>1973</lpage><pub-id pub-id-type="doi">10.1093/molbev/mss075</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Edgar</surname><given-names>RC</given-names></name></person-group><year>2004</year><article-title>MUSCLE: multiple sequence alignment with high accuracy and high throughput</article-title><source>Nucleic Acids Research</source><volume>32</volume><fpage>1792</fpage><lpage>1797</lpage><pub-id pub-id-type="doi">10.1093/nar/gkh340</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ferguson</surname><given-names>NM</given-names></name><name><surname>Galvani</surname><given-names>AP</given-names></name><name><surname>Bush</surname><given-names>RM</given-names></name></person-group><year>2003</year><article-title>Ecological and immunological determinants of influenza evolution</article-title><source>Nature</source><volume>422</volume><fpage>428</fpage><lpage>433</lpage><pub-id pub-id-type="doi">10.1038/nature01509</pub-id></element-citation></ref><ref id="bib23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fitch</surname><given-names>WM</given-names></name><name><surname>Bush</surname><given-names>RM</given-names></name><name><surname>Bender</surname><given-names>CA</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name></person-group><year>1997</year><article-title>Long term trends in the evolution of H(3) HA1 human influenza type A</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>94</volume><fpage>7712</fpage><lpage>7718</lpage><pub-id pub-id-type="doi">10.1073/pnas.94.15.7712</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gog</surname><given-names>J</given-names></name><name><surname>Grenfell</surname><given-names>B</given-names></name></person-group><year>2002</year><article-title>Dynamics and selection of many-strain pathogens</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>99</volume><fpage>17209</fpage><lpage>17214</lpage><pub-id pub-id-type="doi">10.1073/pnas.252512799</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Goldstein</surname><given-names>E</given-names></name><name><surname>Cobey</surname><given-names>S</given-names></name><name><surname>Takahashi</surname><given-names>S</given-names></name><name><surname>Miller</surname><given-names>J</given-names></name><name><surname>Lipsitch</surname><given-names>M</given-names></name></person-group><year>2011</year><article-title>Predicting the epidemic sizes of influenza A/H1N1, A/H3N2, and B: a statistical method</article-title><source>PLOS Medicine</source><volume>8</volume><fpage>e1001051</fpage><pub-id pub-id-type="doi">10.1371/journal.pmed.1001051</pub-id></element-citation></ref><ref id="bib26"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gust</surname><given-names>I</given-names></name><name><surname>Barr</surname><given-names>I</given-names></name><name><surname>O’Bryan</surname><given-names>K</given-names></name><name><surname>Laurie</surname><given-names>K</given-names></name><name><surname>Shaw</surname><given-names>R</given-names></name><name><surname>Hurt</surname><given-names>A</given-names></name><name><surname>Komadina</surname><given-names>N</given-names></name><name><surname>Durrant</surname><given-names>C</given-names></name><name><surname>Sjogren</surname><given-names>H</given-names></name><name><surname>Mastorakos</surname><given-names>T</given-names></name><name><surname>Deed</surname><given-names>N</given-names></name><name><surname>Iannello</surname><given-names>P</given-names></name><name><surname>Tomasov</surname><given-names>C</given-names></name></person-group><year>2006</year><article-title>Annual Report</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, Victorian Infectious Disease Research Laboratory, Australia</comment></element-citation></ref><ref id="bib27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Douglas</surname><given-names>AR</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name></person-group><year>2001</year><article-title>The evolution of human influenza viruses</article-title><source>Philosophical Transactions of the Royal Society of London Series B Biological sciences</source><volume>356</volume><fpage>1861</fpage><lpage>1870</lpage><pub-id pub-id-type="doi">10.1098/rstb.2001.0999</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2002</year><article-title>Annual Report</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib29"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2003</year><article-title>Annual Report</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2004</year><article-title>Annual Report</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib31"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2005a</year><article-title>Characteristics of human influenza A H1N1, A H3N2 and B viruses isolated October 2004 to January 2005</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Hou</surname><given-names>T</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name></person-group><year>2009a</year><article-title>Antigenic and genetic characteristics of human influenza A(H1N1), A(H3N2) and B viruses isolated during October 2008 to February 2009</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib33"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2006a</year><article-title>Characteristics of human influenza AH1N1, AH3N2 and B viruses isolated October 2005 to February 2006</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib34"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name></person-group><year>2007a</year><article-title>Characteristics of human influenza AH1N1, AH3N2 and B viruses isolated September 2006 to February 2007</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib35"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name></person-group><year>2008a</year><article-title>Characteristics of human influenza AH1N1, AH3N2, and B viruses isolated September 2007 to February 2008</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2005b</year><article-title>Characteristics of human influenza AH1N1, AH3N2 and B viruses isolated February to July 2005</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib37"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name></person-group><year>2006b</year><article-title>Characteristics of human influenza AH1N1, AH3N2 and B viruses isolated January to September 2006</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib38"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennet</surname><given-names>M</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name></person-group><year>2007b</year><article-title>Characteristics of human influenza AH1N1, AH3N2 and B viruses isolated February to August 2007</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Hou</surname><given-names>T</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name></person-group><year>2008b</year><article-title>Characteristics of human influenza AH1N1, AH3N2, and B viruses isolated February to August 2008</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Hou</surname><given-names>T</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name></person-group><year>2009b</year><article-title>Antigenic and genetic characteristics of pandemic A(H1N1) viruses and seasonal A(H1N1), A(H3N2) and B viruses isolated during February to August 2009</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hensley</surname><given-names>SE</given-names></name><name><surname>Das</surname><given-names>SR</given-names></name><name><surname>Bailey</surname><given-names>AL</given-names></name><name><surname>Schmidt</surname><given-names>LM</given-names></name><name><surname>Hickman</surname><given-names>HD</given-names></name><name><surname>Jayaraman</surname><given-names>A</given-names></name><name><surname>Viswanathan</surname><given-names>K</given-names></name><name><surname>Raman</surname><given-names>R</given-names></name><name><surname>Sasisekharan</surname><given-names>R</given-names></name><name><surname>Bennink</surname><given-names>JR</given-names></name><name><surname>Yewdell</surname><given-names>JW</given-names></name></person-group><year>2009</year><article-title>Hemagglutinin receptor binding avidity drives influenza A virus antigenic drift</article-title><source>Science</source><volume>326</volume><fpage>734</fpage><lpage>736</lpage><pub-id pub-id-type="doi">10.1126/science.1178258</pub-id></element-citation></ref><ref id="bib42"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hirst</surname><given-names>G</given-names></name></person-group><year>1943</year><article-title>Studies of antigenic differences among strains of influenza A by means of red cell agglutination</article-title><source>The Journal of Experimental Medicine</source><volume>78</volume><fpage>407</fpage><lpage>423</lpage><pub-id pub-id-type="doi">10.1084/jem.78.5.407</pub-id></element-citation></ref><ref id="bib43"><element-citation publication-type="web"><collab>World Health Organization</collab><year>2009</year><article-title>Influenza fact sheet</article-title><comment>Available at <ext-link ext-link-type="uri" xlink:href="http://www.who.int/mediacentre/factsheets/fs211/en/">http://www.who.int/mediacentre/factsheets/fs211/en/</ext-link></comment></element-citation></ref><ref id="bib44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kanegae</surname><given-names>Y</given-names></name><name><surname>Sugita</surname><given-names>S</given-names></name><name><surname>Endo</surname><given-names>A</given-names></name><name><surname>Ishida</surname><given-names>M</given-names></name><name><surname>Senya</surname><given-names>S</given-names></name><name><surname>Osako</surname><given-names>K</given-names></name><name><surname>Nerome</surname><given-names>K</given-names></name><name><surname>Oya</surname><given-names>A</given-names></name></person-group><year>1990</year><article-title>Evolutionary pattern of the hemagglutinin gene of influenza B viruses isolated in Japan: cocirculating lineages in the same epidemic season</article-title><source>Journal of Virology</source><volume>64</volume><fpage>2860</fpage><lpage>2865</lpage></element-citation></ref><ref id="bib45"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kendal</surname><given-names>AP</given-names></name><name><surname>Noble</surname><given-names>GR</given-names></name><name><surname>Skehel</surname><given-names>JJ</given-names></name><name><surname>Dowdle</surname><given-names>WR</given-names></name></person-group><year>1978</year><article-title>Antigenic similarity of influenza A(H1N1) viruses from epidemics in 1977–1978 to Scandinavian strains isolated in epidemics of 1950–1951</article-title><source>Virology</source><volume>89</volume><fpage>632</fpage><lpage>636</lpage><pub-id pub-id-type="doi">10.1016/0042-6822(78)90207-6</pub-id></element-citation></ref><ref id="bib46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Klimov</surname><given-names>AI</given-names></name><name><surname>Garten</surname><given-names>R</given-names></name><name><surname>Russell</surname><given-names>C</given-names></name><name><surname>Barr</surname><given-names>IG</given-names></name><name><surname>Besselaar</surname><given-names>TG</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Engelhardt</surname><given-names>OG</given-names></name><name><surname>Grohmann</surname><given-names>G</given-names></name><name><surname>Itamura</surname><given-names>S</given-names></name><name><surname>Kelso</surname><given-names>A</given-names></name><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Odagiri</surname><given-names>T</given-names></name><name><surname>Smith</surname><given-names>D</given-names></name><name><surname>Tashiro</surname><given-names>M</given-names></name><name><surname>Xu</surname><given-names>X</given-names></name><name><surname>Webby</surname><given-names>R</given-names></name><name><surname>Wang</surname><given-names>D</given-names></name><name><surname>Ye</surname><given-names>Z</given-names></name><name><surname>Yuelong</surname><given-names>S</given-names></name><name><surname>Zhang</surname><given-names>W</given-names></name><name><surname>Cox</surname><given-names>N</given-names></name>, <collab>Writing Committee of the World Health Organization Consultation on Southern Hemisphere InfluenzaVaccine Composition for 2012</collab></person-group><year>2012</year><article-title>WHO recommendations for the viruses to be used in the 2012 Southern Hemisphere Influenza Vaccine: epidemiology, antigenic and genetic characteristics of influenza A (H1N1) pdm09, A (H3N2) and B influenza viruses collected from February to September 2011</article-title><source>Vaccine</source><volume>30</volume><fpage>6461</fpage><lpage>6471</lpage><pub-id pub-id-type="doi">10.1016/j.vaccine.2012.07.089</pub-id></element-citation></ref><ref id="bib47"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Koel</surname><given-names>BF</given-names></name><name><surname>Burke</surname><given-names>DF</given-names></name><name><surname>Bestebroer</surname><given-names>TM</given-names></name><name><surname>van der Vliet</surname><given-names>S</given-names></name><name><surname>Zondag</surname><given-names>GC</given-names></name><name><surname>Vervaet</surname><given-names>G</given-names></name><name><surname>Skepner</surname><given-names>E</given-names></name><name><surname>Lewis</surname><given-names>NS</given-names></name><name><surname>Spronken</surname><given-names>MI</given-names></name><name><surname>Russell</surname><given-names>CA</given-names></name><name><surname>Eropkin</surname><given-names>MY</given-names></name><name><surname>Hurt</surname><given-names>AC</given-names></name><name><surname>Barr</surname><given-names>IG</given-names></name><name><surname>de Jong</surname><given-names>JC</given-names></name><name><surname>Rimmelzwaan</surname><given-names>GF</given-names></name><name><surname>Osterhaus</surname><given-names>AD</given-names></name><name><surname>Fouchier</surname><given-names>RA</given-names></name><name><surname>Smith</surname><given-names>DJ</given-names></name></person-group><year>2013</year><article-title>Substitutions near the receptor binding site determine major antigenic change during influenza virus evolution</article-title><source>Science</source><volume>342</volume><fpage>976</fpage><lpage>979</lpage><pub-id pub-id-type="doi">10.1126/science.1244730</pub-id></element-citation></ref><ref id="bib48"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lemey</surname><given-names>P</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name><name><surname>Welch</surname><given-names>J</given-names></name><name><surname>Suchard</surname><given-names>M</given-names></name></person-group><year>2010</year><article-title>Phylogeography takes a relaxed random walk in continuous space and time</article-title><source>Molecular Biology and Evolution</source><volume>27</volume><fpage>1877</fpage><lpage>1885</lpage><pub-id pub-id-type="doi">10.1093/molbev/msq067</pub-id></element-citation></ref><ref id="bib49"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Li</surname><given-names>Y</given-names></name><name><surname>Bostick</surname><given-names>DL</given-names></name><name><surname>Sullivan</surname><given-names>CB</given-names></name><name><surname>Myers</surname><given-names>JL</given-names></name><name><surname>Griesemer</surname><given-names>SB</given-names></name><name><surname>Stgeorge</surname><given-names>K</given-names></name><name><surname>Plotkin</surname><given-names>JB</given-names></name><name><surname>Hensley</surname><given-names>SE</given-names></name></person-group><year>2013</year><article-title>Single hemagglutinin mutations that alter both antigenicity and receptor binding avidity influence influenza virus antigenic clustering</article-title><source>Journal of Virology</source><volume>87</volume><fpage>9904</fpage><lpage>9910</lpage><pub-id pub-id-type="doi">10.1128/JVI.01023-13</pub-id></element-citation></ref><ref id="bib50"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lin</surname><given-names>J</given-names></name><name><surname>Andreasen</surname><given-names>V</given-names></name><name><surname>Casagrandi</surname><given-names>R</given-names></name><name><surname>Levin</surname><given-names>SA</given-names></name></person-group><year>2003</year><article-title>Traveling waves in a model of influenza a drift</article-title><source>Journal of Theoretical Biology</source><volume>222</volume><fpage>437</fpage><lpage>445</lpage><pub-id pub-id-type="doi">10.1016/S0022-5193(03)00056-0</pub-id></element-citation></ref><ref id="bib51"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lin</surname><given-names>JH</given-names></name><name><surname>Chiu</surname><given-names>SC</given-names></name><name><surname>Shaw</surname><given-names>MW</given-names></name><name><surname>Lin</surname><given-names>YC</given-names></name><name><surname>Lee</surname><given-names>CH</given-names></name><name><surname>Chen</surname><given-names>HY</given-names></name><name><surname>Klimov</surname><given-names>A</given-names></name></person-group><year>2007</year><article-title>Characterization of the epidemic influenza B viruses isolated during 2004–2005 season in Taiwan</article-title><source>Virus Research</source><volume>124</volume><fpage>204</fpage><lpage>211</lpage><pub-id pub-id-type="doi">10.1016/j.virusres.2006.11.005</pub-id></element-citation></ref><ref id="bib52"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lin</surname><given-names>Y</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Collins</surname><given-names>P</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name><name><surname>Wharton</surname><given-names>S</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Lackenby</surname><given-names>A</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Hay</surname><given-names>A</given-names></name></person-group><year>2010</year><article-title>Neuraminidase receptor binding variants of human influenza A (H3N2) viruses resulting from substitution of aspartic acid 151 in the catalytic site: a role in virus attachment?</article-title><source>Journal of Virology</source><volume>84</volume><fpage>6769</fpage><lpage>6781</lpage><pub-id pub-id-type="doi">10.1128/JVI.00458-10</pub-id></element-citation></ref><ref id="bib53"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lin</surname><given-names>Y</given-names></name><name><surname>Xiong</surname><given-names>X</given-names></name><name><surname>Wharton</surname><given-names>S</given-names></name><name><surname>Martin</surname><given-names>S</given-names></name><name><surname>Coombs</surname><given-names>P</given-names></name><name><surname>Vachieri</surname><given-names>SG</given-names></name><name><surname>Christodoulou</surname><given-names>E</given-names></name><name><surname>Walker</surname><given-names>PA</given-names></name><name><surname>Liu</surname><given-names>J</given-names></name><name><surname>Skehel</surname><given-names>JJ</given-names></name><name><surname>Gamblin</surname><given-names>SJ</given-names></name><name><surname>Hay</surname><given-names>AJ</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><name><surname>McCauley</surname><given-names>JW</given-names></name></person-group><year>2012</year><article-title>Evolution of the receptor binding properties of the influenza A (H3N2) hemagglutinin</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>109</volume><fpage>21474</fpage><lpage>21479</lpage><pub-id pub-id-type="doi">10.1073/pnas.1218841110</pub-id></element-citation></ref><ref id="bib54"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Matsuzaki</surname><given-names>Y</given-names></name><name><surname>Sugawara</surname><given-names>K</given-names></name><name><surname>Takashita</surname><given-names>E</given-names></name><name><surname>Muraki</surname><given-names>Y</given-names></name><name><surname>Hongo</surname><given-names>S</given-names></name><name><surname>Katsushima</surname><given-names>N</given-names></name><name><surname>Mizuta</surname><given-names>K</given-names></name><name><surname>Nishimura</surname><given-names>H</given-names></name></person-group><year>2004</year><article-title>Genetic diversity of influenza B virus: the frequent reassortment and cocirculation of the genetically distinct reassortant viruses in a community</article-title><source>Journal of Medical Virology</source><volume>74</volume><fpage>132</fpage><lpage>140</lpage><pub-id pub-id-type="doi">10.1002/jmv.20156</pub-id></element-citation></ref><ref id="bib55"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Hou</surname><given-names>T</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name><name><surname>Halai</surname><given-names>C</given-names></name></person-group><year>2010a</year><article-title>Report prepared for the WHO annual consultation on the composition of influenza vaccine for the Northern Hemisphere</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib56"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Halai</surname><given-names>C</given-names></name><name><surname>Cross</surname><given-names>K</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name></person-group><year>2011a</year><article-title>Report prepared for the WHO annual consultation on the composition of influenza vaccine for the Northern Hemisphere</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib57"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Halai</surname><given-names>C</given-names></name><name><surname>Cross</surname><given-names>K</given-names></name></person-group><year>2012</year><article-title>Report prepared for the WHO annual consultation on the composition of influenza vaccine for the Northern Hemisphere</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib58"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Hou</surname><given-names>T</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Halai</surname><given-names>C</given-names></name><name><surname>Cross</surname><given-names>K</given-names></name><name><surname>Kloess</surname><given-names>J</given-names></name></person-group><year>2010b</year><article-title>Report prepared for the WHO annual consultation on the composition of influenza vaccine for the Southern Hemisphere</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib59"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McCauley</surname><given-names>J</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Zheng</surname><given-names>X</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Whittaker</surname><given-names>L</given-names></name><name><surname>Cattle</surname><given-names>N</given-names></name><name><surname>Halai</surname><given-names>C</given-names></name><name><surname>Cross</surname><given-names>K</given-names></name></person-group><year>2011b</year><article-title>Report prepared for the WHO annual consultation on the composition of influenza vaccine for the Southern Hemisphere</article-title><comment>Technical report, WHO Collaborating Centre for Reference and Research on Influenza, National Institute for Medical Research, UK</comment></element-citation></ref><ref id="bib60"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McDonald</surname><given-names>NJ</given-names></name><name><surname>Smith</surname><given-names>CB</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name></person-group><year>2007</year><article-title>Antigenic drift in the evolution of H1N1 influenza A viruses resulting from deletion of a single amino acid in the haemagglutinin gene</article-title><source>Journal of General Virology</source><volume>88</volume><fpage>3209</fpage><lpage>3213</lpage><pub-id pub-id-type="doi">10.1099/vir.0.83184-0</pub-id></element-citation></ref><ref id="bib61"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Muyanga</surname><given-names>J</given-names></name><name><surname>Matsuzaki</surname><given-names>Y</given-names></name><name><surname>Sugawara</surname><given-names>K</given-names></name><name><surname>Kimura</surname><given-names>K</given-names></name><name><surname>Mizuta</surname><given-names>K</given-names></name><name><surname>Ndumba</surname><given-names>I</given-names></name><name><surname>Muraki</surname><given-names>Y</given-names></name><name><surname>Tsuchiya</surname><given-names>E</given-names></name><name><surname>Hongo</surname><given-names>S</given-names></name><name><surname>Kasolo</surname><given-names>FC</given-names></name><name><surname>Numazaki</surname><given-names>Y</given-names></name><name><surname>Nakamura</surname><given-names>K</given-names></name></person-group><year>2001</year><article-title>Antigenic and genetic analyses of influenza B viruses isolated in Lusaka, Zambia in 1999</article-title><source>Archives of Virology</source><volume>146</volume><fpage>1667</fpage><lpage>1679</lpage><pub-id pub-id-type="doi">10.1007/s007050170055</pub-id></element-citation></ref><ref id="bib62"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nakagawa</surname><given-names>N</given-names></name><name><surname>Nukuzuma</surname><given-names>S</given-names></name><name><surname>Haratome</surname><given-names>S</given-names></name><name><surname>Go</surname><given-names>S</given-names></name><name><surname>Nakagawa</surname><given-names>T</given-names></name><name><surname>Hayashi</surname><given-names>K</given-names></name></person-group><year>2002</year><article-title>Emergence of an influenza B virus with antigenic change</article-title><source>Journal of Clinical Microbiology</source><volume>40</volume><fpage>3068</fpage><lpage>3070</lpage><pub-id pub-id-type="doi">10.1128/JCM.40.8.3068-3070.2002</pub-id></element-citation></ref><ref id="bib63"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nakajima</surname><given-names>K</given-names></name><name><surname>Nakajima</surname><given-names>S</given-names></name><name><surname>Nerome</surname><given-names>K</given-names></name><name><surname>Takeuchi</surname><given-names>Y</given-names></name><name><surname>Sugiura</surname><given-names>A</given-names></name><name><surname>Oya</surname><given-names>A</given-names></name></person-group><year>1979</year><article-title>Genetic relatedness of some 1978–1979 influenza H1N1 strains to 1953 H1N1 strain</article-title><source>Virology</source><volume>99</volume><fpage>423</fpage><lpage>426</lpage><pub-id pub-id-type="doi">10.1016/0042-6822(79)90022-9</pub-id></element-citation></ref><ref id="bib64"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nakajima</surname><given-names>S</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name><name><surname>Kendal</surname><given-names>AP</given-names></name></person-group><year>1981</year><article-title>Antigenic and genomic analyses of influenza A(H1N1) viruses from different regions of the world, February 1978 to March 1980</article-title><source>Infection and Immunity</source><volume>32</volume><fpage>287</fpage><lpage>294</lpage></element-citation></ref><ref id="bib65"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nakajima</surname><given-names>S</given-names></name><name><surname>Nishikawa</surname><given-names>F</given-names></name><name><surname>Nakamura</surname><given-names>K</given-names></name><name><surname>Nakajima</surname><given-names>K</given-names></name></person-group><year>1992</year><article-title>Comparison of the HA genes of type B influenza viruses in herald waves and later epidemic seasons</article-title><source>Epidemiology &amp; Infection</source><volume>109</volume><fpage>559</fpage><lpage>568</lpage><pub-id pub-id-type="doi">10.1017/S0950268800050548</pub-id></element-citation></ref><ref id="bib66"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nelson</surname><given-names>MI</given-names></name><name><surname>Holmes</surname><given-names>EC</given-names></name></person-group><year>2007</year><article-title>The evolution of epidemic influenza</article-title><source>Nature Reviews Genetics</source><volume>8</volume><fpage>196</fpage><lpage>205</lpage><pub-id pub-id-type="doi">10.1038/nrg2053</pub-id></element-citation></ref><ref id="bib67"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nerome</surname><given-names>R</given-names></name><name><surname>Hiromoto</surname><given-names>Y</given-names></name><name><surname>Sugita</surname><given-names>S</given-names></name><name><surname>Tanabe</surname><given-names>N</given-names></name><name><surname>Ishida</surname><given-names>M</given-names></name><name><surname>Matsumoto</surname><given-names>M</given-names></name><name><surname>Lindstrom</surname><given-names>SE</given-names></name><name><surname>Takahashi</surname><given-names>T</given-names></name><name><surname>Nerome</surname><given-names>K</given-names></name></person-group><year>1998</year><article-title>Evolutionary characteristics of influenza B virus since its first isolation in 1940: dynamic circulation of deletion and insertion mechanism</article-title><source>Archives of Virology</source><volume>143</volume><fpage>1569</fpage><lpage>1583</lpage><pub-id pub-id-type="doi">10.1007/s007050050399</pub-id></element-citation></ref><ref id="bib68"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Oh</surname><given-names>M</given-names></name><name><surname>Raftery</surname><given-names>A</given-names></name></person-group><year>2001</year><article-title>Bayesian multidimensional scaling and choice of dimension</article-title><source>Journal of the American Statistical Association</source><volume>96</volume><fpage>1031</fpage><lpage>1044</lpage><pub-id pub-id-type="doi">10.1198/016214501753208690</pub-id></element-citation></ref><ref id="bib69"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Osterholm</surname><given-names>M</given-names></name><name><surname>Kelley</surname><given-names>N</given-names></name><name><surname>Manske</surname><given-names>J</given-names></name><name><surname>Ballering</surname><given-names>K</given-names></name><name><surname>Leighton</surname><given-names>T</given-names></name><etal/></person-group><year>2012</year><article-title>The compelling need for game-changing influenza vaccines: an analysis of the influenza vaccine enterprise and recommendations for the future</article-title><publisher-name>Technical report, Center for Infectious Disease Research &amp; Policy</publisher-name></element-citation></ref><ref id="bib70"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pagel</surname><given-names>M</given-names></name><name><surname>Meade</surname><given-names>A</given-names></name><name><surname>Barker</surname><given-names>D</given-names></name></person-group><year>2004</year><article-title>Bayesian estimation of ancestral character states on phylogenies</article-title><source>Systematic Biology</source><volume>53</volume><fpage>673</fpage><lpage>684</lpage><pub-id pub-id-type="doi">10.1080/10635150490522232</pub-id></element-citation></ref><ref id="bib71"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pereira</surname><given-names>MS</given-names></name><name><surname>Chakraverty</surname><given-names>P</given-names></name></person-group><year>1982</year><article-title>Influenza in the United Kingdom 1977–1981</article-title><source>Epidemiology &amp; Infection</source><volume>88</volume><fpage>501</fpage><lpage>512</lpage></element-citation></ref><ref id="bib72"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Puzelli</surname><given-names>S</given-names></name><name><surname>Frezza</surname><given-names>F</given-names></name><name><surname>Fabiani</surname><given-names>C</given-names></name><name><surname>Ansaldi</surname><given-names>F</given-names></name><name><surname>Campitelli</surname><given-names>L</given-names></name><name><surname>Lin</surname><given-names>YP</given-names></name><name><surname>Gregory</surname><given-names>V</given-names></name><name><surname>Bennett</surname><given-names>M</given-names></name><name><surname>D’Agaro</surname><given-names>P</given-names></name><name><surname>Campello</surname><given-names>C</given-names></name><name><surname>Crovari</surname><given-names>P</given-names></name><name><surname>Hay</surname><given-names>A</given-names></name><name><surname>Donatelli</surname><given-names>I</given-names></name></person-group><year>2004</year><article-title>Changes in the hemagglutinins and neuraminidases of human influenza B viruses isolated in Italy during the 2001–02, 2002–03, and 2003–04 seasons</article-title><source>Journal of Medical Virology</source><volume>74</volume><fpage>629</fpage><lpage>640</lpage><pub-id pub-id-type="doi">10.1002/jmv.20225</pub-id></element-citation></ref><ref id="bib73"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pybus</surname><given-names>O</given-names></name><name><surname>Suchard</surname><given-names>M</given-names></name><name><surname>Lemey</surname><given-names>P</given-names></name><name><surname>Bernardin</surname><given-names>F</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name><name><surname>Crawford</surname><given-names>FW</given-names></name><name><surname>Gray</surname><given-names>RR</given-names></name><name><surname>Arinaminpathy</surname><given-names>N</given-names></name><name><surname>Stramer</surname><given-names>SL</given-names></name><name><surname>Busch</surname><given-names>MP</given-names></name><name><surname>Delwart</surname><given-names>EL</given-names></name></person-group><year>2012</year><article-title>Unifying the spatial epidemiology and molecular evolution of emerging epidemics</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>109</volume><fpage>15066</fpage><lpage>15071</lpage><pub-id pub-id-type="doi">10.1073/pnas.1206598109</pub-id></element-citation></ref><ref id="bib74"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raymond</surname><given-names>F</given-names></name><name><surname>Caton</surname><given-names>A</given-names></name><name><surname>Cox</surname><given-names>N</given-names></name><name><surname>Kendal</surname><given-names>A</given-names></name><name><surname>Brownlee</surname><given-names>G</given-names></name></person-group><year>1986</year><article-title>The antigenicity and evolution of influenza H1 haemagglutinin, from 1950–1957 and 1977–1983: two pathways from one gene</article-title><source>Virology</source><volume>148</volume><fpage>275</fpage><lpage>287</lpage><pub-id pub-id-type="doi">10.1016/0042-6822(86)90325-9</pub-id></element-citation></ref><ref id="bib75"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rota</surname><given-names>PA</given-names></name><name><surname>Wallis</surname><given-names>TR</given-names></name><name><surname>Harmon</surname><given-names>MW</given-names></name><name><surname>Rota</surname><given-names>JS</given-names></name><name><surname>Kendal</surname><given-names>AP</given-names></name><name><surname>Nerome</surname><given-names>K</given-names></name></person-group><year>1990</year><article-title>Cocirculation of two distinct evolutionary lineages of influenza type B virus since 1983</article-title><source>Virology</source><volume>175</volume><fpage>59</fpage><lpage>68</lpage><pub-id pub-id-type="doi">10.1016/0042-6822(90)90186-U</pub-id></element-citation></ref><ref id="bib76"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Russell</surname><given-names>CA</given-names></name><name><surname>Jones</surname><given-names>TC</given-names></name><name><surname>Barr</surname><given-names>IG</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name><name><surname>Garten</surname><given-names>RJ</given-names></name><etal/></person-group><year>2008</year><article-title>The global circulation of seasonal influenza A (H3N2) viruses</article-title><source>Science</source><volume>320</volume><fpage>340</fpage><lpage>346</lpage><pub-id pub-id-type="doi">10.1126/science.1154137</pub-id></element-citation></ref><ref id="bib77"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shapiro</surname><given-names>B</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name><name><surname>Drummond</surname><given-names>A</given-names></name></person-group><year>2006</year><article-title>Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences</article-title><source>Molecular Biology and Evolution</source><volume>23</volume><fpage>7</fpage><lpage>9</lpage><pub-id pub-id-type="doi">10.1093/molbev/msj021</pub-id></element-citation></ref><ref id="bib78"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shaw</surname><given-names>MW</given-names></name><name><surname>Xu</surname><given-names>X</given-names></name><name><surname>Li</surname><given-names>Y</given-names></name><name><surname>Normand</surname><given-names>S</given-names></name><name><surname>Ueki</surname><given-names>RT</given-names></name><name><surname>Kunimoto</surname><given-names>GY</given-names></name><name><surname>Hall</surname><given-names>H</given-names></name><name><surname>Klimov</surname><given-names>A</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name><name><surname>Subbarao</surname><given-names>K</given-names></name></person-group><year>2002</year><article-title>Reappearance and global spread of variants of influenza B/Victoria/2/87 lineage viruses in the 2000–2001 and 2001–2002 seasons</article-title><source>Virology</source><volume>303</volume><fpage>1</fpage><lpage>8</lpage><pub-id pub-id-type="doi">10.1006/viro.2002.1719</pub-id></element-citation></ref><ref id="bib79"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Smith</surname><given-names>DJ</given-names></name><name><surname>Lapedes</surname><given-names>AS</given-names></name><name><surname>de Jong</surname><given-names>JC</given-names></name><name><surname>Bestebroer</surname><given-names>TM</given-names></name><name><surname>Rimmelzwaan</surname><given-names>GF</given-names></name><name><surname>Osterhaus</surname><given-names>AD</given-names></name><name><surname>Fouchier</surname><given-names>RA</given-names></name></person-group><year>2004</year><article-title>Mapping the antigenic and genetic evolution of influenza virus</article-title><source>Science</source><volume>305</volume><fpage>371</fpage><lpage>376</lpage><pub-id pub-id-type="doi">10.1126/science.1097211</pub-id></element-citation></ref><ref id="bib80"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Squires</surname><given-names>R</given-names></name><name><surname>Noronha</surname><given-names>J</given-names></name><name><surname>Hunt</surname><given-names>V</given-names></name><name><surname>García-Sastre</surname><given-names>A</given-names></name><name><surname>Macken</surname><given-names>C</given-names></name><name><surname>Baumgarth</surname><given-names>N</given-names></name><name><surname>Suarez</surname><given-names>D</given-names></name><name><surname>Pickett</surname><given-names>BE</given-names></name><name><surname>Zhang</surname><given-names>Y</given-names></name><name><surname>Larsen</surname><given-names>CN</given-names></name><name><surname>Ramsey</surname><given-names>A</given-names></name><name><surname>Zhou</surname><given-names>L</given-names></name><name><surname>Zaremba</surname><given-names>S</given-names></name><name><surname>Kumar</surname><given-names>S</given-names></name><name><surname>Deitrich</surname><given-names>J</given-names></name><name><surname>Klem</surname><given-names>E</given-names></name><name><surname>Scheuermann</surname><given-names>RH</given-names></name></person-group><year>2012</year><article-title>Influenza research database: an integrated bioinformatics resource for influenza research and surveillance</article-title><source>Influenza and Other Respiratory Viruses</source><volume>6</volume><fpage>404</fpage><lpage>416</lpage><pub-id pub-id-type="doi">10.1111/j.1750-2659.2011.00331.x</pub-id></element-citation></ref><ref id="bib81"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Stevens</surname><given-names>DJ</given-names></name><name><surname>Douglas</surname><given-names>AR</given-names></name><name><surname>Skehel</surname><given-names>JJ</given-names></name><name><surname>Wiley</surname><given-names>DC</given-names></name></person-group><year>1987</year><article-title>Antigenic and amino acid sequence analysis of the variants of H1N1 influenza virus in 1986</article-title><source>Bulletin of the World Health Organization</source><volume>65</volume><fpage>177</fpage><lpage>180</lpage></element-citation></ref><ref id="bib82"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Webster</surname><given-names>R</given-names></name><name><surname>Kendal</surname><given-names>A</given-names></name><name><surname>Gerhard</surname><given-names>W</given-names></name></person-group><year>1979</year><article-title>Analysis of antigenic drift in recently isolated influenza A (H1N1) viruses using monoclonal antibody preparations</article-title><source>Virology</source><volume>96</volume><fpage>258</fpage><lpage>264</lpage><pub-id pub-id-type="doi">10.1016/0042-6822(79)90189-2</pub-id></element-citation></ref><ref id="bib83"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wiley</surname><given-names>D</given-names></name><name><surname>Wilson</surname><given-names>I</given-names></name><name><surname>Skehel</surname><given-names>J</given-names></name></person-group><year>1981</year><article-title>Structural identification of the antibody-binding sites of Hong Kong influenza haemagglutinin and their involvement in antigenic variation</article-title><source>Nature</source><volume>289</volume><fpage>373</fpage><lpage>378</lpage><pub-id pub-id-type="doi">10.1038/289373a0</pub-id></element-citation></ref><ref id="bib84"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Xu</surname><given-names>X</given-names></name><name><surname>Lindstrom</surname><given-names>SE</given-names></name><name><surname>Shaw</surname><given-names>MW</given-names></name><name><surname>Smith</surname><given-names>CB</given-names></name><name><surname>Hall</surname><given-names>HE</given-names></name><name><surname>Mungall</surname><given-names>BA</given-names></name><name><surname>Subbarao</surname><given-names>K</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name><name><surname>Klimov</surname><given-names>A</given-names></name></person-group><year>2004</year><article-title>Reassortment and evolution of current human influenza A and B viruses</article-title><source>Virus Research</source><volume>103</volume><fpage>55</fpage><lpage>60</lpage><pub-id pub-id-type="doi">10.1016/j.virusres.2004.02.013</pub-id></element-citation></ref></ref-list></back><sub-article article-type="article-commentary" id="SA1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.01914.024</article-id><title-group><article-title>Decision letter</article-title></title-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Losick</surname><given-names>Richard</given-names></name><role>Reviewing editor</role><aff><institution>Harvard University</institution>, <country>United States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see <ext-link ext-link-type="uri" xlink:href="http://elife.elifesciences.org/review-process">review process</ext-link>). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.</p></boxed-text><p>[Editors’ note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The two decision letters after peer review are shown below.]</p><p>Thank you for choosing to send your work entitled “Integrating influenza antigenic dynamics with molecular evolution” for consideration at <italic>eLife</italic>. Your article has now been peer reviewed and we regret to inform you that your work will not be considered further for publication at this stage. Your submission has been evaluated by a Senior editor and 2 reviewers, and the decision was reached after discussions between the reviewers.</p><p>The reviewers and the Senior editor found this extension of antigenic cartography most interesting, both methodologically with the introduction of a Bayesian framework, and from the inclusion of more clades and H1 and B data. The central issue, however, is that we are not convinced of a causal link between drift and incidence. The correlation between clades could simply be driven by the fact that H3N2 has more drift and higher incidence. Secondly, the correlation across years within a given clade could be driven by sampling biases. For example, if H1N1 is reported more than usual in a given year, it will typically have more isolates subjected to HI assays, which by itself might make it appear to have drifted more. (We note, however, that this issue might be addressable if the authors were to draw a random sample of the isolates such that the number per year were equal.)</p><p>In sum, we are concerned that the analysis suggests a bigger connection between drift and incidence than actually exists. It is not clear if there is correlation within clades (these plots were not shown), and the across-clade correlation could be at least partly an artifact of the pooling of clades. In addition, the across-clade and within-clade effects could be amplified by sampling bias. Given, however, the extreme importance of this work to understanding influenza evolution and vaccine selection and the potential to provide a quantitative assessment of the association between drift (as measured by cartography) and incidence, the reviewers and editor would be willing to consider a suitably revised submission with major revisions that convinced us that the correlation is true or that there is perhaps no correlation between drift and incidence (or conceivably that antigenic cartography is not a good way to measure drift).</p><p><italic>Reviewer #1 comments</italic>:</p><p>This paper is exceptional in many ways, but also contains some flaws that need to be addressed by revisions. If these flaws are addressed, I would be highly supportive of publication.</p><p>This paper deals with the antigenic evolution of influenza. A foundational paper in Science in 2004 by Smith et al introduced “antigenic cartography,” the technique used to monitor antigenic drift and select the influenza vaccine. This paper makes a clear methodological improvement on the original antigenic cartography technique. The new approach integrates phylogenetics, allowing inclusion of viral sequences and isolation dates. This paper also shows that accounting for virus and serum effects improves cartography. As the authors briefly note, the new method is also extensible to evolutionary questions. All of these improvements are made using a freely available phylogenetic software program that is the standard in the field. These methodological improvements would immediately merit publication in a technique-specific journal.</p><p>In addition, this paper presents biological results that should interest virologists, public health officials, and evolutionary biologists. While these results do not really alter the current understanding of influenza antigenic evolution, they extend this understanding from H3N2 to other clades, provide a more detailed analysis than has previously been performed for any clade, and quantify factors that have previously been characterized only qualitatively.</p><p>I do, however, have some major critiques:</p><p>• It is difficult to understand the biological results without grasping technical aspects of the computational approach. In my specific comments, I suggest some changes.</p><p>• I do not concur that <xref ref-type="fig" rid="fig5">Figure 5</xref> indicates “antigenic drift drives incidence rates.” There are problems with making the correlations in <xref ref-type="fig" rid="fig5">Figure 5</xref> across all four clades, since the clades have different average rates of drift and incidence. The conclusion would be supported if there was correlation between incidence and rate within clades, or if the correlation across clades exceeded the correlation of the clade averages. But as it stands, <xref ref-type="fig" rid="fig5">Figure 5</xref>'s correlations are just due to the fact that the four clades differ in the average rates, which does not imply that drift drives incidence. This paper is worth publishing even if a proper analysis fails to find that drift drives incidence, because currently the relationship is widely assumed without quantitative analysis. However, it is important to get this right as it forms the basis for influenza vaccine selection. I describe my concerns in more detail in the specific comments.</p><p>• The authors need to explain where they got the incidence data, how they chose the date ranges, specify when they are using relative versus absolute incidence, and provide raw data as supporting material. I describe my concerns in more detail in the specific comments.</p><p>• The improvement from inclusion of serum effects deserves comment and explanation if possible (are the effects due to the serum source)? Table 1 should include a model with virus effects but no serum effects. I describe my concerns in more detail in the specific comments.</p><p>Major points in more detail:</p><p>1) I have concerns about <xref ref-type="fig" rid="fig5">Figure 5</xref>, which the authors use to support their claim that “antigenic drift drives incidence rates.” The authors first establish the well-known fact that H3N2 incidence is highest, followed by H1N1 and then B. They also find that relative incidence is correlated with the rate of antigenic drift. However, this does not imply causality in terms of the higher average drift driving the higher average incidence. The authors do not claim any causality in this correlation between average drift and incidence in the four clades, and I am therefore fine with this part of the analysis. The problems arise in <xref ref-type="fig" rid="fig5">Figure 5A</xref>. The authors find a significant correlation between drift and incidence taken over all years and clades, and then use this to argue that drift drives incidence. I would agree with this conclusion if higher drift was associated with higher incidence with a correlation that is better than that obtained simply by comparing the averages of the four clades. But I don't think this is true. In <xref ref-type="fig" rid="fig5">Figure 5A</xref>, the authors are averaging over all clades, making the correlation in 5A a trivial consequence of the fact that H3N2 has higher average incidence and drift. Even if the rate of drift and incidence were constant year-over-year for each clade (and simply differed among clades), the authors would observe the correlation that they report. Put another way; imagine that every year the drift and incidence in each clade was equal to its average. Then <xref ref-type="fig" rid="fig5">Figure 5A</xref> would in effect correspond to simply recalculating the correlation between average drift and incidence in a scenario where each point is included as many times as there are years being examined. The more years that were included the higher the P-value would get because the number of data points would increase, but really the single actual trend (that H3N2 is higher in average drift and incidence) is just being counted multiple times. In order to draw a conclusion stronger that drift drives incidence, the authors need to show that incidence and drift are correlated within each clade individually, or else standardize the incidence so that the mean and variance for each individual clade is zero and one. It is not clear to me that there is any correlation between the drift and incidence within any of the individual clades. A similar problem affects <xref ref-type="fig" rid="fig5">Figure 5B</xref> - for example, since H3N2 has the highest drift, it will always tend to be associated with lower drift in other clades since the other clades inherently have lower average drift. But this does not imply direct interference between clades. I am open to further discussion about this point, but I do not see how <xref ref-type="fig" rid="fig5">Figure 5</xref> implies that antigenic drift drives incidence, or that there is dynamical interference across clades. By the way, I do not think that a lack of correlation would be a disqualifying concern in terms of publication. Finding no evidence that antigenic drift drives incidence is just as important as finding that it does. But the claim needs to be correct.</p><p>2) The incidence data are poorly explained. In the first paragraph of the Epidemiological consequences of antigenic drift section, the authors use relative incidence. In the next paragraph, are they switching to absolute incidence? This is not clear. If they are switching to absolute incidence, I don't think they ever explain in the Methods where that data comes from. In either case, what are the justifications for using absolute versus relative incidence? Also, why do they not analyze incidence prior to 1998/1999? Finally, because each influenza season spans two calendar years, why do they not break up the data by season rather than year?</p><p>3) An interesting result is that estimating the serum effects improves the performance a great deal (more than including the phylogenetic data, in fact!). It suggests that there may be systematic differences between the sera. Can this be attributed to the serum itself (such as whether it is goat versus ferret), or to the particular lab or study? Could the authors correlate the estimated serum effects back to the originating source for that serum to check? As a related point, I was surprised that inclusion of the virus effects led to only minor improvement, since prior work (http://www.ncbi.nlm.nih.gov/pubmed/19900932) suggests that some viruses are generally more resistant to HI than others. However, the virus effects are only included in a model (#9 in Table 1) where the serum effects are already included, and it is possible to imagine that including just one of these terms somehow helps correct for both effects. Can the authors include a tenth model in Table 1 that includes the virus effects but not the serum effects? This would clarify if serum effects are actually more important than virus effects, or simply whether inclusion of either one individually is more helpful than both together.</p><p><italic>Reviewer #2 comments</italic>:</p><p>The authors extend earlier work on “antigenic cartography” — that is, low-dimensional embeddings of viral strains using dimensionality reduction techniques, in order to quantify antigenic groupings of viral isolates. What is novel here compared to prior work is the introduciton of a Bayesian framework for this mapping process, the observation that antigenic drift within a clade correlates with clade-specific disease incidence each season, and anti-correlates with drift in other clades. The authors also introduce a phenomonological model of antigenic variation based on diffusion, and interpret antigenic drift in terms of fitted diffusion coefficiants. Finally, the authors provide antigenic maps for more clades of influenza (H3N2, H1N1, B/Vic, and B/Yam) than in previous publications.</p><p>Understanding antigenic drift of influenza in quantitative terms is clearly of great practical importance, and also an interesting intellectual problem in its own right. And it is nice to see antigenic maps for so many viral clades. However, I do not feel that the technical advances in “mapping” strains introduced here provide us much more confidence in the antigenic locations of strains than prior techniques do. Indeed, the authors themselves note that the average predictive error of this new methods is comparable to that of Smith et al. (2004). What might be more valuable, perhaps, are the results relating inferred antigenic drift and influenza incidence each season, by clade. But these results are quite possibly driven by sampling biases (see below), and I am not really convinced of their validity — at least not without serious efforts to remove such sampling biases. Finally, the discussion of a “diffusion” model of drift was extremely confusing to me, and the fitted diffusion coefficients do not have a clear meaning or interpretation.</p><p>Serious concerns follow:</p><p>1) The authors do not seem to discuss a problematic aspect of their results relating inferred drift to influenza disease incidence — namely that biased sampling of clades, in each season, could cause the observed correlations. If clades were sampled for HI assays unequally in each season, as I suspect, then this fact alone might cause the trend towards apparently more drift in the clade that was sampled most intensively in each season (and to which most ILI was attributed). This is an obvious possible confound for the analysis presented in <xref ref-type="fig" rid="fig4">Figure 4</xref>, and it should be ruled out by simulation of constant true rates of antigenic drift, variable sampling proportions in each season, and reconstructed drift using BMDS.</p><p>2) Likewise, in <xref ref-type="fig" rid="fig5">Figure 5</xref>, the negative correlation between drift in different clades in each season could, again, be driven by variation in the number of strains per clade that were subjected to HI each season. The authors could rule this out either by simulation or, more simply, be repeating their analysis after subsampling an equal number of isolates per clade each season for inclusion into the BMDS.</p><p>3) I found the section fitting diffusion coefficients (in different branches) to the antigenic maps confusing — if only because strict diffusion (in one or two dimensions) has no advection term and therefore no tendency to move in one direction or another; whereas the data clearly show an advective tendency (moving to the “right” over time in antigenic dimension 1). I presume the authors attempt to deal with this by imposing a prior (eq. 12) for the location of a virus based on its location in a molecular phylogeny. But this would seem to conflate antigenic drift, which the authors wish to quantify using a diffusion coefficient, with genetic mutations (many of which are driven by selection for antigenic escape). In other words, this hybrid approach of assuming a prior based on a strain's genotype, and then fitting a diffusion coefficient to summarize strength of drift, does not seem to be a pure measure of drift. What exactly the fitted diffusion coefficient means is extremely unclear to me, in any formal sense, as the procedure is so ad-hoc.</p><p>4) How do the antigenic maps shown compare to BMDS applied to pairwise AA hamming distances alone? How many serious discrepancies that are outside the confidence intervals on map reconstruction? In other words, the authors should demonstrate that the HI data actually provide substantively different results for antigenic grouping than genetic data do alone. This was an important contention of Smith et al. (2004), but it was based on the position of only a handful of viruses in that paper. Do the authors have more convincing evidence in this study that the antigenic data are providing substantial extra information beyond the genetic data?</p><p>[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]</p><p>Thank you for resubmitting your work entitled “Integrating influenza antigenic dynamics with molecular evolution” for consideration at <italic>eLife</italic>. Your submission has been evaluated by a Senior editor and the original two reviewers.</p><p>Both reviewers were pleased with the revised manuscript and only a small number of issues remain to be addressed before acceptance. These are: whether virus effects could be due to avidity, clarifying the meaning of tau in Table 2, expanding on the rationale for subsampling in the Punctuated evolution section, the apparent discrepancy between <xref ref-type="fig" rid="fig4">Figure 4</xref> and its legend, eliminating the orphan paragraph described in point #3 below, and a paragraph in the Discussion summarizing the main biological results. These points are explained in the reviewers’ comments below.</p><p>1) I like how the authors have included “virus effects” alone in the new Table 1. At least one “virus effect” could be overall receptor avidity, and Plotkin and Hensley have a recent paper (Journal of Virology, 87:9904) showing that avidity can influence antigenic clustering. It might be worthwhile to include a sentence on the possibility that “virus effects” could be a manifestation of avidity?</p><p>2) In Table 2 and the related discussion, the authors discuss the scaled effective population size N<sub>e</sub> * τ. They never define what tau represents, and I don't think it is safe to assume that the reader will know this — I certainly don't. More interpretation here would be helpful.</p><p>3) In the “Punctuated evolution and its epidemiological consequences” section, the part about subsampling to look at whether drift associates with number of isolates should be expanded. I would suggest starting a new paragraph at the current “We test to see...” sentence that briefly explains the rationale for why this test is being done (rationale articulated by other reviewer in original critiques). I also think that it would be nice to have a table or figure somehow representing the actual results of this analysis.</p><p>4) <xref ref-type="fig" rid="fig4">Figure 4</xref> legend refers to “The mean posterior scaled effective populations... is shown for each virus.” These are not actually shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>, at least not in a way that is obvious to me.</p><p>5) My comments where the original reason that the authors removed the argument for the across lineage correlation in incidence. However, now ‘Punctuated evolution and its epidemiological consequences’ section has this orphan paragraph beginning “Although the general correlation between rate of antigenic drift...” This paragraph doesn't seem to make sense in the context of the presented data any more, as the paper no longer has any information about across lineage correlations, so it can't even be seen what they are saying may not be causal. I think this paragraph either needs to be dramatically expended or probably better eliminated. Maybe the previous paragraph could then just get a wrap-up sentence interpreting the results to suggest a strong relationship between drift and incidence within each lineage.</p><p>6) Although the Conclusion is fine, I feel that it might benefit from a paragraph summarizing the main biological results as regards different rates of drift in lineages and the correlation between drift and incidence within lineages. These biological results are not really mentioned in the current Conclusion.</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.01914.025</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p>[Editors’ note: the author responses to the first round of peer review follow.]</p><p>Reviewer #1 comments:</p><p><italic>1) I have concerns about</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5</italic></xref><italic>, which the authors use to support their claim that “antigenic drift drives incidence rates.” The authors first establish the well-known fact that H3N2 incidence is highest, followed by H1N1 and then B. They also find that relative incidence is correlated with the rate of antigenic drift. However, this does not imply causality in terms of the higher average drift driving the higher average incidence. The authors do not claim any causality in this correlation between average drift and incidence in the four clades, and I am therefore fine with this part of the analysis. The problems arise in</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5A</italic></xref><italic>. The authors find a significant correlation between drift and incidence taken over all years and clades, and then use this to argue that drift drives incidence. I would agree with this conclusion if higher drift was associated with higher incidence with a correlation that is better than that obtained simply by comparing the averages of the four clades. But I don't think this is true. In</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5A</italic></xref><italic>, the authors are averaging over all clades, making the correlation in 5A a trivial consequence of the fact that H3N2 has higher average incidence and drift. Even if the rate of drift and incidence were constant year-over-year for each clade (and simply differed among clades), the authors would observe the correlation that they report. Put another way; imagine that every year the drift and incidence in each clade was equal to its average. Then</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5A</italic></xref> <italic>would in effect correspond to simply recalculating the correlation between average drift and incidence in a scenario where each point is included as many times as there are years being examined. The more years that were included the higher the P-value would get because the number of data points would increase, but really the single actual trend (that H3N2 is higher in average drift and incidence) is just being counted multiple times. In order to draw a conclusion stronger that drift drives incidence, the authors need to show that incidence and drift are correlated within each clade individually, or else standardize the incidence so that the mean and variance for each individual clade is zero and one. It is not clear to me that there is any correlation between the drift and incidence within any of the individual clades. A similar problem affects</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5B</italic></xref> <italic>- for example, since H3N2 has the highest drift, it will always tend to be associated with lower drift in other clades since the other clades inherently have lower average drift. But this does not imply direct interference between clades. I am open to further discussion about this point, but I do not see how</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5</italic></xref> <italic>implies that antigenic drift drives incidence, or that there is dynamical interference across clades. By the way, I do not think that a lack of correlation would be a disqualifying concern in terms of publication. Finding no evidence that antigenic drift drives incidence is just as important as finding that it does. But the claim needs to be correct</italic>.</p><p>This is a very astute criticism. We see how differing overall incidence between clades could have given an artifactual signal in our previous year-to-year drift vs incidence comparisons. In this revision, we have reanalyzed the data in the way suggested; we show that year-to-year antigenic drift and incidence are correlated within each clade individually, arriving at correlation coefficients of 0.51, 0.29, 0.44 and 0.14 for A/H3N2, A/H1N1, B/Vic and B/Yam respectively. None of these correlations are significant on their own, however observing four correlation coefficients of this magnitude is highly unlikely under a null model derived from bootstrap permutations (p = 0.018). Because the increase in incidence tends to follow periods of pronounced antigenic drift, we conclude that there appears to be a causal relationship between antigenic change and increased incidence.</p><p>However, in redoing this analysis on a lineage-by-lineage basis, we lost much of the signal for interference between lineages. We think there may still be something there, but the nuanced analysis that this issue deserves seems beyond the scope of the paper. We have decided to instead drop the discussion of interference between lineages.</p><p><italic>2) The incidence data are poorly explained. In the first paragraph of the Epidemiological consequences of antigenic drift section, the authors use relative incidence. In the next paragraph, are they switching to absolute incidence? This is not clear. If they are switching to absolute incidence, I don't think they ever explain in the Methods where that data comes from. In either case, what are the justifications for using absolute versus relative incidence</italic>?</p><p>In revising this section in the manuscript, we have made the source of the incidence data and its construction much more clear. In addition, we have removed the relative vs absolute incidence confusion, sticking instead with one measure: ILI × proportion of viral isolates attributable to a lineage.</p><p><italic>Also, why do they not analyze incidence prior to 1998/1999</italic>?</p><p>The 1998/1999 season is the earliest we have that properly distinguishes B/Vic and B/Yam in the CDC data.</p><p><italic>Finally, because each influenza season spans two calendar years, why do they not break up the data by season rather than year</italic>?</p><p>This would be much preferable. However, many virus isolates used in this analysis lack temporal resolution beyond the year of sampling. Because of this, we decided to stick with just year of isolation for the present analysis.</p><p><italic>3) An interesting result is that estimating the serum effects improves the performance a great deal (more than including the phylogenetic data, in fact!). It suggests that there may be systematic differences between the sera. Can this be attributed to the serum itself (such as whether it is goat versus ferret), or to the particular lab or study? Could the authors correlate the estimated serum effects back to the originating source for that serum to check</italic>?</p><p>We would suggest that a serum with a larger effect contains a more concentrated and active set of antibodies than a serum with a smaller effect. The increased number of antibodies could be due to experimental variation in serum extraction and processing or due to variation in immune response and timing between ferrets, i.e., some ferrets may mount an immediate and strong immune response, while others may mount a weaker response. This causes variation in overall strength of the serum. We try to control for the overall strength when looking at patterns of cross-reactivity through the use of ‘serum effects’. Some differences in serum effects could be tracked down to particular studies, but this work is beyond the scope of the current study. Here, we’ve essentially treated serum effect as a nuisance parameter. We’ve revised the text to discuss this as well as describe why estimating serum effects improves model performance over fixing serum effects.</p><p><italic>As a related point, I was surprised that inclusion of the virus effects led to only minor improvement, since prior work (</italic><ext-link ext-link-type="uri" xlink:href="http://www.ncbi.nlm.nih.gov/pubmed/19900932"><italic>http://www.ncbi.nlm.nih.gov/pubmed/19900932</italic></ext-link><italic>) suggests that some viruses are generally more resistant to HI than others. However, the virus effects are only included in a model (#9 in Table 1) where the serum effects are already included, and it is possible to imagine that including just one of these terms somehow helps correct for both effects. Can the authors include a tenth model in Table 1 that includes the virus effects but not the serum effects? This would clarify if serum effects are actually more important than virus effects, or simply whether inclusion of either one individually is more helpful than both together</italic>.</p><p>The inclusion of ‘virus effects’ was meant to capture exactly this observation, that some viruses may be generally more resistant to HI. To further assess their importance, we followed this suggestion and included test error for a model that estimates virus effects, but leaves serum effects fixed at maximum titers. In this case, we observe similar, but not quite as substantial, improvements to test error as the model that estimates serum effects, but does not include virus effects. From this observation, we conclude that estimating either virus or serum effects both improve the model.</p><p>Reviewer #2 comments:</p><p><italic>1) The authors do not seem to discuss a problematic aspect of their results relating inferred drift to influenza disease incidence—namely that biased sampling of clades, in each season, could cause the observed correlations. If clades were sampled for HI assays unequally in each season, as I suspect, then this fact alone might cause the trend towards apparently more drift in the clade that was sampled most intensively in each season (and to which most ILI was attributed). This is an obvious possible confound for the analysis presented in</italic> <xref ref-type="fig" rid="fig4"><italic>Figure 4</italic></xref><italic>, and it should be ruled out by simulation of constant true rates of antigenic drift, variable sampling proportions in each season, and reconstructed drift using BMDS</italic>.</p><p>We tested to see if there might be an bias in the estimates of year-to-year anti- genic drift based on number of virus isolates collected by correlating correlating drift between years i and i − 1 against the ratio of the number of isolates from year i to the number of isolates from year i−1. We found no significant correlation (Pearson’s r = −0.01, p = 0.411), suggesting our results to be unbiased with regard to sample count. We have included this analysis in the manuscript.</p><p><italic>2) Likewise, in</italic> <xref ref-type="fig" rid="fig5"><italic>Figure 5</italic></xref><italic>, the negative correlation between drift in different clades in each season could, again, be driven by variation in the number of strains per clade that were subjected to HI each season. The authors could rule this out either by simulation or, more simply, be repeating their analysis after subsampling an equal number of isolates per clade each season for inclusion into the BMDS</italic>.</p><p>The above analysis applies to this correlation as well.</p><p><italic>3) I found the section fitting diffusion coefficients (in different branches) to the antigenic maps confusing — if only because strict diffusion (in one or two dimensions) has no advection term and therefore no tendency to move in one direction or another; whereas the data clearly show an advective tendency (moving to the “right” over time in antigenic dimension 1). I presume the authors attempt to deal with this by imposing a prior (eq. 12) for the location of a virus based on its location in a molecular phylogeny. But this would seem to conflate antigenic drift, which the authors wish to quantify using a diffusion coefficient, with genetic mutations (many of which are driven by selection for antigenic escape). In other words, this hybrid approach of assuming a prior based on a strain's genotype, and then fitting a diffusion coefficient to summarize strength of drift, does not seem to be a pure measure of drift. What exactly the fitted diffusion coefficient means is extremely unclear to me, in any formal sense, as the procedure is so ad-hoc</italic>.</p><p>We agree that applying the standard measure of diffusion coefficient D based on displacement vs time, without accounting for advection was problematic. We have substantial revised the text to focus on direct parameter inference of drift parameter μ and diffusion volatility parameter σ<sub>x</sub>, properly separating advection and volatility in the diffusion process. The section “Antigenic evolution across influenza lineages” most reflects these changes, including the addition of a new Table 2.</p><p><italic>4) How do the antigenic maps shown compare to BMDS applied to pairwise AA hamming distances alone? How many serious discrepancies that are outside the confidence intervals on map reconstruction? In other words, the authors should demonstrate that the HI data actually provide substantively different results for antigenic grouping than genetic data do alone. This was an important contention of Smith et al. (2004), but it was based on the position of only a handful of viruses in that paper. Do the authors have more convincing evidence in this study that the antigenic data are providing substantial extra information beyond the genetic data</italic>?</p><p>We have revised the manuscript to include a thorough analysis of the relation- ship between genetic distance and antigenic distance. This is new <xref ref-type="fig" rid="fig1">Figure 1</xref>. Rather than constructing BMDS maps with pairwise AA distances, we take a more direct approach and compare pairwise antigenic distance from a BMDS model using only HI data (model 2 in Table 1) and pairwise genetic distances. We examine both pairwise AA distance and pairwise phylogenetic distance, as phylogenetic distance was the basis for our evolutionary diffusion model. We find fairly modest correlations in most cases case (between 0.10 for B/Yam and 0.68 for A/H3N2). Genetic data provides some predictive power for antigenic distance, but is a rather weak predictor alone. This was a big part of our rationale for attempting a joint genetic/antigenic model.</p><p>[Editors’ note: the author responses to the re-review follow.]</p><p><italic>1) I like how the authors have included “virus effects” alone in the new Table 1. At least one “virus effect” could be overall receptor avidity, and Plotkin and Hensley have a recent paper (Journal of Virology, 87:9904) showing that avidity can influence antigenic clustering. It might be worthwhile to include a sentence on the possibility that “virus effects” could be a manifestation of avidity</italic>?</p><p>We appreciate this suggestion. Including the biological explanation for why we observe virus effects in the form of decreased or increased overall HI reactivity is very important. We’ve revised this section to include references to virus avidity and relabeled ‘virus effects’ to ‘virus avidities’. This has the additional benefit of being more transparent of a term than the opaque ‘effect.’</p><p>With the change from ‘virus effect’ to ‘virus avidity’ made, we chose to make a similar biological realignment of ‘serum effect’ to ‘serum potency’, i.e. some sera have higher potency than other sera, allowing them to inhibit hemagglutination at lower concentrations than other sera. The use of potency here is meant to align with the neutralizing antibody literature that distinguishes neutralization potency from neutralization breadth. Antigenic cartography has not traditionally measured breadth of hemagglutination inhibition.</p><p><italic>2) In Table 2 and the related discussion, the authors discuss the scaled effective population size N</italic><sub><italic>e</italic></sub> <italic>* τ. They never define what tau represents, and I don't think it is safe to assume that the reader will know this — I certainly don't. More interpretation here would be helpful</italic>.</p><p>We’ve revised the manuscript to clarify the definition and interpretation of both Ne and τ.</p><p><italic>3) In the “Punctuated evolution and its epidemiological consequences” section, the part about subsampling to look at whether drift associates with number of isolates should be expanded. I would suggest starting a new paragraph at the current “We test to see...” sentence that briefly explains the rationale for why this test is being done (rationale articulated by other reviewer in original critiques). I also think that it would be nice to have a table or figure somehow representing the actual results of this analysis</italic>.</p><p>We’ve expanded out this sentence to a paragraph following the paragraph on the year-to-year drift vs incidence correlation. We give rationale for the test, explain the bootstrap procedure, give p-values for both combined and separate analyses across lineages and provide a figure showing a scatterplot of the data.</p><p><italic>4)</italic> <xref ref-type="fig" rid="fig4"><italic>Figure 4</italic></xref> <italic>legend refers to “The mean posterior scaled effective populations... is shown for each virus.” These are not actually shown in</italic> <xref ref-type="fig" rid="fig4"><italic>Figure 4</italic></xref><italic>, at least not in a way that is obvious to me</italic>.</p><p>Thank you for catching this. Estimates of N<sub>e</sub>τ had been included in <xref ref-type="fig" rid="fig4">Figure 4</xref>, but were moved to Table 2 and the <xref ref-type="fig" rid="fig4">Figure 4</xref> legend was not updated accordingly. This has been fixed to leave just the estimates in Table 2.</p><p><italic>5) My comments where the original reason that the authors removed the argument for the across lineage correlation in incidence. However, now ‘Punctuated evolution and its epidemiological consequences’ section has this orphan paragraph beginning “Although the general correlation between rate of antigenic drift...” This paragraph doesn't seem to make sense in the context of the presented data any more, as the paper no longer has any information about across lineage correlations, so it can't even be seen what they are saying may not be causal. I think this paragraph either needs to be dramatically expended or probably better eliminated. Maybe the previous paragraph could then just get a wrap-up sentence interpreting the results to suggest a strong relationship between drift and incidence within each lineage</italic>.</p><p>We agree with this advice. We have replaced this paragraph with a wrap-up sentence as suggested.</p><p><italic>6) Although the Conclusion is fine, I feel that it might benefit from a paragraph summarizing the main biological results as regards different rates of drift in lineages and the correlation between drift and incidence within lineages. These biological results are not really mentioned in the current Conclusion</italic>.</p><p>We have revised the Conclusion to include more discussion of the biological results.</p></body></sub-article></article>