The global circulation of seasonal influenza A (H3N2) viruses.

Abstract

Antigenic and genetic analysis of the hemagglutinin of approximately 13,000 human influenza A (H3N2) viruses from six continents during 2002-2007 revealed that there was continuous circulation in east and Southeast Asia (E-SE Asia) via a region-wide network of temporally overlapping epidemics and that epidemics in the temperate regions were seeded from this network each year. Seed strains generally first reached Oceania, North America, and Europe, and later South America. This evidence suggests that once A (H3N2) viruses leave E-SE Asia, they are unlikely to contribute to long-term viral evolution. If the trends observed during this period are an accurate representation of overall patterns of spread, then the antigenic characteristics of A (H3N2) viruses outside E-SE Asia may be forecast each year based on surveillance within E-SE Asia, with consequent improvements to vaccine strain selection.

Full text

Page 1

DOI: 10.1126/science.1154137
, 340 (2008);
320
Science
et al.Colin A. Russell,
(H3N2) Viruses
The Global Circulation of Seasonal Influenza A

www.sciencemag.org (this information is current as of April 28, 2008 ):
The following resources related to this article are available online at
http://www.sciencemag.org/cgi/content/full/320/5874/340
version of this article at:
including high-resolution figures, can be found in the online
Updated information and services,
http://www.sciencemag.org/cgi/content/full/320/5874/340/DC1
can be found at:
Supporting Online Material
found at:
http://www.sciencemag.org/cgi/content/full/320/5874/340#related-content
, 9 of which can be accessed for free:
cites 35 articles
This article
can be
related to this article
A list of selected additional articles on the Science Web sites

http://www.sciencemag.org/cgi/content/full/320/5874/340#otherarticles
http://www.sciencemag.org/cgi/collection/epidemiology
Epidemiology
:
subject collections
This article appears in the following
http://www.sciencemag.org/about/permissions.dtl
in whole or in part can be found at:
this article
permission to reproduce
of this article or about obtaining
reprints
Information about obtaining
registered trademark of AAAS.
is aScience2008 by the American Association for the Advancement of Science; all rights reserved. The title
CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005.
(print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 2

in net calcification rate and gross community
production but had no noticeable effect on the
ratio of calcification to photosynthesis. Other spe-
cies need to be investigated in light of the var-
iability encountered in response to changing PCO2
between coccolithophore species that are repre-
sentative of low and mid-latitudes (25).
Future research is needed to fully constrain
productivity changes over the Anthropocene pe-
riod, extend our understanding of calcification
changes at different latitudes and in different
ocean basins, and quantify how changing ballast
will affect export production. The widely held
assumptionthatallcoccolithophoreswilldecrease
their calcification under elevated PCO2 needs
reappraisal in the light of our laboratory and field
observations that demonstrate enhanced PIC pro-
duction and cell size under high PCO2conditions
and the resilience of calcifying phytoplankton in
the geological record (34). Our analyses are high-
ly relevant to ocean biogeochemical modeling
studies and underline the physiological and
ecologicalversatilityofcoccolithophoresandtheir
evolutionary adaptation through changes in ocean
carbonate chemistry associated with past and
projected PCO2levels.
References and Notes
1. E. Paasche, Phycologia 49, 503 (2002).
2. J. A. Kleypas et al., Science 284, 118 (1999).
3. J. Bijma, H. J. Spero, D. W. Lea, B. E. Bemis, in Use of
Proxies in Paleoceanography: Examples from the South
Atlantic, G. Fischer, G. Wefer, Eds. (Springer, Berlin,
1999), pp. 489–512.
4. U. Riebesell et al., Nature 407, 364 (2000).
5. I. Zondervan, R. E. Zeebe, B. Rost, U. Riebesell, Global
Biogeochem. Cycles 15, 507 (2001).
6. B. Delille et al., Global Biogeochem. Cycles 19, GB2023,
10.1029/2004GB002318 (2005).
7. G. Langer et al., Geochem. Geophys. Geosyst. 7, Q09006
(2006).
8. S. Trimborn, G. Langer, B. Rost, Limnol. Oceanogr. 52,
2285 (2007).
9. R. A. Feely et al., Science 305, 362 (2004).
10. K. P. Boessenkool, I. R. Hall, H. Elderfield, I. Yashayaev,
Geophys. Res. Lett. 34, 10.1029/2007GL030285 (2007).
11. Materials and methods are available as supporting
material on Science Online.
12. K. Caldeira, M. E. Wickett, Nature 425, 365 (2003).
13. J. Bollmann, J. O. Herrle, Earth Planet. Sci. Lett. 255,
273 (2007).
14. Z. S. Kolber, O. Prasil, P. G. Falkowski, Biochim. Biophys.
Acta 1367, 88 (1998).
15. This “balance point” [the calcification-to-photosynthesis
ratio at which a bloom has zero net impact on
atmospheric CO2(C:P)] was calculated as having a
value of about 1.5 at [DIC] = 2050 mmol kg−1, [Alk] =
2300 meq kg−1, temperature = 15°C, and salinity = 35.
The value of the balance point C:P ratio exhibits some
variability with in situ conditions. For instance, it varies in
the range 1.0 to 1.8 as in situ conditions vary in the
ranges [DIC] = 2000 to 2300 mmol kg−1, [Alk] = 2200 to
2400 meq kg−1, temperature = 10 to 30°C and salinity =
33 to 37. Its value will decrease by about 20% as PCO2
increases from 280 ppmv to 700 ppmv (other conditions
remaining constant) (16).
16. M. Frankignoulle, C. Canon, J.-P. Gattuso, Limnol.
Oceanogr. 39, 456 (1994).
17. T.R.Anderson,P.Pondaven,Deep-SeaRes.I50,573(2003).
18. S. Burkhardt, I. Zondevan, U. Riebesell, Limnol.
Oceanogr. 44, 683 (1999).
19. N. A. Nimer, M. J. Merrett, New Phytol. 123, 673 (1993).
20. H. Z. Wang, I. N. McCave, J. Geol. Soc. London 147, 373
(1990).
21. M. Frenz, K. H. Baumann, B. Boeckel, R. Hoppner,
R. Henrich, J. Sediment. Res. 75, 464 (2005).
22. I. N. McCave, I. R. Hall, Geochem. Geophys. Geosyst. 7,
Q10N05 (2006).
23. J. A. Flores, F. J. Sierro, Micropaleontology 43, 321 (1997).
24. M. Frenz, R. Henrich, Sedimentology 54, 391 (2007).
25. L. Beaufort, I. Probert, N. Buchet, Geochem. Geophys.
Geosyst. 8, Q09011, 10.1029/2006GC00149.
26. M. E. Hill, Micropaleontology 21, 227 (1975).
27. J. R. Young, P. Ziveri, Deep-Sea Res. II 47, 1679 (2000).
28. P. Ziveri, K. H. Baumann, B. Bockel, J. Bollmann,
J. Young, in Coccolithophores: From Molecular Processes
to Global Impact, H. Thierstein, J. Young, Eds. (Springer,
Berlin, 2004), pp. 403–428.
29. A. McIntyre, A. W. H. Bé, Deep-Sea Res. 14, 561 (1967).
30. D. Archer, E. Maier-Reimer, Nature 367, 260 (1994).
31. S. Barker, J. A. Higgins, H. Elderfield, Philos. Trans. R.
Soc. London Ser. A 361, 1977 (2003).
32. T. Tyrrell, R. E. Zeebe, Geochim. Cosmochim. Acta 68,
3521, 10.1016/j.gca.2004.02.018 (2004).
33. J. C. Zachos et al., Science 308, 1611 (2005).
34. S. J. Gibbs, P. R. Bown, J. A. Sessa, T. J. Bralower,
P. A. Wilson, Science 314, 1770 (2006).
35. K. H. Baumann, H. Andruleit, B. Bockel, M. Geisen,
H. Kinkel, Palaontol. Z. 79, 93 (2005).
36. A. J. Poulton, T. R. Adey, W. M. Balch, P. M. Holligan,
Deep-Sea Res. II 54, 538 (2007).
37. A. Sciandra et al., Mar. Ecol. Prog. Ser. 261, 111 (2003).
38. D. L. Royer, R. A. Berner, I. P. Montañez, N. J. Tabor,
D. J. Beerling, GSA Today 14, 10.1130/1052-5173(2004)
0142.0.CO;2 (2004).
39. C. D. Keeling, T. P. Whorf, in Trends: A Compendium
of Data on Global Change (Carbon Dioxide Information
Analysis Center, Oak Ridge National Laboratory, U.S.
Department of Energy, Oak Ridge, TN, 2005).
40. J. D. L. van Bleijswik, R. S. Kempers, M. J. Veldhuis,
J. Phycol. 30, 230 (1994).
41. The authors acknowledge M. Hill for manufacturing
the bubbling flasks, B. Alker for her assistance in PIC
preparation and analysis, D. Hydes for access to the
Versatile Instrument for the Determination of Titration
Alkalinity instrument, R. Head for POC analysis, and
R. Gibson for assistance with PIC and FRRF analysis.
We thank H. Medley for laboratory assistance and
J. Elliot for useful discussions. We are grateful to the
master, officers, crew, and scientific party of the RRS
Charles Darwin cruise CD159, in particular I. N. McCave
and H. Elderfield. We are grateful to O. M. Schofield,
P. A. Tyler, and T. Anderson for discussions on the
manuscript. We thank K. Davis for assistance with
graphic illustrations. This work was supported by
the Royal Society research grant no. 24437 (M.D.I.-R.)
and by the Betty and Gordon Moore Foundation Marine
Microbiology Investigator Award (flow cytometry analysis)
(E.V.A.). The field work was supported by the UK Natural
Environment Research Council RAPID Program. P.R.H.
acknowledges support from Natural Environment
Research Council (NERC) grant no. NER/S/S/2004/12772.
R.E.M.R. and I.R.H. gratefully acknowledge NERC
grant no. NER/T/S/2002/00980.
Supporting Online Material
www.sciencemag.org/cgi/content/full/320/5874/336/DC1
Materials and Methods
Figs. S1 to S3
Tables S1 and S2
References
13 December 2007; accepted 3 March 2008
10.1126/science.1154122
The Global Circulation of Seasonal
Influenza A (H3N2) Viruses
Colin A. Russell,1Terry C. Jones,1,2,3Ian G. Barr,4Nancy J. Cox,5Rebecca J. Garten,5
Vicky Gregory,6Ian D. Gust,4Alan W. Hampson,4Alan J. Hay,6Aeron C. Hurt,4Jan C. de Jong,2
Anne Kelso,4Alexander I. Klimov,5Tsutomu Kageyama,7Naomi Komadina,4Alan S. Lapedes,8
Yi P. Lin,6Ana Mosterin,1,3Masatsugu Obuchi,7Takato Odagiri,7Albert D. M. E. Osterhaus,2
Guus F. Rimmelzwaan,2Michael W. Shaw,5Eugene Skepner,1Klaus Stohr,9Masato Tashiro,7
Ron A. M. Fouchier,2Derek J. Smith1,2*
Antigenic and genetic analysis of the hemagglutinin of ~13,000 human influenza A (H3N2)
viruses from six continents during 2002–2007 revealed that there was continuous circulation in
east and Southeast Asia (E-SE Asia) via a region-wide network of temporally overlapping epidemics
and that epidemics in the temperate regions were seeded from this network each year. Seed strains
generally first reached Oceania, North America, and Europe, and later South America. This evidence
suggests that once A (H3N2) viruses leave E-SE Asia, they are unlikely to contribute to long-term
viral evolution. If the trends observed during this period are an accurate representation of overall
patterns of spread, then the antigenic characteristics of A (H3N2) viruses outside E-SE Asia may
be forecast each year based on surveillance within E-SE Asia, with consequent improvements
to vaccine strain selection.
I
viruses infect 5 to 15% of the global population,
resulting in ~500,000 deaths annually (1). De-
spite substantial progress in many areas of influ-
enza research, questions such as when and to
what extent the virus will change antigenically,
and to what extent viruses spread globally, re-
main unanswered. A fundamental issue behind
these questionsis whetherepidemics are the con-
nfluenza A (H3N2) virus is currently the ma-
jor cause of human influenza morbidity and
mortality worldwide. On average, influenza
sequenceoflow-levelpersistenceofvirusesfrom
thepreviousepidemicorwhethertheyareseeded
from epidemics in other regions and, if so, from
where (2–8).
Addressing these issues of local persistence
andglobalspreadisvitallyimportantfordesigning
optimal surveillance and control strategies. If epi-
demics were regularly seeded from an outside re-
gion and if the source region of seed strains could
be identified, it may be possible to forecast which
variants would appear in epidemics in seeded
18 APRIL 2008 VOL 320
SCIENCE
www.sciencemag.org
340
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 3

regions and, consequently, to optimize vaccine
strainselection.Alternatively,ifvirusespersistwith-
in a region, evolve, and reemerge to cause the next
epidemic, intervention strategies targeting virus
circulation between epidemics might be effective
in minimizing subsequent epidemics.
TheeightgenesegmentsofinfluenzaAviruses
reassort, leading to complicated phylogenetic
patterns at the genomic scale (4, 8–10). The gene
segment coding for the hemagglutinin (HA) is of
major importance because the HA protein is the
primary target of the protective immune response.
Consequently, the HA is the focus of public health
surveillance and the primary component of cur-
rently licensed influenza vaccines. We used anti-
genic and genetic analyses of the HA as a marker
to investigate the global evolution and epidemiol-
ogy of influenza A (H3N2) viruses from 2002 to
2007 and to determine whether influenza epidem-
ics arise from locally persisting strains or whether
epidemics are seeded from other regions.
Antigenic Evolution
Antigenic cartography has shown that the anti-
genic evolution of A (H3N2) virus, since its ap-
pearance in humans in 1968, can be represented
by a two-dimensional (2D) antigenic map (11).
Since 2002, the antigenic evolution of A (H3N2)
viruses has roughly followed a line away from
the A/Sydney/5/1997-like viruses that predomi-
nated in 1998 through the A/Fujian/441/2002-
likevirusestotheA/California/7/2004-likeviruses
to the A/Wisconsin/67/2005-like strains that pre-
dominatedin2006and2007.Figure1Ausesthis
directionalbiastomakea2Dplottoshowspatial
antigenicevolutionandepidemiologyinoneplot.
Previously,Smithetal.(11)showedthat,from
1968to2003,theantigenicevolutionofA(H3N2)
virus was punctuated: Periods of relative stasis
lasting from 3 to 8 years were followed by rapid
antigenic change, resulting in transitions to new
antigenic clusters that necessitated an update of
the influenza virus vaccine strain. During this
time, several clusters also exhibited intracluster
antigenicevolution,necessitatingawithin-cluster
update of the vaccine strain. We find a similar
pattern of intracluster antigenic evolution from
2002 to 2007. During this time, antigenic evo-
lutionprogressedawayfromA/Sydney/5/1997at
an average rate of 2.13 antigenic units per year
(Fig. 1A). A distance of two antigenic units,
representing a fourfold difference in hemaggluti-
nation inhibition (HI) assay titer, is generally
considered as a sufficient antigenic difference to
warranta vaccine update.TheA(H3N2)compo-
nent of the influenza vaccine was updated four
times during this period. A core component of
vaccinestrainselectioninvolvesidentifyingemerg-
ing antigenic variants. If an emerging variant is
judgedlikelytocauseepidemicsintheupcoming
influenza season, the vaccine is updated to con-
tain a representative of the new strain.
Wefinddifferencesintheamountofantigenic
variation seen during an epidemic in different re-
gions and from year to year in the same region
(Fig. 1A). Despite such spatial and temporal heter-
ogeneities,theantigenicevolutionhasbeenmarked-
lyhomogeneousonaglobalscale.Anexplanation
for this homogeneity could be that viruses circu-
lategloballyratherthanpersistandevolvelocally.
To search for global patterns in the source of
emerging variants, we measured which regions
were leading or trailing antigenically and found
that, from 2002 to 2007, newly emerged strains
oftheA(H3N2)subtypeappearedinE-SEAsian
countries, on average, ~6 to 9 months earlier than
they appeared in other regions, with long delays
toSouthAmerica,typicallyofanadditional~6to
9 months (Fig.2A). Though A (H3N2) viruses in
E-SE Asian countries are on average more anti-
genically advanced, there is sufficient variability
fromseasontoseason(coloredcirclesinFig.2A)
suchthatnooneparticularcountryintheregionis
consistently most advanced. Thailand, Malaysia,
and Japan are exceptions to the Asia-leading pat-
tern, being less antigenically advanced than the
rest of the region.
OneinterpretationofthisAsia-leadingpattern
isthatnewvariantsemergefirstinE-SEAsiaand
subsequently seed other regions of the world. An
alternative but more complex explanation is that
this pattern is the product of independent local
persistence in multiple regions and parallel evo-
lution in which similar antigenic variants emerge
independently worldwide as a result of similar
selection pressures. To test between these two
interpretations, we must answer the fundamental
long-standing question of whether influenza vi-
ruses persist in a region, and could thus undergo
parallel evolution, or whether regions are regu-
larly seeded from external regions.
About 10% of the ~13,000 A (H3N2) viruses
analyzed antigenically were also analyzed genet-
ically by sequencing the HA1 domain of the he-
magglutinin(12).Thissubsetwasarepresentative
sampleofall~13,000isolates(fig.S1B)andthus
wassuitableforinvestigatingtheancestryofstrains
andthefundamentalissueoflocalpersistencever-
susseedingintheglobalcirculationofA(H3N2)
viruses.Thegeneticprogressionovertime(Fig.1B)
shows similar average patterns to the antigenic
data, with Asia leading [as previously shown for
Taiwan (13)] and South America trailing (Fig. 2,
A and B). However, there were important differ-
ences (China in 2005 and Oceania in 2005). For
influenzavaccinestrainselection,genetic-antigenic
differences are resolved in favor of the antigenic
data,becausethehumoralimmunesystem“sees”
the virus phenotype, not the genotype.
Persistence Versus Seeding
Source of inter-epidemic strains. The simplest
test of persistence versus seeding is to examine
the origin of strains isolated between epidemics.
If viruses persist locally, at least some of the
inter-epidemic strains would be descended from,
and thus more closely related to, strains from the
previous epidemic than to strains from outside
the region. Alternatively, if there was no persist-
ence, inter-epidemic strains would be more sim-
ilar to strains from elsewhere.
We sequenced the HA1 domains of 52 inter-
epidemic strains isolated in Oceania (primarily
AustraliaandNewZealand),NorthAmerica,and
Japan from June 2002 to September 2006. None
of these inter-epidemic strains was more similar
to strains from the previous local epidemic than
to externally circulating strains (Fig. 3). This re-
sult is evidence for external seeding and against
local persistence.
Even when done well, inter-epidemic surveil-
lance yields relatively small amounts of data that
can never completely rule out the existence of
local virus persistence between epidemics, espe-
cially of any low-pathogenic variants that pro-
duce subclinical infections. The test described in
the next section has the advantage of using all
available sequence data rather than being limited
tointer-epidemicdata.Nevertheless,alltestsmust
take into account the effects of external introduc-
tions during local epidemics (14).
Evolutionary relationship of strains from one
epidemic to the next in a region. As described
by Nelson et al. (4, 8), if epidemic strains persist
locally and give rise to the next local epidemic,
thosestrainsshouldbe morecloselyrelatedtoone
another than to strains isolated in other regions,
andaphylogenetictreeofthedatawouldlooklike
thatdepictedinfig.S2A.Conversely,ifepidemics
were seeded from outside a region, the epidemic
strains would be more similar to contemporary
strains from outside that region than to strains
from the previous local epidemic (fig. S2B).
Following the methodology of Nelson et al.
(4, 8), we constructed a phylogenetic tree of the
HA1 domain of the hemagglutinin from the se-
quencedsubsetoftheglobalsurveillancedata(Fig.
1C and fig. S3A). In this tree, the HA1 of the
viruses in each epidemic in a temperate region
(four in North America, five in Oceania, four in
Europe, and four in Japan) and each epidemic in a
subtropicalregion(threeinHongKong)descended
from externally circulating strains, not from strains
in the previous local epidemic (Fig. 1, C and D).
The topology of this tree is more similar to that in
fig. S2B than to that in fig. S2A. This result is also
evidence for external seeding and against persist-
ence. For other regions, including most tropical
and subtropical regions, there were fewer se-
quences, and it was not possible to conclusively
differentiate between persistence and seeding.
1Department of Zoology, University of Cambridge, Cambridge,
UK.
Rotterdam,Netherlands.3UniversitatPompeuFabra,Barcelona,
Spain.4World Health Organization (WHO) Collaborating Centre
for Reference and Research on Influenza, Melbourne, Australia.
5WHO Collaborating Center for Influenza, Centers for Disease
Control and Prevention, Atlanta, GA, USA.6WHO Collaborating
Centre for Influenza, National Institute for Medical Research
(NIMR), London, UK.7WHO Collaborating Center for Influenza,
National Institute for Infectious Diseases, Tokyo, Japan.
8Theoretical Division, Los Alamos National Laboratory, Los
Alamos, NM, USA.9Novartis Vaccines and Diagnostics, Cam-
bridge, MA, USA.
*To whom correspondence should be addressed. E-mail:
dsmith@zoo.cam.ac.uk
2Department of Virology, Erasmus Medical Centre,
www.sciencemag.org
SCIENCE
VOL 32018 APRIL 2008
341
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 4

024681012 14
2002
2002.5
2003
2003.5
2004
2004.5
2005
2005.5
2006
2006.5
2007
Antigenic distance from Sydney/5/1997
Time
A
0.040.0450.05
Tree distance from Wuhan/359/1995
0.0550.060.065 0.070.0750.080.085
2002
2002.5
2003
2003.5
2004
2004.5
2005
2005.5
2006
2006.5
2007
Time
B
CD
TW-1554-2004-04-10
TAIWAN/1563/2004-2004-07-08
NINGBO/997/2004-2004-09-06
TIANJIN/263/2004-2004-09-06
TIANJIN/273/2004-2004-09-28
KOBE/189/2004-2004-11-22
CHEJU/1845/2004-2004-12-24
NEPAL/1660/2004-2004-07-02
PERTH/1/2005-2005-01-04
MS-05020500070-2005-02-27
JIANGXI/169/2005-2005-03-17
RI-2005100001-2005-01-24
NY-17460-2005-01-05
GA-05C0191488-2005-01-06
TAIWAN/1562/2004-2004-08-06
MALAYSIA/25/2004-2004-09-15
JIANGXI/206/2005-2005-03-30
TEXAS/6/2004-2004-09-02
MALAYSIA/1875/2004-2004-09-06
CA-S71051-2004-09-11
WAKAYAMA/1/2005-2005-01-19
HI-05-0137-2005-01-04
FL-JVT-15282-2005-03-10
VE-254155-2005-08-19
KYOTO/3/2005-2005-02-05
NEPAL/1680/2004-2004-07-02
NEPAL/1670/2004-2004-07-02
KHABAROVSK/9/2005-2005-01-27
KAMPHAENGPHET/3524/2004-2004-11-02TAIWAN/51/2005-2005-01-27
GUNMA/508/2004-2004-12-07
SAITAMA/43/2004-2004-12-21
CHRISTCHURCH/104/2004-2004-09-07
DARWIN/1/2004-2004-07-08
CHRISTCHURCH/215/2004-2004-09-13
180oW120oW 60oW 0o
60oE 120oE 180oW
60oS
30oS
0o
30oN
60oN
Longitude
E
Latitude
Fig. 1. Global patterns in antigenic and genetic
evolution over time. (A) Antigenic distance from A/
Sydney/5/1997virusofallisolatesplottedagainsttime
ofisolation.Oneunitofantigenicdistancecorresponds
toatwofolddilutionofantiserumintheHIassay.Each
point corresponds to a laboratory-confirmed influenza
A(H3N2) isolate,with thecolorofthe pointindicating
theregionofgeographicoriginasshownin(E).Thethickblacklineisthebest-fitstatisticalmodel(aloessspline)fittedthroughalldatapointstoshowthetrendovertime.
Pointsinadvanceofthesplineareantigenicallyadvanced,whereasstrainsbehindthesplineareantigenicallylagging.(B)Geneticversionof(A)forallsequencedstrains
withdistancemeasuredtotheroot,A/Wuhan/359/1995,ofamaximumlikelihoodnucleotidephylogenetictree(C).Thethickblacklineisthesameasin(A)butforthe
genetic data. (C) Phylogenetic tree of HA1 nucleotide sequences color-coded by geographic origin (E), including strain names and isolation dates. We constructed the
initialtreewiththePhyMLsoftwarepackageversion2.4.5(38),with1567nucleotidesequences(12)andA/Wuhan/359/1995astheroot,usingGTR+I+G4(thegeneral
time-reversiblemodelwiththeproportionofinvariantsitesandthegammadistributionofamong-siteratevariationwithfourratecategoriesestimatedfromtheempirical
data)[determinedbyModelTest(39)]astheevolutionarymodel.GARLIversion0.951(40)wasrunonthebesttreefromPhyMLfortwomilliongenerationstooptimize
tree topology and branch lengths. Figure S3A provides a “zoom-able” version of this image. (D) Partial detail of (C). (E) Color-coded geographic setting for (A) to (D).
18 APRIL 2008 VOL 320
SCIENCE
www.sciencemag.org
342
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 5

Thisevidenceforexternalseedingandagainst
persistence agrees with full-genome analyses of
NewYorkstate,Australia,andNewZealanddata
that show global migration of A (H3N2) viruses
rather than local persistence (4, 8–10, 15). In ad-
dition, Nelson et al. (8) find evidence compatible
with either northern-to-southern hemisphere mi-
gration or migration from tropical regions, in-
cluding Southeast Asia.
Source of Seeding
Given this evidence for seeding and against local
persistence,weareleftwiththeinterpretationthat
the E-SE Asia–leading pattern (Fig. 2, A and B)
implies that new variants emerge first in E-SE
Asia and then seed the rest of the world. The
phylogenetic tree provides further evidence to
support this interpretation, showing that the an-
cestors of strains in temperate regions typically
originate in E-SE Asia, with the “trunk” of the
phylogenetictreetypicallyoccupiedbyE-SEAsian
strains (Fig. 1, C and D) and with, on average,
E-SEAsianstrainsclosertothetrunk(P<0.001)
than strains from all other regions (Fig. 2C).
The above analyses, in addition to being evi-
dence for an “out of E-SE Asia” hypothesis, are
also evidence against several other long-standing
unresolved hypotheses for the global circulation
of influenza viruses, as follows.
Out-of-China. If China alone were the source
of all new variants and effectively seeded the rest
of the world (16), then Chinese strains would be
(i) closer to the trunk than strains from all other
regions each year and (ii) consistently antigeni-
cally and genetically advanced relative to strains
from other regions, both of which we do not find
(Fig.2).Commensuratewithpreviouslypublished
studies, we find new variants are sometimes first
detected in China (15, 17, 18); however, we also
findthatnewvariantsaresometimesfirstdetected
in other countries in E-SE Asia (Fig. 2).
Out-of-tropics. In this hypothesis, epidemics
in regions outside the tropics are seeded from the
tropics (7, 19). If true, A (H3N2) viruses would
need to circulate continually in the tropics and
would give rise to one of two evolutionary
patterns. One pattern would arise if tropical Asia,
Africa,andSouthAmericawerewell connected
epidemiologically to one another; in this case,
all three regions would be similarly antigenical-
ly and genetically advanced and closer to the
trunk than nontropical regions. The other pattern
would arise if the three tropical regions were
poorly connected epidemiologically to one an-
other; in this case, there would be independent
genetic lineages for each tropical region. There is
currently not enough data to include tropical
Africainthisanalysis.However,fortropicalAsia
and South America, neither of these patterns is
observed (Figs. 1C and 2 and fig. S3A) (14).
Seedingbystrainsmovingbetweenthenorth-
ern and southern hemispheres. If this hypothesis
were true, then each year epidemics in the
northern hemisphere would be seeded by viruses
from epidemics in the southern hemisphere and
vice versa (20–22). The phylogenetic tree for the
HA1 domain (Fig. 1C and fig. S3A) shows no
evidenceforepidemicstrainsinthenorthernhemi-
spherebeingdescendantfromstrainsepidemicin
South America or Africa. The tree shows limited
evidence for Oceania playing a role in seeding a
minorityofepidemicsinthenorthernhemisphere
(14) but at a level insufficient to support this
hypothesis as the dominant mechanism of the
global circulation of influenza viruses. This
hypothesis also fails to explain how viruses from
Asia, which is almost entirely contained within
the northern hemisphere, lead antigenically and
genetically and are closest to the trunk of the
phylogenetic tree.
Local persistence with seeding only at cluster
transitions. Though there was no major cluster
transition during our study period, there has been
an average of 2.13 units of antigenic evolution
eachyear.Evenso,intemperateregions,nolocal
persistence could be detected, and each epidemic
was seeded by exogenous strains. The drift vari-
ants observed in this study have emerged from
E-SE Asia; however, because we have not seen
a major cluster transition of the magnitude of
Wuhan 1995 to Sydney 1997 (~4.7 antigenic
units), we can neither exclude that in such a case
a new variant could emerge outside E-SE Asia
nor that it could affect seeding patterns.
The E-SE Asian Circulation Network
For E-SE Asia to seed epidemics in multiple re-
gions of the world, influenza virus must circulate
continually in E-SE Asia. But how?
−3 −2−1
Mean antigenic distance from spline
0123
China
Taiwan
Hong Kong
South Korea
USA
Mexico
Singapore
Phillipines
Europe
Peru
Egypt
Japan
Russia
Australia/NZ
Malaysia
Canada
Thailand
South Africa
Chile
Brazil
Argentina
India
Colombia
Middle East
Paraguay


2002
2002.5
2003
2003.5
2004
2004.5
2005
2005.5
2006
2006.5
2007
−15−12−9 −6 −3 0 3 6 9 12 15
Months
−9−8−7−6 −5−4−3−2−10123456789
x 10
−3
E&SE Asia
China
Japan
N. America
Europe
Oceania
S. America
Mean genetic distance from spline


2002
2003
2004
2005
2006
2007
−15−12−9 −6 −3 0 3 6 9 12 15
Months
01234567891011
−3
x 10
E&SE Asia
China
Japan
N. America
Oceania
Europe
S. America
Mean genetic distance to trunk


2002
2003
2004
2005
2006
2007
A
B
C
Fig. 2. Evolutionarily leading and trailing regions. (A) Black circles indicate the average antigenic
distance to the spline of Fig. 1A for all strains isolated in a region, and the thin horizontal black line
indicates the SEM. Colored circles split this overall average by epidemic; circle color indicates time. The
spline can also be interpreted as a function of time; thus, time is shown as a second x axis. (B) Similar to
(A) but based ongeneticdistanceto spline from Fig.1B.(C) Geneticdistance totrunk of thephylogenetic
tree by region and season. We algorithmically defined the trunk of the tree in Fig. 1C (14) and calculated
the tree distance of each strain to the trunk. Average distance to trunk was calculated per region and per
season. The black circles indicate the overall average per region, the thin horizontal black line indicates
the SEM, and colored circles indicate seasonal averages. The mean for E-SE Asia is different from that of
Oceania (P < 0.00001), North America (P < 0.001), Europe (P < 0.01), and South America (P < 0.0001).
www.sciencemag.org
SCIENCE
VOL 32018 APRIL 2008
343
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 6

It is generally considered that influenza vi-
ruses continually circulate in tropical countries
(7, 23–27) and, if this were true, it would explain
how influenza viruses could persist in tropical
Asia. Indeed, circulation in an endemic core area
that seeds satellite areas has been shown to be a
key epidemiological process for the continual cir-
culationofantigenicallystablepathogens(28,29).
Reports based on influenza-like illness (ILI) or
influenza and pneumonia mortality (IPM) data
describe continual circulation in the tropics (23).
However,severalvirusesother thaninfluenzacan
cause ILI and IPM, and studies from tropical
countriesbasedonviralisolationsshowamarked
seasonality for influenza epidemics, with peaks
usually occurring during periods of high rainfall
(30–35). In agreement with these studies based
on virus isolation, our virus isolation study also
finds that influenza has clear epidemic peaks and
deep troughs in all regions, including the four
tropical and four subtropical E-SE Asian coun-
tries for which there are sufficient data to detect
an epidemic signal. Thus, continuous circulation
in individual tropical countries is unlikely to be
the mechanism for persistence in E-SE Asia.
However, more data from a wide diversity of
locations are needed to fully understand seasonal
forcing and to definitively exclude local persist-
ence as an element of transmission dynamics in
tropical and subtropical areas of E-SE Asia.
Another possibility for continual circulation
is that viruses pass from epidemic to epidemic
among countries via the mobile human popula-
tion. Figure 4, A and C, shows that there is suf-
ficientvariabilityinthetimingofepidemicswithin
E-SE Asia such that the virus could circulate
continuously in this way as a result of the tem-
poral overlap of epidemics. Much of the varia-
bility in the timing of epidemics is likely to be
linked to the heterogeneity in the timing of lower
2002.5
C
20032003.5 20042004.520052005.520062006.5
B
2002.5 20032003.520042004.5
Time
2005 2005.52006 2006.5
E
2002.5 2003 2003.520042004.5 20052005.52006 2006.5
0
0.02
0.04
0.06
0.08
0.1
A
2002.5
D
20032003.520042004.5 20052005.520062006.5
0
0.02
0.04
0.06
0.08
0.1
Laboratory confirmed H3N2 infections
2002.5 20032003.520042004.5 20052005.520062006.5
0
0.02
0.04
0.06
0.08
0.1
80oE 100oE 120oE 140oE 160oE 180oE
40oS
20oS
0o
20oN
40oN
60oN F
Longitude
Latitude
Fig. 4. Synchrony of epidemics in east Asia and the South Pacific. (A)
Epidemics in east Asia. The y axis shows laboratory-confirmed H3N2
infections per 2 weeks as a proportion of the total number of laboratory-
confirmed H3N2 infections over the study period in each location. (B) Strains
on the trunk of the phylogenetic tree are of particular evolutionary
importance in testing for virus migration among countries. In (B) and (E),
there is a circle for every strain on the trunk of the phylogenetic tree (figs.
S3A and S4). The purpose is to show where the trunk strains were isolated
[top row color code from (A), bottom row from (C)] and when they were
isolated, to assess the epidemiological activity at the time of isolation. Cyan
circles represent E-SE Asian strains but in locations not shown in (F). (C)
Same as (A) but for tropical Southeast Asia. (D) Same as (A) but for Australia
and New Zealand. (E) Same as (B), but the top row are Oceanian strains
[cyan circles represent strains from cities in Australia not shown in (F)], and
the bottom row are strains from North America (blue) and Russia and
Ukraine (yellow). (F) Geographic setting for (A) to (E).
Fig. 3. The genetic re-
lationshipofinterseason-
alstrainstostrainsinthe
previous local epidemic
and to strains epidemic
in other regions. Inter-
seasonal strains are de-
fined as strains isolated
morethan1monthafter
the end of the previous
localepidemicandmore
than1monthbeforethe
beginningofthenextlo-
cal epidemic. For each
interseasonal strain, the
phylogenetic tree dis-
tance was calculated to
the closest strain in the
previousepidemicandto
the closest strain found
outsidetheregioninthe
previous 4 months. The
diagonal line is 1:1 and
isincludedforreference.
0 0.0020.004
Tree distance from strains in all external locations
0.0060.008 0.0100.0120.0140.016
0
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
Tree distance from local previous epidemic


USA
Oceania
Japan
18 APRIL 2008 VOL 320
SCIENCE
www.sciencemag.org
344
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 7

temperatures and rainy seasons (19, 33, 36). We
thushypothesizethatthevariabilityofepidemics,
combined with the interconnectedness of E-SE
Asiancountries,formsanE-SEAsian circulation
network that maintains influenza virus in the re-
gion by passing from epidemic to epidemic.
If such a network existed, we would expect a
temporal and phylogenetic progression of E-SE
Asianvirusesonthetrunkofphylogenetictreeas
viruses pass from epidemic to epidemic within
thenetwork.FigureS4showssuchaprogression,
and Fig. 4, B and E, shows the relationship of
these trunk strains to the timing of epidemics.
Trunkstrainswereisolatedintemperate,subtrop-
ical,andtropicalregionsofE-SEAsia,indicating
that all three climatic regions of E-SE Asia are
part of the circulation network. To test whether
the non–E-SE Asian strains on the trunk indicate
that the circulation network includes countries
outside of E-SE Asia or whether they represent
one-way seeding events out of E-SE Asia, we ex-
aminedthephylogenetictree(Fig.1Candfig.S3A).
We found only limited instances of such seeding
backintoE-SEAsia,withclearevidencethatmost
E-SEAsianstrainsweredirectlydescendentfrom
other E-SE Asian strains (14)—thus indicating
thatthetemporallyoverlappingepidemicsinE-SE
Asia form a circulation network that, during the
study period, has been mostly closed to external
reseeding.
E-SE Asia’s strong travel and trade connec-
tions to Oceania, North America, and Europe
(14, 37) facilitate the rapid movement of new in-
fluenza virus variants into those areas and thus
explain the relatively small lag in antigenic and
geneticadvancementseeninthoseregions(Fig.2,
A and B). Also, though it is unclear how much
travel there must be between two locations for
themtobeepidemiologicallywell-connected,South
America’s 6- to 9-month antigenic lag (Fig. 2A)
may be attributable to its paucity of direct connec-
tions with E-SE Asia (fig. S5). South America’s
strong travel connections to Europe and North
America, but not to E-SE Asia, could result in a
seeding hierarchy where strains are first seeded
intoNorthAmericaandEuropeandfromthereto
South America (Fig. 5). Most strains appear to
circulate in this simple hierarchy, and even those
strainsthatcirculate ina more complexhierarchy
stilloriginateinE-SEAsia(14).Thus,theextinc-
tionofmanyH3lineages—akeycharacteristicof
the H3 phylogeny—may, in addition to the accu-
mulation of deleterious mutations (25), also be
due to reaching the end of this hierarchy.
Surveillance and Vaccine Strain Selection
A major practical function of WHO’s Global
Influenza Surveillance Network is to assist reg-
ulatory authorities to recommend which strains
shouldbeincludedininfluenzavaccines.Expand-
ing surveillance within the E-SE Asian circula-
tion network will aid the early detection of the
emergence and spread of new variants and could
help to more precisely define the network. Such
surveillanceiscrucialforoptimizingvaccinestrain
selectionforcountrieswithinthenetworkandfor
forecasting which variants will seed epidemics in
the restoftheworld,consequently increasing vac-
cine efficacy and ultimately reducing influenza
morbidity and mortality worldwide.
Given the importance of the HA, it is the
only portion of the virus genome that is currently
sequenced routinely within the WHO Global
Influenza Surveillance Network. Recently, whole-
genomesequencinginitiativeshaveprovidedim-
portant insights into the genesis and spread of
reassortment viruses, their rapid migration, and
thecocirculationofmultiplelineages(4,8,9,15).
Expanded sequencing of whole genomes will
provideadditionalmarkersfortrackingtheglobal
migration of viruses and reveal potential differ-
ences between the global evolution of the HA
and the other gene segments. Such sequencing
effortsshouldincludestrainsfromE-SEAsiaand
be linked with antigenic data on HA and, in the
longer term, with phenotype changes determined
by other virus genes to fully understand the se-
lection pressures on influenza viruses and their
epidemiology.
The data used in this study were generated by
theWHOGlobalInfluenzaSurveillanceNetwork.
Although there are biases in surveillance data,
these biases do not have a substantial effect on
the results (14). The methods we have used are
generic and, although applied here to human
influenza A (H3N2) viruses, are broadly appli-
cable to influenza viruses in other species and
to other pathogens.
Summary
We present evidence from antigenic and genetic
analyses of HA that, from 2002 to 2007, influ-
enza A (H3N2) virus epidemics worldwide were
seeded each year by viruses that originated in
E-SEAsia.Wefindevidencethattemporallyover-
lapping epidemics in E-SE Asia create a circula-
tionnetworkinwhichinfluenzaA(H3N2)viruses
continually circulate within the region by passing
from epidemic to epidemic. E-SE Asia’s strong
travel and trade connections with Oceania, North
America,andEurope,coupledwithweakconnec-
tionstoSouthAmerica,couldexplaintheseeding
hierarchyobservedinthisperiodwherenewvirus
variants first seed epidemics in Oceania, North
America,andEuropeandlaterinSouthAmerica.
Themostlyone-waynature ofthishierarchysug-
geststhat,onceA(H3N2)virusesleaveE-SEAsia,
they are unlikely to contribute to long-term viral
evolution. If the trends observed during this pe-
riod are an accurate representation of overall pat-
terns of spread, then the antigenic characteristics
of A (H3N2) viruses outside E-SE Asia may be
forecast each year based on surveillance within
E-SEAsia,withconsequent improvements to vac-
cine strain selection and reductions in influenza
A(H3N2)morbidityandmortality.Intensifiedsur-
veillance, including whole-genome sequencing,
and better understanding of the evolutionary
selection pressures in E-SE Asia would further
improve vaccine strain selection worldwide and
potentially make influenza virus evolution more
predictable.
References and Notes
1. K. Stohr, Lancet Infect. Dis. 2, 517 (2002).
2. Commission on Acute Respiratory Diseases, Am. J. Hyg.
47, 290 (1948).
3. J. A. Dudgeon, C. H. Stuart-Harris, C. H. Andrewes,
R. E. Glover, W. H. Bradley, Lancet 248, 627 (1946).
4. M. I. Nelson et al., PLoS Pathog. 2, e125 (2006).
5. R. M. Taylor, Am. J. Public Health 39, 171 (1949).
6. S. B. Thacker, Epidemiol. Rev. 8, 129 (1986).
7. C. Viboud, W. J. Alonso, L. Simonsen, PLoS Med. 3,
e89 (2006).
8. M. I. Nelson, L. Simonsen, C. Viboud, M. A. Miller,
E. C. Holmes, PLoS Pathog. 3, e131 (2007).
9. E. C. Holmes et al., PLoS Biol. 3, e300 (2005).
10. E. Ghedin et al., Nature 437, 1162 (2005).
11. D. J. Smith et al., Science 305, 371 (2004).
12. Sequences were deposited in the GenBank database
(accession numbers EU501119 to EU502618 and
EU514616 to EU514683). Table S1 contains the
sequence name, accession number, and country of
isolation for each strain.
13. S. R. Shih et al., J. Clin. Microbiol. 43, 1651 (2005).
14. Materials and methods are available as supporting
material on Science Online.
15. L. Simonsen et al., Mol. Biol. Evol. 24, 1811 (2007).
16. K. F. Shortridge, Chin. Med. J. (Engl.) 110, 637 (1997).
17. N. J. Cox, T. L. Brammer, H. L. Regnery, Eur. J. Epidemiol.
10, 467 (1994).
18. N. J. Cox, K. Subbarao, Annu. Rev. Med. 51, 407
(2000).
19. W. J. Alonso et al., Am. J. Epidemiol. 165, 1434
(2007).
20. W. P. Glezen, R. B. Couch, in Viral Infections of Humans,
A. S. Evans, Ed. (Plenum Medical Book Company, New
York, 1989), pp. 419–449.
Fig. 5. Schematic of the dominant seeding hierarchy of seasonal influenza A (H3N2) viruses. The
structure of the network within E-SE Asia is unknown.
www.sciencemag.org
SCIENCE
VOL 32018 APRIL 2008
345
RESEARCH ARTICLES
on April 28, 2008
www.sciencemag.org
Downloaded from

Page 8

21. J. S. Nguyen-Van-Tam, in Textbook of Influenza,
K. G. Nicholson, R. G. Webster, A. J. Hay, Eds.
(Blackwell Science, London, 1998), pp. 181–206.
22. C. Viboud et al., Emerg. Infect. Dis. 10, 32 (2004).
23. K. A. Fitzner, S. M. McGhee, A. J. Hedley, K. F. Shortridge,
Hong Kong Med. J. 5, 87 (1999).
24. A. S. Monto, Int. Congr. Ser. 1263, 3 (2004).
25. M. I. Nelson, E. C. Holmes, Nat. Rev. Genet. 8, 196 (2007).
26. J. M. Simmerman et al., Vaccine 23, 182 (2004).
27. C. M. Wong et al., PLoS Med. 3, e121 (2006).
28. B. T. Grenfell, O. N. Bjornstad, J. Kappey, Nature 414,
716 (2001).
29. B. T. Grenfell, B. M. Bolker, Ecol. Lett. 1, 63 (1998).
30. F. T. Chew, S. Doraisingham, A. E. Ling,
G. Kumarasinghe, B. W. Lee, Epidemiol. Infect. 121,
121 (1998).
31. T. S. David-West, A. R. Cooke, Bull. WHO 51, 103 (1974).
32. E. de Arruda et al., J. Infect. Dis. 164, 252 (1991).
33. S. Doraisingham, K. T. Goh, A. E. Ling, M. Yu, Bull. WHO
66, 57 (1988).
34. A. Dosseh, K. Ndiaye, A. Spiegel, M. Sagna, C. Mathiot,
Am. J. Trop. Med. Hyg. 62, 639 (2000).
35. B. L. Rao, K. Banerjee, Bull. WHO 71, 177 (1993).
36. L. P.-C. Shek, B.-W. Lee, Paediatr. Respir. Rev. 4, 105
(2003).
37. L. Hufnagel, D. Brockmann, T. Geisel, Proc. Natl. Acad.
Sci. U.S.A. 101, 15124 (2004).
38. S. Guindon, O. Gascuel, Syst. Biol. 52, 696 (2003).
39. D. Posada, K. A. Crandall, Bioinformatics 14, 817
(1998).
40. D. J. Zwickl, thesis, University of Texas (2006).
41. We thank the many individuals throughout the WHO
Global Influenza Surveillance Network, particularly those
in National Influenza Centers, for their enormous
contributions to surveillance; the maintainers of the
Influenza Sequence Database (www.flu.lanl.gov),
D. Burke, D. Horton, G. Lewis, N. Lewis, B. Mansell,
D. M. Smith, K. Wuichet, and J.-C. Yeh; and the reviewers
whose comments and suggestions substantially improved
the manuscript. This work was supported by an NIH
Director’s Pioneer Award to D.J.S., part of the NIH
roadmap for medical research, through grant number
DP1-OD000490-01. R.A.M.F. is supported by National
Institute of Allergy and Infectious Diseases–NIH contract
HHSN266200700010C, as well as by the De Nederlandse
Organisatie voor Wetenschappelijk Onderzoek
Netherlands Influenza Vaccine Research Centre. The
Melbourne WHO Collaborating Centre for Reference and
Research on Influenza is supported by the Australian
Government Department of Health and Aging. The WHO
Collaborating Centre for Influenza, NIMR, UK, is funded
by The Medical Research Council (UK). For the antigenic
cartography software, see www.antigenic-cartography.
org. The conclusions presented in this paper are those of
the authors and do not necessarily reflect those of the
funding agencies.
Supporting Online Material
www.sciencemag.org/cgi/content/full/320/5874/340/DC1
Materials and Methods
Figs. S1 to S6
Table S1
References
13 December 2007; accepted 19 March 2008
10.1126/science.1154137
REPORTS
Generalized Voice-Leading Spaces
Clifton Callender,1Ian Quinn,2Dmitri Tymoczko3*
Western musicians traditionally classify pitch sequences by disregarding the effects of five musical
transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model
this process mathematically, showing that it produces 32 equivalence relations on chords, 243
equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which
both chords and chord sequences are represented. This model reveals connections between
music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations,
and suggests a way to understand similarity between chord types.
T
ways: as anordered pitch sequence (forexample,
an ascending C-major arpeggio starting on
middle C), an unordered collection of octave-
free note-types (for example, a C major chord),
an unordered collection of octave-free note-types
modulo transposition (for example, a major
chord), and so on. Musicians commonly abstract
away from five types of information: the octave
in which notes appear, their order, their specific
pitchlevel,whetherasequenceappearsright-side
up or upside down (inverted), and the number of
times a note appears. Different purposes require
different information; consequently, there is no
one optimal degree of abstraction.
Here we model this process. We represent
pitches by the logarithms of their fundamental
frequencies,settingmiddleCat60andtheoctave
equal to 12. A musical object is a sequence of
pitches ordered in time or by instrument (1): The
object (C4, E4, G4) can represent consecutive
pitches played by a single instrument or a
o interpret music is to ignore information.
A capable musician can understand the
sequence of notes (C4, E4, G4) in various
simultaneous event in which the first instrument
plays C4, the second E4, and the third G4. (In-
struments can be ordered arbitrarily.) Musicians
generate equivalence classes (2, 3) of objects by
ignoring five kinds of transformation: octave
shifts (O), which move any note in an object into
anyotheroctave;permutations(P),whichreorder
an object; transpositions (T), which move all the
notes in an object in the same direction by the
sameamount;inversions(I),whichturnanobject
upside down; and cardinality changes (C), which
insert duplications into an object (4) (fig. S1 and
Table 1). (Note that O operations can move just
one of an object’s notes, whereas T operations
move all notes.) We can form equivalence rela-
tions with any combination of the OPTIC opera-
tions, yielding 25= 32 possibilities.
Amusicalprogressionisanorderedsequence
of musical objects. Let F be a collection of
musical transformations, with f , f1,:::,fn∈ F.
The progression ( p1, …, pn) is uniformly F-
equivalent to [ f(p1), …, f(pn)] and individually
F-equivalent to [ f1(p1), …, fn(pn)]. Uniform
equivalence uses a single operation to transform
each object in the first progression into the
corresponding object in the second; individual
equivalence may apply different operations to a
progression’s objects (fig. S2). The OPTIC
operations can be applied uniformly, individual-
ly, or not at all, yielding 35= 243 equivalence
relations on progressions.
A number of traditional music-theoretical
conceptscanbeunderstoodinthisway,including
chord (OPC), chord type (OPTC), set class
(OPTIC), chord-progression (individual OPC),
voice leading (uniform OP), pitch class (single
notes under O), and many others [table S1 and
(4)]. We can also combine OPTIC operations in
new ways, producing new music-theoretical
tools. For example, analogs to voice leadings
1College of Music, Florida State University, Tallahassee, FL
32306, USA.
Haven, CT 06520, USA.
University, Princeton, NJ 08544, USA.
*To whom correspondence should be addressed. E-mail:
dmitri@princeton.edu
2Music Department, Yale University, New
3Music Department, Princeton
Table 1. Equivalence relations and quotient spaces produced by the five principal transformations
in Western music theory. Here, x is a point in Rn, 1 represents (1, …, 1), and Snis the symmetric
group of order n.
Equivalence relationSpace
Rn
Tn
None
Octave
Transposition
x ~Ox + 12i, i ∈ Zn
x ~Tx + c1, c ∈ RRn−1or Tn−1(if in conjunction with O)
(orthogonal projection creates a
barycentric coordinate system)
add /Sn
Add / Z2[or /(Sn× Z2) if in
conjunction with P]
Infinite dimensional “Ran space”
Permutation
Inversion
x ~Ps(x), s ∈ Sn
x ~I–x
Cardinality(…, xi, xi+1…) ~C
(…, xi, xi, xi+1…)
18 APRIL 2008VOL 320
SCIENCE
www.sciencemag.org
346
on April 28, 2008
www.sciencemag.org
Downloaded from