Recent advances in inferring viral diversity from high-throughput sequencing data

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ContentslistsavailableatScienceDirect

Virus

Research

jo u r n al hom e p ag e :w w w . e l s e v i e r . c o m / l o c a t e / v i r u s r e s

Review

Recent

advances

in

inferring

viral

diversity

from

high-throughput

sequencing

data

Susana

Posada-Cespedes

a,b

_,

_David

_Seifert

a,b

_,

_Niko

_Beerenwinkel

a,b,∗

a_Department_of_Biosystems_Science_and_Engineering,_ETH_Zurich,_Basel,_Switzerland

b_SIB,_Basel,_Switzerland

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received24June2016

Receivedinrevisedform

23September2016 Accepted24September2016 Availableonlinexxx Keywords: Viralquasispecies Geneticdiversity Haplotypereconstruction Next-generationsequencing

a

b

s

t

r

a

c

t

RapidlyevolvingRNAvirusesprevailwithinahostasacollectionofcloselyrelatedvariants,referred toasviralquasispecies.Advancesinhigh-throughputsequencing(HTS)technologieshavefacilitated theassessmentofthegeneticdiversityofsuchviruspopulationsatanunprecedentedlevelofdetail. However,analysisofHTSdatafromviruspopulationsischallengingduetoshort,error-pronereads.In ordertoaccountforuncertaintiesoriginatingfromtheselimitations,severalcomputationalandstatistical methodshavebeendevelopedforstudyingthegeneticheterogeneityofviruspopulation.Here,wereview methodsfortheanalysisofHTSreads,includingapproachestolocaldiversityestimationandglobal haplotypereconstruction.Challengesposedbyaligningreads,aswellastheimpactofreferencebiases ondiversityestimatesarealsodiscussed.Inaddition,weaddresssomeoftheexperimentalapproaches designedtoimprovethebiologicalsignal-to-noiseratio.Inthefuture,computationalmethodsforthe analysisofheterogeneousviruspopulationsarelikelytocontinuebeingcomplementedbytechnological developments.

Contents

1. Introduction...00

2. Experimentalprotocolsforimprovederrorcorrectionandviraldiversityestimation...00

3. Alignmentofsequencingreads...00

3.1. Reference-basedmapping...00

3.2. Denovoassembly ... 00

4. Inferenceofviraldiversity...00

4.1. Detectingsingle-nucleotidevariantsinviruspopulations...00

4.1.1. AnalysisworkﬂowsforSNVcalling...00

4.2. Localdiversityestimation...00

4.3. Globalhaplotypereconstruction...00

4.3.1. Read-graphbasedmethodsforhaplotypereconstruction ... 00

4.3.2. Probabilisticmethodsforhaplotypereconstruction ... 00

4.3.3. Denovoassemblyofviralhaplotypes...00

4.3.4. Hierarchicalclusteringoflongreadsforreconstructionviralhaplotypes...00

4.3.5. Choiceofsoftware...00

5. Conclusionsandfuturedirections...00

Acknowledgements ... 00

AppendixA. Supplementarydata...00

References...00

∗ Correspondingauthor

E-mailaddress:[email protected](N.Beerenwinkel).

http://dx.doi.org/10.1016/j.virusres.2016.09.016

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1. Introduction

TheevolutionarydynamicsofRNAviruses,suchasthehuman immunodeficiency virus (HIV), the hepatitis C virus (HCV), or influenzavirus,ischaracterizedbyhighmutationrates,short gen-erationtimesandlargepopulationsizes(Duffyetal.,2008).Under theseconditions,acollectionofnon-identicalbutrelatedgenetic variantsisabletoco-existwithinthehost.Thisensembleof vari-antshasbeenreferredtoasaviralquasispecies(Domingoetal., 2005;LauringandAndino,2010).Thetermquasispecieswasfirst usedbyEigenandSchuster(1977),inthecontextoftheirworkon molecularevolution(EigenandSchuster,1978,1978).The quasis-peciesmodelwasintroducedbymeansofatheoreticalframework usingchemicalkineticstodescribethemutationandselection pro-cessesgoverningtheevolutionofself-replicatingmacromolecules. Invirology,thequasispeciesmodelhasbeenadoptedtodescribe theevolutionarydynamicsofRNAvirusesatthepopulationlevel (Nowak,1992;DomingoandHolland,1997).

Mutationandselectionareoneofthedrivingforcesofevolution inRNAviruses.Largelyduetothelackofproof-readingcapability oftheRNApolymerases(i.e.,RNA-dependentRNApolymeraseand RNA-dependentDNApolymeraseorreverse transcriptase),RNA virusesexhibithighmutationrates(Duffyetal.,2008).Forinstance, themutationrateofHIV-1isontheorderof10−5 substitutions perpositionpergeneration(Duffyetal.,2008;ManskyandTemin, 1995).Asaconsequenceofthesehighmutationrates,newviral strainsareproducedineveryreplicationcyclebymeansofpoint mutations,insertionsand deletions.Anothercommonsourceof variabilityinRNAvirusesisrecombination.Arecombinationevent cantakeplacewhenatleasttwodifferentviralstrainsinfectthe samecell,givingrisetoanewstrainwhichisamosaicofits pro-genitors.Ontheotherhand,selectivepressuresactuponthevirus populationasawhole,shapingthedistributionofviralstrains.For instance,inresponsetochangingenvironments,thevirus popu-lationquicklyadaptsbyselectingpreexistingstrainswithhigher ﬁtness(BonhoefferandNowak,1997).Asaresult,oneorfewviral strainsdominate,surroundedbyalargecloudoflow-frequency variants.

Theheterogeneousmixtureofviralstrainsappearstoconfer numerousadvantagestotheviruspopulation,includingtheability toescapefromthehost’simmuneresponse(Nowaketal.,1991; Kurodaetal.,2010;WooandReifman,2012;Boruckietal.,2013), andthedevelopmentofresistancetovaccines(Gaschenetal.,2002) andantiviraldrugs(Johnsonetal.,2008).Furthermore,the exist-enceofdifferentviralstrainshassigniﬁcantimplicationsforviral pathogenesis,virulence,persistenceanddiseaseprogression,and likelycontributestotissuetropism(Vignuzzietal.,2006;Tsibris etal.,2009;Rozeraetal.,2014).Therobustadaptabilityfeatured byRNAviruses,whichisrelatedtotheirgeneticheterogeneityis, thus,ofclinicalrelevance.Infact,manyoftheinfectiousdiseases whichhavejeopardizedandstillareathreattopublichealthare causedbyRNAviruses,includingHIV,HCV,Inﬂuenzavirus,Ebola virusandZikavirus.

BeforetheestablishmentofHTStechnologies,Sanger sequenc-ingwasthemethodofchoiceforanalyzingvirussamples.Even today,itremainsthegoldstandardformanyclinicalapplications. However,bulksequencingonlyallowsfordeterminingthe con-sensussequenceoftheviruspopulation.Theconsensussequence is an aggregate of all variants within the population. Conse-quently,itis dominatedbyhighly abundantstrainsand cannot beusedtoassessthelinkageofmutationsinindividualvariants (Wirden et al., 2005; Zagordi et al.,2010).Further experimen-talimprovements,including isolation of individualviralstrains through cloning (Domingo, 2015) or limiting dilutions (Palmer etal.,2005),allowtoacquireabetter,yetsmall,sampleofthe vari-antswithintheviruspopulation.Thisisbecausetheseprotocolsare

labor-andtime-intensiveand,thus,scalabilityremainsalimiting factor.

Thesensitivity and scalability issues areprogressivelybeing overcomeby a setof newer technologies, which allowto pro-ducemassivevolumesofgenomicdatainarelativelyshorttime byparallelizationofthesequencingreactions.Thesetechnologies arecollectivelyreferredtoashigh-throughputsequencing(HTS), massivelyparallelsequencing(MPS),next-generationsequencing (NGS) or ultra-deep sequencing (UDS). HTS technologies allow anin-depth characterization ofthe geneticdiversity in hetero-geneous virus populations by directly sequencing many of the viralstrains. Furthermore, provided that thesequencing cover-ageissufﬁcientlyhigh,itispossibletodetectmutationspresent in lessabundantstrains, whereas consensusSangersequencing has a 20% detection threshold. However, low-frequency muta-tionsare particularlyrelevantin thecontext ofdrugresistance, sincetheymayfacilitateviraladaptationleadingtotreatment fail-ure (Metzner et al., 2009; Gianella and Richman, 2010; Avidor et al., 2013; Vandenhende et al., 2014). Therefore, studying the genetic diversity of the virus population as a whole is more informative than focusing solely on the dominant viral strains.

HTStechnologieshavethepotentialtoprovidea representa-tivesampleoftheviruspopulation.However,manyHTSplatforms generatelargeamountsofsequencingreadswithshortreadlengths andrelativelyhigherrorrates.Thesefactors,inconjunctionwith errorsassociated withsample preparation(e.g.,RNAextraction, reversetranscriptionandPCRamplificationbiases),pose compu-tationalandstatisticalchallengesforinferringintra-hostgenetic diversity from HTS reads (Beerenwinkel et al., 2012; McElroy etal.,2014).Forinstance,manysingle-nucleotidevariants(SNVs) arepresentatlowfrequenciesandarethereforedifficultto dis-tinguish from technical errors. In addition, reconstructing the populationstructurefromsequencingreadsischallengingbecause thenumberofunderlyingviralstrainsisunknown,someofthem existatlowrelativeabundances,andthediversityamongstrains canbe low (i.e.,somevariants withinthe populationexhibit a smallgeneticdistance).Fromthetechnicalperspective, reconstruc-tionoffull-lengthhaplotypesischallengingbecausesequencing reads are typically shorter than the viral genome and do not cover the genome or the genetic region of interest uniformly. Tothisend,recentadvancesinsingle-moleculesequencingseem promising, as platforms commercialized by Pacific Biosciences and Oxford Nanopore offer very long reads (>10kb).However, higher error-rates and lower throughput compared to prede-cessorHTS platformsstill limit applicability of single-molecule sequencers.

Nevertheless,HTStechnologieshavealreadyprovenusefulin differentfieldsrelatedtovirology,includingvirusdiscovery(Cheval etal.,2011),characterizationofvirusbiodiversityfoundin differ-entenvironments(alsoknownasviromeprofiling)(Hurwitzand Sullivan,2013),estimationoffitnesslandscapesofviralpopulations (Seifertetal.,2015),characterizationofintra-hostvirusdiversity andpopulationdynamics(Kurodaetal.,2010).

Thisreviewisstructuredasfollows.First,weaddress experi-mentalprotocolswhichhavebeenrecentlydesignedtoovercome limitations associated with short and error-prone reads (Sec-tion 2). These sequencing protocols and accompanying data analysispipelineshaveenabledcorrectionoftechnicalerrors,as wellasreconstructionof viralhaplotypes.Next,acknowledging that alignment of sequencingreads is in most cases a prereq-uisiteforsubsequentanalyses,strategies forreadalignmentare brieﬂy discussedin Section 3, aswell asremaining challenges. Lastly,wedescribecomputationalmethodsdevelopedforstudying thegeneticdiversity ofviruspopulations fromHTSreads (Sec-tion4).

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2. Experimentalprotocolsforimprovederrorcorrection

andviraldiversityestimation

Abasicworkﬂowforviralsequencingprojectsincludes sam-plepreparation,choiceofsequencingplatform,qualityassurance, readalignmentandidentiﬁcationofgeneticvariants.The sensitiv-ityofcomputationalmethodsforvariantdetectioncanbeimproved byidentifyingandcorrectingerrorsintroducedduringupstream librarypreparationandsequencingsteps.Although,several error-correctionalgorithmshavebeendesignedtoimprovedataquality (Zagordietal.,2010;Skumsetal.,2012),thisissuehasbeenalso addressedfromanexperimentaldesignperspective.

Oneoftheﬁrstandtodatemostpopularmethodtoremove theoverwhelmingmajorityoferrorsintroducedbythePCRstep involvestheuseofshortrandomk-mers fortaggingsequences. Thesek-mers–invirologymorecommonlyknownasprimerIDs– areproducedaspartoftheoligonucleotideproductionstep. Dur-ingthereversetranscription,thesespecializedprimersareused insteadofstandardRTprimers.Allproducedoff-springmolecules will have the same unique tag, which can be employed after sequencingtocollapseallreadswiththesametagintoone consen-sussequence(Kindeetal.,2011;Jabaraetal.,2011).Inthisway, mosterrorsareremovedviamajorityvoting.TheprimerID proto-colcanalsobeusedtoestimatetheerrorrateofthePCRbranching process,bymakingaﬁrst-orderapproximationforthenumberof errorsintroducedinearlycycles(Seifertetal.,2016).Ifthenumber ofcollisionsiscontrolledfor,thentheprimerIDprotocolpossesses theabilitytodetectfailuresinthepreparativesteps,whichiscrucial forassertingthecorrectnessinclinicaldiagnostics.

The primerID protocol can however not remove errors introducedintheligationstepofthePCRorduringreverse tran-scription(Seifertetal.,2016).Thelatterisbecausetemplatesare only redundantly resampled in the PCR step. In addition, it is known,thatlaboratoryreversetranscriptase(RT)enzymeshave highererrorratesthancommonPCRenzymesemployed(Seifert etal.,2016).Thus,inturn,mostoftheerrorsstemfromRT substitut-ions. The novelcircle sequencing (CirSeq) protocol can correct errorsintheearlyphaseoftheprotocolbyredundantly incorpo-ratingthetemplateonto theDNAtemplatemultipletimes.This featisachievedbycircularizingtheRNAandreversetranscribing itmultipletimes.PCRmutationscanberemovedbymajorityvote, whereasRTmutationscanberemovedbymajoritybetween tan-demcopiesonthesametemplate(Louetal.,2013).TheCirSeq protocolmakestheﬁdelitytrade-offbydrasticallydecreasingthe realistic fragmentsizefor increasedsensitivity.Lastly, boththe standardprimerIDprotocolandCirSeqallowforstudyingviruses onlyonanamplicon level.Whileamplicon-basedsequencingis relevantfordrugresistanceloci,itbecomescumbersomeand labo-riousatbesttoperformwhole-genomesequencinginthisfashion. AnextensionofprimerIDstovariable-lengthgenomicregionsalso involvescircularizingoftheRNA.Insteadoftranscribingthe cir-cularizedtemplate multipletimeslikeCirSeqdoes, theprotocol Barcode-directedAssemblyforExtra-longSequences(BAsE-Seq) randomlyfragmentsthecircularized DNA, leadingtotemplates withvaryinglengths(Hongetal.,2014).Thesevariablelength tem-platesallowforimprovedhaplotypephasing.UsingtheBAsE-Seq protocolanddataanalysispipeline,ithasbeenpossibleto recon-structviralhaplotypesof3kbinlength(Hongetal.,2014).

Finally,whilealltheprotocolsprovideanattractivepathfor errorcorrectionorphasingofhaplotypesbeyondlocalscope,they stilldohavepracticaldrawbacks.CirSeqandBAsE-Seqbothinclude acircularization,abiochemicalstepthatiskineticallyunfavorable and henceinefﬁcient.Thisin turnwillrequirehighinput tem-plateconcentrations,whichmightbeproblematicinsettingswith lowviralloads,asinHIVclinicaldiagnostics(AcevedoandAndino, 2014).

3. Alignmentofsequencingreads

A fundamentalanalysisstep ininferring viraldiversity from sequencedataisreadalignment.Sequencingreadscanbeeither mappedtotheirlikelygenomicregionoforiginorassembledde novo.Theformerstrategy,dubbedreference-basedmapping,isthe mostwidespreadchoice,althoughdenovoassemblyofsequencing readsintoaconsensussequencehasgainedincreasinginterestin recentyears(Yangetal.,2013;Manguletal.,2014;Jayasundara etal.,2015;Malhotraetal.,2016).

3.1. Reference-basedmapping

Mapping sequencing reads onto a reference genome relies on theexistence of suchreference sequence. In fact,reference sequenceshavebeenestablishedformanyvirusesofclinical rel-evance.However,aligningsequencingreads againstareference sequencemayintroducebiases(Archeretal.,2010).Assume,e.g., that the virus population contains both, strains which closely resemblethereferencesequence,aswellasstrainswhichdiverge strongly from thereference. Theformer willbe more likely to alignsuccessfullyagainstthereferencethanthelatter.Typically, poor-qualityalignmentsareignoredinsubsequentanalyses.Thus, distantly related sub-populations tend to be underrepresented whileestimatingviraldiversity.Acommonpracticetoovercome thisissueistoﬁrstalignthereadstoanexistingreferencegenome and then generate a consensussequence using a position-wise majorityvote.Subsequently,readsarealignedtothenew consen-sussequence(Astrovskayaetal.,2011;Hongetal.,2014).Thereby, itisexpectedthatreadsthatwerenotoriginallymapped,maythen bemappedtotheconsensussequence.Inprinciple,theprocessof generatingaconsensusfrommappedreadsandrealignmentcan beiterativelyrepeateduntilthereisnogaininthepercentageof mappedreads.

Anotherchallengeinmappingsequencingreadsarisesfroma technicalviewpoint.Nowadays,HTStechnologiesoffer sequenc-ing of several million reads in a single experiment. Due to the large volumes of sequencing reads, traditional algorithms for sequence alignment, such as the Needleman–Wunsch and Smith–Watermanalgorithms,arecomputationallyverycostly.The time complexityfor each alignmentdepends ontheproductof thelengthofthereferencesequencemultipliedbythelengthof the read. Over the past years, and in order tokeep pace with thesequencingthroughput,awide varietyof readmappershas beendeveloped.Readmappersrelyondifferentindexing strate-giesimprovinguponthequadratictimecomplexityoftraditional algorithms.

Based onindexing techniquesimplemented bythe different read mappers,theycanbegroupedintotwo categories(Liand Homer, 2010): algorithms based on(i) hash tables or (ii) pre-ﬁx/sufﬁxtrees.Amongsoftwarepackagesbelongingtotheformer group, Stampy (Lunter and Goodson, 2011) and MOSAIK (Lee etal.,2014)havebeenemployedformappingsequencingreads frommixed samples ofvirus populations(Mangulet al.,2014; Astrovskayaetal.,2011;PanditanddeBoer,2014;Cuevasetal., 2015;Zaninietal.,2015).Thelattercategoryincludesalgorithms such as BWA (Li and Durbin, 2009), BWA-SW (Li and Durbin, 2010),Bowtie(Langmeadetal.,2009)andBowtie2(Langmeadand Salzberg,2012)whichemploytheFerragina–Manzini(FM)index (FerraginaandManzini,92127)basedontheBurrows–Wheeler transform(Burrowsand Wheeler,1994).Severalreview articles andbenchmarkstudieshavebeenpublishedandmayproveuseful toguideselectionofanadequatetoolforagivenapplication(Bao etal.,2011;Fonsecaetal.,2012;Cabocheetal.,2014).

Run time is a critical aspect, especially when dealing with largeeukaryoticgenomes,suchasthehumangenome.Intheory,

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5'

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Fig.1. Placementofgapsinhomopolymericregions.Inthishypotheticalalignment,

fourreadsarealignedagainstawindowofthereferencesequence(black)

consist-ingof20nt.Thedeletionobservedinmostofthereadsislikelytocorrespondto

polymeraseslippageerrors.However,sincethedeletionappearstobeabundant,it

islikelytobepickedupasatruevariant.

Bowtie(Langmeadetal.,2009)andBWA(LiandDurbin,2009), e.g.,align reads in time linearto sequence length,becausethe datastructure of theindex only requires queryingthe read. In practice,andin ordertoprovide efﬁcientsolutionsfor aligning reads,mostmapperscomplementindexingstrategieswith differ-entheuristics.Nowadays,itispossibletomapabout1gigabases (e.g.,10million100bpreads)perCPU-hour(Langmeadetal.,2009; Langmead and Salzberg, 2012). Processing reads from smaller viralgenomes can appear asa simplerproblem. However, this is only partially true due to a comparatively higher variability of viral genomes. Particularly, heuristics employed to improve runtimesoftentimesimplya reductioninsensitivity and accu-racy. For highly variable viral genomes, inaccurate alignments mayresultinalignmentbiasesandanon-negligiblelossofdata, whicharepropagatedintosubsequentanalysissteps(Archeretal., 2010).

Placementofgapsisyetanotherchallengeinsequence align-ment.Themostparsimoniousalignment,i.e.,thealignmentwith thefewestgaps,isnotnecessarilythemostconsistentwiththe structureof aviruspopulation. Thereisevidencethat supports both frameshift mutations and longer deletions as sources of geneticvariationinviruspopulations(Berthetetal.,1997;Audsley et al., 2010; Guglietta et al., 2010; Reguera et al., 2011; Park etal.,2014).Ontheotherhand,insertionsanddeletionsarenot alwaystruesourcesof variability.The primarysourceof errors of somesequencing platforms, such as Roche454, Ion Torrent (LifeTechnologies) and Pacific Biosciencesplatforms, are inser-tionsanddeletions(collectivelyreferredtoasindels)(Lomanetal., 2012).However,mostreadaligners havedeficienciesindealing withindels.Sometoolsdonotsupportgappedalignments,such asBowtie(Langmeadetal.,2009),andothers restrictthe num-ber of gaps that are allowed per alignment, such as SOAP (Li etal.,2008)andBWA(LiandDurbin,2009).Moreimportantly, readalignerssupportinggappedalignmentstendtoplaceindels inhomopolymericregionseitheratthebeginningortheend of suchregions,whichleadstocallingspuriousvariants(Fig.1).To overcometheselimitations,amultiplesequencealignment(MSA) approachusingstatisticalmodels,suchasprofilehiddenMarkov models(profile-HMM)(Mount,2009;Yoon,2009),couldprovide abettersolutiontothereadalignmentproblem.Thisisbecause, features sharedamongrelated sequences arecaptured through position-specificscores.Ifthereexistevidenceinthepopulation of,e.g.,adeletioninagivenlocation,openingagapinthe align-ment is allowed with higher probability at this site compared to other positions. Alignment of protein families is an exam-pleof a successful application employing profile-HMMs (Eddy, 2003).

3.2. Denovoassembly

As mentioned earlier, reference biases can be induced by thealignment ofthesequencing readstoa reference sequence that highly diverges fromthe sampled population. In order to

Fig.2. Availablesoftwareforassessingviralgeneticdiversity.Differentmethodsare

groupedaccordingtotheirscope,i.e.,SNVcallingandlocalorglobalreconstruction,

andtheirabilitytouseinformationfrompaired-endreads.

circumventreferencebiases,aconsensussequencecanbe assem-bleddenovo.Moreover,forvirusdiscoveryapplications,denovo assemblyofsequencingreadsintoa consensussequencesisthe onlychoice.

Thecoreconceptindenovoassemblyistomergeoverlapping readsintolongerstretchesofDNA,calledcontigs,andthenmerge contigsintoscaffoldsinordertoreconstructafull-lengthgenome. Geneticheterogeneityof viruspopulations rendersthedenovo assemblyofthereferenceviralgenomemorechallengingcompared tohaploidordiploidorganisms.However,virusgenomesare rela-tivelyshorterandgenerallydonotexhibitlargerepetitiveelements comparedto,e.g.,thehumangenome.

Severaldenovoassemblershavebeentailoredtomixedviral samples(Warrenetal.,2007;Hennetal.,2012;Yangetal.,2012; Huntetal.,2015).Amongthem,thesoftwareVICUNA(Yangetal., 2012)constructsconsensussequencesofviralgenomesby includ-ingmoreheuristicsandcuratingthecreatedreferencesequencing usinganumberoftechniques.Itcreatescontigsonthebasisofde Bruijngraphs,employingmultiplesequencealignmentsoftarget genomestofurtherimprovethequalityofthecontigs.Duetothe verysmallsizeofthecontigsincomparison tolargeeukaryotic genomes,VICUNAcanaffordtovalidateand extendthecontigs topossiblyfull-sizegenomescales,byﬁlteringlikelycontaminant readsandimprovingsinglebasecallsusingthebasepileupsfrom thedata.

4. Inferenceofviraldiversity

On the basis of research objectives, genetic diversity of virus populations can be studied at different genomic scales (Beerenwinkeletal.,2012):(i)position-wise,byidentifying single-nucleotidevariants(SNV),(ii)atalocalscale,byidentifyingpatterns ofSNVsthatco-occuratadistancesmallerthantheaverageread length,and(iii)ataglobalscale,byphasingmutationsover dis-tanceslongerthanthereadlength(cf.Fig.2).

In the following, we describe computational methods for studyingviral geneticdiversity in accordance withthe classiﬁ-cation scheme introduced above and focusing on most recent developments.

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4.1. Detectingsingle-nucleotidevariantsinviruspopulations Amajorchallengeinvariantcallingconcernsthedetectionof rareSNVs.Inprinciple,detectinglow-frequencymutationsis possi-bleduetohighcoveragesthatcanbeattainedusingHTSplatforms. However,theseparationofgeneticvariantsfromtechnicalnoise constitutesoneofthemainchallengesofthedataanalysis.While conservativethresholdsforcallingvariantslimitthesensitivityof theSNVcaller,callingallvariantsresultsinpoorprecision.Hence, bothhighsensitivityandprecisionaredesirablefeaturesfor detec-tinglow-frequencymutations.

Variousstatisticalmodelsaccountingforsequencingerrorshave beenproposedtoboostsensitivitylimits.Thenumberoferrorsat eachgenomicpositionhasbeenmodeledusingPoisson(Yangetal., 2013;Wangetal.,2007;Wilmetal.,2012),binomial(Macalalad etal.,2012)andbeta-binomialdistributions(Flahertyetal.,2012; Gerstung etal., 2012;McElroy etal., 2013).Provided readsare mappedontoareferencesequence,anSNViscalledassuchwhen anon-referencebaseisobservedmoreoftenthanexpectedunder agivenerrormodel.However,imperfectampliﬁcation,aswellas otherunknownbiases,usuallyresultsinahigher-than-expected varianceofthenucleotidecounts,aneffectknownas overdisper-sion.Amongtheproposedmethods,beta-binomialmodelsareable tocaptureoverdispersion(Gerstungetal.,2012).Bycontrast, Pois-sonandbinomialmodelsdonotallowforindependentlyadjusting meanandvariance,andthereforecannotaccountfor overdisper-sion.Forinstance,theratiobetweenthemeanandthevariance inthePoissondistributionisequaltoone.Sincetheerrormodel determineswhethertheprevalenceofanon-referencebaseis sig-niﬁcant,overdispersioncanresultinsystematicerrorsandhence shouldbeaccountedforingeneral.

InadditiontohighlysensitivemethodsforSNVcalling,precision isalsocritical.Thisisbecausethenumberoftruenegativesis,in general,expectedtobegreaterthanthenumberoftruepositives. Inordertoreducefalsepositives,severaltoolsresortto estimat-ingposition-specificerrorrates.Employedstrategiesfallintothree categories:(i)methodsintegratingthequalityscoreswhen mod-elingdistributionoferrors(Yangetal.,2013;Wilmetal.,2012; Macalaladetal.,2012;Isakovetal.,2015),(ii)anapproachusing adaptivequalityfilterstoruleoutnoisybase-calls(Verbistetal., 2015),and(iii)methodsresortingtoacontrolsamplefor estimat-ingthebackgroundnoise(Flahertyetal.,2012; Gerstungetal., 2012).Inthefirstcase,andassumingsequencingreadshavebeen mappedtoareferencesequence,non-referencebasesateachlocus aremodeledasindependentBernoullirandomvariables,eachof whichhasadistinctsuccessprobability(Yangetal.,2013;Wilm et al., 2012; Macalalad et al., 2012; Isakov et al., 2015).These probabilitiesareassumedtobeafunctionofqualityscoresof indi-vidualbases.A tooldubbedVirVarSeq(Verbistetal.,2015)is a representativeof thesecondcategory. In this case,an adaptive quality-thresholdisestimatedfor eachdeep-sequencedsample. Thequalitythresholdisdeterminedbymodelingthedistribution ofqualityscoresasamixtureofthreetruncated-Gaussians. Com-ponentsatthelowerendofthequalityspectrumareinterpreted astwotypesoferrors,whilethethirdcomponentisinterpretedas reliablecallsandeverynucleotidevariantistreatedassuch.Inthe thirdcase,variantcountsinaheterogeneousviruspopulationsare comparedagainstcountsinahomogeneouscontrolsample,aiming atcapturingcontext-specificerrors(Flahertyetal.,2012;Gerstung etal.,2012).Thecontrolsamplecanbeacquired,e.g.,bysequencing monoclonalviralstrains.

Furtherimprovementsinprecisioncanbeattainedifsystematic errorsaretakenintoaccount.Forinstance,inthecaseof paired-endsequencing,thereisgrowingevidencethatsequencingerrors dependonthesequencingdirectionandaremorelikelytooccuron onestrandthantheother(Guoetal.,2012).Thus,severalmethods

Table1

Comparisonofpipelinesforvariantcalling.

ViVan VirVarSeq

OS Lin,Win Unix/Lin

Language Python Perl,R

Dependencies Pythonmodules, ea-utils,SAMtools,bwa

Rpackages,Perl modules,Fortran compiler,bwa

Availability No Yesa

Interface CLI/web-server CLI

Platform Illumina Illumina

Inputformat–reads FASTQ FASTQ

Inputformat–ref. FASTA FASTA

Pre-processing Qualitytrimmingb _None

Alignment Reference-based mapping Reference-based mappingand realignmentagainst consensus

Variantcalling CompositeBernoulli

errormodel

Adaptivequality

ﬁltering

Applications Coxsackievirus,

Chikungunyavirus

HCV

Reference Isakovetal.(2015) Verbistetal.(2015)

OS,operatingsystem;Lin,Linux;Mac,MacOSX;Win,Windows;Unix,

Unix-compatible operatingsystems. Platform,sequencingplatforms are speciﬁedif

pipelinewastestedonrealdatasets,asreportedontheoriginalpublication.Input

format–reads/reference;FASTA,text-basedformatforstoringbiologicalsequences;

FASTQ,text-basedformatforstoringbiologicalsequencesandcorrespondingquality

scores.

a_{http://sourceforge.net/projects/virtools/?source=directory}_.

b_Quality_trimming_is_carried_out_by_fastq-mcf,_a_tool_from_the_ea-utils_toolkit.

haveincorporatedstatisticaltestsforstrandbias(Yangetal.,2013; Wilmetal.,2012;McElroyetal.,2013).

4.1.1. AnalysisworkﬂowsforSNVcalling

Overthelastyears,providingcomprehensivesolutionsforthe analysisofgenomicdatahasbecomeanevidentnecessity(Leipzig, 2016).Tothisend,SNVcallershavebeenintegratedinto bioinfor-maticspipelines.PipelinessuchasViralVarianceAnalysis(ViVan) (Isakovetal.,2015)andVirVarSeq(Verbistetal.,2015)facilitate thecharacterizationofthegeneticdiversityofviruspopulations, deliveringSNVsfromrawsequences.Thesepipelinescombine sev-eralprocessingsteps,includingqualityassessment,readalignment andvariantcalling(cf.Table1),aswellasdownstreamanalysesto improveinterpretabilityoftheresults. ViVan,e.g.,provides sev-eralmetricsandstatisticsonpopulationdiversity,transitionsand transversionbiases,synonymousandnon-synonymousmutations, andgene-by-genestatistics(Isakovetal.,2015).

AnoverviewoftwosurveyedpipelinesisgiveninTable1.We havelistedsomefeatures,whichincludeprogramminglanguages, dependencies,supportedsequencingplatforms,inputformatsand analysissteps.Itcanbeseenthatthesetoolsaresimilarinmany ways.Forinstance,bothpipelinesaretailoredtoIlluminareads, inthesensethatqualityscoresareincorporatedunderthe inter-pretationprovidedbyIlluminaplatforms.Otheraspects,suchas dependenciesonthird-party softwareand beingcommand line tools,makeitnecessaryfortheend-usertohaveatleast interme-diatecomputerskills.

4.2. Localdiversityestimation

The linkage information between loci is lost when calling variants at individual genetic sites. One way to detect linkage betweennucleotidevariantsisbyidentifyingstatistically signiﬁ-cantpatternsofco-variationinthesequencingreads.Suchpairs or higher-order patterns of mutationsare often referred to as phasedsites.Phasingnucleotidevariantsinvolvesdetecting muta-tionswhichareobservedtogetheronmultiplesitesandoccurmore

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oftenthanexpectedbychance.Indeed,geneticrelationshipsamong multiplesiteshavebeenexploitedinsoftwarepackagessuchas V-phaser(Macalaladetal.,2012)anditsextensionV-phaser2(Yang etal.,2013),VirVarSeq(Verbistetal.,2015),ViVaMBC(Verbistetal., 2015), CoVaMa(Routhetal.,2015)andShoRAH(McElroyetal., 2013).Anadditionaladvantageofconsideringmultiplesites simul-taneouslyisthatthedetectionlimit(i.e.,theminimumfrequency atwhichvariantsaredetectable)canbeloweredbelowthe techni-calnoiselevel(McElroyetal.,2013),withaconcomitantincrease instatisticalpower.

Softwarepackagesexploitinglinkageinformationcanbe sub-divided into three categories (cf. Table 2). First, methods that have been tailored to performing variant calling at the codon level(Verbistetal.,2015,2015).SoftwareViVaMBC(Virus Vari-antModel-BasedClustering)isarepresentativeofthiscategory. Itadoptsaprobabilisticapproachforreadclusteringinwindows consistingoftripletsofnucleotides. Underlyingviralstrainsare modeledasthecomponentsofamultinomialmixturemodel.A limitationofthismethodisthatanupperboundonthenumberof variantsshouldbespeciﬁedapriori.Methodsfallinginthesecond categoryincludeV-phaser(Macalaladetal.,2012;Yangetal.,2013) andCoVaMa(Routhetal.,2015).Thesemethodsarenotlimited toadjacentpositionsandaretailoredtoidentifyingpairsof co-occurringvariants.Inordertoestimateadetectionthresholdfor eachpairofloci,V-phasermodelsthenumberofmismatchesat bothsitesbyconstructingacompositemodelofindependent,but notidenticallydistributed,Bernoullirandomvariables(Macalalad etal.,2012).Ontheotherhand,softwareCoVaMa(Co-Variation Mapper)constructscontingencytablesforeverypairoflociand everypairofvariants,inordertocomputethelinkage disequili-brium(LD).A3-cutoffruleisemployedforassessingsigniﬁcance ofLDvalues.

Thethirdcategoryincludesmethodsinwhichthelocaldiversity estimationisfurtherextendedtowindowsofthereferencegenome spannedbyindividualreads.Thegoalhereistophaseallvariant siteswithinsuchgenomicregions.Atthisscale,localhaplotype reconstructioncanberegardedasa clusteringproblem. Abasic schemeincludes:(i)clusteringreadsbasedonpairwisesimilarities, (ii)identifyingtheclustercentersaspredictedhaplotypes,and(iii) usingtheclustersizesasestimatesofthehaplotypefrequencies.

ThesoftwareShoRAH(ShortReadAssemblyintoHaplotypes) is a representative of the third category (Zagordi et al., 2010). ShoRAHimplementslocaldiversityestimation,coupledtoSNV call-ing(McElroyetal.,2013),aswellasglobalhaplotypereconstruction (Erikssonetal.,2008).Localhaplotypereconstructionisformulated asaprobabilisticclusteringapproachperformedinaBayesian fash-ion.Inatraditionalclusteringproblem,thenumberofcomponent shouldbespeciﬁedbeforehand.However,thenumberof under-lyingviralstrainsis,ingeneral,unknown.Hence,andinorderto capturethisuncertainty,aDirichletprocessisemployedasaprior probabilitydistribution.Assignmentofsequencingreadstoclusters isperformediterativelyonthebasisofsequencesimilarity.Inevery iteration,sequencingreadsareassignedwithacertainprobability toeitheranexistingclusteroranewcluster.Inthisway,the num-berofcomponentscanbeinferredfromthedata,insteadofﬁxingit apriori.Thecentroidsofreadclustersarethelocallyreconstructed haplotypes.Thesepredictedhaplotypesareusedtocorrecterrors withinreadclusters.Errorcorrectionisconductedasaprevious steptoglobalhaplotypereconstruction(cf.Section4.3.1).

Other software packages have resorted to local haplotype reconstructionasthestartingpointforglobalhaplotypeinference (Jayasundaraetal.,2015;ProsperiandSalemi,2012;Töpferetal., 2013; Prabhakaran et al.,2014), and are described in thenext section.

Localhaplotypereconstructioncanbesufﬁcientforsome appli-cationswherethefocusisonagenomicregionwhichcanbefully

coveredbyindividualreads.Forinstance,inHIV-1infection,itis particularlyrelevanttostudyemergenceofdrug-resistance muta-tionsingeneswhoseproteinproductsaretargetedbydrugs.One suchgeneistheviralproteasegene,whichisonly297ntlong.

Someof thevariantcallershavebeendevisedfor either454 or Illumina sequencing reads. Among the differences between thesetwosequencingplatforms,thedifferenttypesof predom-inant errors, interpretation of the quality scores, read length andthroughputcanbepointedout.Thelatterpoint concerning sequencingcoverageisrelevantforthescalabilityofthesetools. Forinstance,V-phaserandShoRAH(Prabhakaranetal.,2014), orig-inallytestedon454sequencingreads,havebeenobservedtoscale poorlywhenthecoverageisontheorderoftensofthousandsreads. Inaddition,methodsspecializedfor454sequencingdatadonot makeuseoftheinformation providedbypaired-endreads.The advantageofusingpairinginformationisthatdistancebetween phasedsitescanbeextendedtolongerstretchesconstrainedonly bytheinsertsize.

4.3. Globalhaplotypereconstruction

Methodsforlocaldiversityestimationarelimitedbythelength ofthesequencedfragments.Correlatedpairsorhigher-order pat-ternsofmutationscannotbelinkedatdistanceslongerthanthe averagereadlength.Ontheotherhand,theaiminglobalhaplotype reconstructionistoinferthegeneticsequencesandfrequenciesof theunderlyingviralstrainsoveragenomicregionofinterest(e.g., asinglegene)oracrosstheentiregenome.Ineithercase,thesize ofthegenomicregionexceedsthereadlength.

Over the last decade, HTS platforms have been optimized either in terms of increased throughput and read length, or decreasederrorrates.Alongwithtechnologicaldevelopments, sev-eralmethodshavebeenproposedtoefficientlysolvetheglobal reconstruction problem from relatively short and error-prone reads.Manyofthesemethodswereoriginallydevisedforhandling 454/Rochesequencingreads(Astrovskayaetal.,2011;Prosperiand Salemi,2012;Westbrooksetal.,2008;Jojicetal.,2008;Zagordi etal.,2011),asitwasthefirstwidely-usedHTSplatform.Owing tothe bettercost-effectiveness and higher coverage offeredby Illuminasequencingplatforms,thefocusshiftedtowardsthis tech-nologyinrecentyears(Manguletal.,2014;Jayasundaraetal.,2015; Töpferetal.,2014).Asthenumberofreadsandsequencing cover-ageincreased,moreefficientalgorithmswererequiredtomeetthe sequencingthroughput.Morerecently,so-calledthirdgeneration sequencingplatformsaregraduallybecomingthemethodofchoice (Dilerniaetal.,2015;Artyomenkoetal.,2016;Quicketal.,2016),as latesttechnologiesofferreadlengthsoftensofkilobases(kb).These developmentsarebeingdrivenbyPacificBiosciences(PacBio)(Eid etal.,2009)andOxfordNanopore(SchneiderandDekker,2012).

Anorthogonalclassiﬁcationofthecomputationalmethodsfor viralhaplotypesreconstructionfromHTSreadshasbeenproposed by Beerenwinkelet al. (2012). Algorithmsproposed until2012 weredividedintoread-graphbasedmethods(cf.Section4.3.1), probabilistic models(cf. Section4.3.2)and de novo reconstruc-tion(cf.Section4.3.3).Anewcategoryisintroducedhere,namely haplotypereconstructionusinglongsequencingreads.Since meth-odsdesignedfortheanalysisoflongsequencingreadsarebased onhierarchicalclustering,wehavenamedthemassuch(cf. Sec-tion4.3.4).

Methods basedontheread graph, probabilistic models,and algorithmsbasedonhierarchicalclusteringrelyonthealignment ofsequencingreadsforthepositioningandorientationofthereads withrespecttoareferencesequence.Ontheotherhand,denovo quasispeciesreconstructionmethodsdonotrelyontheexistence ofareferencegenomeandhaplotypesarereconstructeddirectly fromthesequencingreads.Intheformercase,areferencesequence

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Table2

Methodsforlocaldiversityestimation.

Software Platform Category Approach Output Applications Avail. Ref.

VirVarSeq Illumina Codon-based calling

Adaptive qualityﬁltering

Codonvariants HCV,HIV Yes Verbistetal.(2015)

ViVaMBC 454,Illumina Codon-based

calling

Probabilistic clustering

Codonvariants HCV(NS3) Yes Verbistetal.(2015)

V-Phaser/V-Phaser2 454,Illumina Co-occurrence

ofpairsof

variants

Composite

Bernoullierror

model

Variantpairs HIV-1,WNV Yesa _Macalalad_et_al.₍₂₀₁₂₎

andYangetal.(2013)

CoVaMa IIllumina Co-occurrence

ofpairsof

variants

Linkage disequilibrium

Variantpairs HIV(prot) Yes Routhetal.(2015)

ShoRAH 454,Illuminab _Local_windows _{Probabilistic}

clustering

Local haplotypes, SNVs

HIV(pol),HCV Yes McElroyetal.(2013)

andZagordietal. (2010)

Sequencingplatformsarespeciﬁedifsoftwarewastestedonrealdatasets,asreportedontheoriginalpublication.Avail.,availability.Ref.,references.

a_Registration_required.

b_Test_for_strand_bias_in_SNV_calling.

couldhavebeenpreviouslyobtained,e.g.,bysequencingthe sam-pleviaSangersequencing,orassemblingthereadsdenovointoa singleconsensussequence(Hennetal.,2012;Manguletal.,2014; Jayasundaraetal.,2015).

Inthefollowing,wedescribeinmoredetaildifferentstrategies forviralhaplotypereconstruction.Lastly,wediscusschallengesin choosingahaplotypereconstructiontoolforstudyingdiversityin mixedviralsamples(cf.Section4.3.5).

4.3.1. Read-graphbasedmethodsforhaplotypereconstruction The generalworkﬂow of methods based on theread graph includesmappingofsequencingreads,errorcorrection,haplotype reconstructionandhaplotypefrequencyestimation(cf.Fig.3).The

setofmappedreads,possiblyerror-correctedreads,isusedtobuild agraphwiththeaimofidentifyingasetofpathsastheviral hap-lotypes.

Thereadgraphisadirectedgraphwithvertices correspond-ingtonon-redundantreadsandedgesconnectingreadsthatagree on their non-empty overlap (Eriksson et al., 2008). A read is non-redundantifitisnotfullycontainedwithinanyotherread. Furthermore,overlapping positionsbetween pairs ofreads and directionalityoftheedgesaredeterminedbythereadalignment(cf. Fig.4).Asimilarformulationofthereadgraphwasindependently proposedby Westbrookset al. (2008),in which all sequencing readsareincludedasnodes.Inthiscase,amorecompactgraph isobtainedbycomputingtheminimumtransitivereductionofthe

Table3

Softwarepackagesforhaplotypereconstructionbasedonthereadgraph.

Software Sequencingmode Errorhandling Haplotype reconstruction

Haplotype frequency estimation

Avail. Ref.

ShoRAH Shotgunand amplicon-based

Probabilistic clustering

Minimalpathcover EM Yes Zagordietal.

(2011)

ViSpA Shotgun Binomialerror

model

Max-bandwidth paths

EM Yes Astrovskayaetal.

(2011)

ShotMCF Shotgun Probabilistic

assignmentof

readstocandidate

haplotypes

NAa _Normalized_ﬂow _Yes _Skums_et_al.₍₂₀₁₃₎

VirA(AmpMCF) Amplicon-based Error-corrected

reads

Multi-commodity ﬂows

Normalizedﬂow Yes Skumsetal.(2013)

BIOA Amplicon-based Error-corrected

readsb Max-bandwidth paths Frequency balancinginforked nodes

Yes Mancusoetal. (2012)

QuRe Amplicon-based Poissonerror

model Distribution matching Haplotypesin decreasingorderof abundance

Yes Prosperiand Salemi(2012)

ViQuaS PEc _Mutation_calling _Distribution

matching

Minimum

frequencyof

constituent vertices

Yes Jayasundaraetal. (2015) HaploClique PEc _{Probabilistic} sequencesimilarity criterion Iterativelymerging max-cliques Normalizedread counts

Yes Töpferetal.(2014)

QColors PEc _{Error-corrected} reads Minimumvertex coloring NId _No _Huang_et_al.₍₂₀₁₁₎ VGA PEc _{High-ﬁdelity} sequencing protocol Minimumvertex coloring

EM Yes Manguletal.

(2014)

Avail.,availability.Ref.,references.

a_Candidate_haplotypes_are_generated_using_the_{max-bandwidth}_method_of_software_ViSpA.

b_Software_KEC₍_Skums_et_al.,₂₀₁₂₎_was_used_for_error_correction.

c _PE,_paired-end_reads._If_available,_information_from_paired-end_reads_is_taken_into_account.

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Fig.3. Schematicworkﬂowforglobalhaplotypereconstructionbasedontheread

graph.Ahypotheticalviruspopulationconsistingofthreeviralstrainsisdeep

sequenced.Readsoriginatedfromdifferentstrainsareidentiﬁedbydistinct

col-orsinthediagram.Aftersequencing,readsarealignedagainstareferencegenome

(black).Typically,alignedreadsarecorrectedforerrors,depictedhereasredcrosses.

Correctedreadsareusedforbuildingthereadgraphandcandidatehaplotypesare

reconstructedaspathsinthereadgraph.Nodeswithvariouscolorsindicatethat

cer-tainregionsaresharedamongdifferentviralstrains.Finally,therelativefrequencies

ofthereconstructedhaplotypesareestimated.

readgraph(Westbrooksetal.,2008).Theideahereistomaximally reducethenumberofedgeswhilemaintainingtheexistenceof paths.

Sourceandsinknodesaretypicallyaddedtothereadgraph(cf. graynodesinFig.3).Asourcenodeisconnectedtoallreadvertices withnoparentsandasinknodeisconnectedtoallreadvertices withnochildren.Thereby,anypathfromsourcetosinkcorresponds toaplausiblehaplotype.Sincenoteverypossiblepathcorresponds toatruehaplotype,andfindingallpossiblepathsleadsto overes-timationofthediversityofthepopulation,thetaskistofindan optimalsetofpathscorrespondingtolikelyviralhaplotypes(cf. Fig.4c).Severalframeworkshavebeenproposedfor reconstruc-tingviralhaplotypesusingthereadgraph,e.g.,byformulatingthe problemasaminimalpathcoverproblem(Erikssonetal.,2008; Zagordietal.,2011),asanetworkflowproblem(Westbrooksetal., 2008;Skumsetal.,2013),asamaximum-bandwidthpathproblem (Astrovskayaetal.,2011;Mancusoetal.,2011)orusingmaximal cliqueenumeration(Töpferetal.,2014)(cf.Table3).Inthelatter case,theoptimizationproblemisnotformulatedasfindingpaths inthereadgraph,butratheriterativelymergingfullyconnected clustersofreadnodes,i.e.,maximalcliques,inthereadgraphinto haplotypesofincreasinglength.

Recentapproachesforhaplotypereconstructioninclude meth-odswhichhavebeentailoredtoIlluminareads,suchasVGA(Viral Genome Assembler) (Mangulet al., 2014), HaploClique (Töpfer etal., 2014)and ViQuaS (Jayasundaraet al.,2015,2015).Some ofthesemethodswerebuiltuponpreviousalgorithmicideas,but adjustedtohandle largervolumesofinput readstypically pro-ducedbyIllumina platforms(cf.SupplementaryTableS2). VGA isbasedontheconflictgraphintroducedbyHuangetal.(2011), whereasViQuaSusesthecombinatorialapproachforhapolotype reconstructionproposedby Prosperiet al.(2011). Otherrecent developmentsinclude methodsreformulatingthenetwork flow optimizationproblem(Astrovskayaetal.,2011;Westbrooksetal., 2008;Mancusoetal.,2012)asamulti-commodityflowapproach (Skumsetal.,2013).Hereafter,weexplaintheserecentmethods forhaplotypereconstructioninmoredetail.Foracomprehensive reviewofpreviouslyavailabletools,werefertoBeerenwinkeletal. (2012),aswellastoTable3whichsummarizesgeneralaspects concerningread-graphbasedmethods.

ThesoftwareShotMCF(Skumsetal.,2013)isanextensionofthe ViralSpectrumAssembly(ViSpA)pipeline(Astrovskayaetal.,2011) fortheestimationofhaplotypefrequencies.Haplotype frequen-ciesareestimatedsolvinganetworkflowproblemwithmultiple commodities,i.e.,flowdemands.Eachcommoditycorrespondsto acandidatehaplotypegeneratedbyViSpAandtheflowthrougha vertexisproportionaltocorrespondinghaplotypefrequencies. Par-ticularly,andinordertoaccountfortechnicalerrors,flowvariables areweightedbytheprobabilitythatcorrespondingreadsoriginate fromagivencandidatehaplotype.

ShotMCF hasbeen designed for shotgunHTS reads. A simi-lar approach,using multi-commodityflows,hasbeen proposed for haplotype reconstruction using amplicon-based sequencing (Skumsetal.,2013).Undersequencingprotocolsbasedon ampli-cons,readsareproducedfrompre-definedwindowsofareference sequence.Bydesign,thestartingandendingpositionsofthe ampli-conswithrespecttoareferencegenomeareknown,aswellasthe overlapbetweenamplicons.AmpMCFexploitsthisblockstructure oftheampliconsforconstructingthereadgraph.Inthisframework, theobjectiveistofindasetofpathsinthereadgraphwhich col-lectivelycoverallreadswhileminimizingthetotalflow.Themain limitationofthismethodisthatthenumberofcommodities,i.e., haplotypes,needstobespecifiedinadvance.Thismethodhasbeen integratedintotheViralQuasispeciesAssemblerpipeline(VirA).

Anotheranalysispipelineforviralquasispeciesreconstruction hasbeenimplementedinthesoftwareViQuaS.Thissoftwareuses

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Fig.4. Buildingthereadgraph.(a)Inthisexample,agenomicregionoflength43bpiscoveredbysevenreads,eachoflength20bp.Sequencingreadsarealignedagainsta

referencesequence(black)andfoursegregatinglociareidentiﬁed(asterisks).(b)Fromtherealalignment,thereadgraphisconstructedbasedonﬁvenon-redundantreads;

segregatingsitesareindicatedbyasterisks.(c)Twocandidatehaplotypescoveringallreadscanbeproposedfromthegraphandonepossiblesolutionisshownashighlighted

pathsincyanandorange.Inthisexample,closestsegregatingsitesarefurtherapartthanaregionthatcanbecoverbyanyread.Therefore,thereisnodirectevidenceof

whethertheseSNVsoccurinthesameviralstrain.

areference-assisteddenovoassemblystrategyforreconstruction ofhaplotypes,whichconsistsofthreesteps.First,readsarealigned againstareferencegenomeand,subsequently,dividedintotwo groupsdependingonwhetherornoteachreadhasbeenperfectly alignedtothereference. Readswhichdidnot alignedperfectly to thereference genome are assembled into contigs using the denovo assembly softwareSSAKE (Warrenet al., 2007).In the secondstep,contigsarealignedagainstthereferenceand SNVs arenaïvelydetected.Itmayhappenthat readsoriginatingfrom differentstrainshaveasufﬁcientoverlap,suchthattheyare assem-bledinto thesame contig.Therefore, in thelast step, chimeric errorsarecorrectedonthebasisofreadssupportingco-occurring SNVs. If there is noevidence of linking mutations, the contigs are partitioned accordingly. For theglobal reconstruction, con-tigsarecombinedintoglobalhaplotypesusingavariationofthe combinatorialapproachproposedbyProsperietal.(2011).Ona benchmarkstudy,itwasobservedthatthepipelinereconstructeda highnumberoffalsepositives,whichwasattributedtofalseinsilico recombinants(Jayasundaraetal.,2015),i.e.,haplotypeswhichhave beenwronglyreconstructedasthecompositionofdifferentviral strains.Inordertoimproveonprecision,aprobabilisiticapproach hasbeenproposedforestimatingthenumberofunderlyingstrains intheviruspopulation(Jayasundaraetal.,2015).Thisestimateis thenusedasathresholdvalueforthenumberofcandidatepaths constructedfromthereadgraph.

AmorerecentsoftwarebasedonthereadgraphisHaploClique (Töpferetal.,2014).Inthisframework,thereadgraphisbuiltwith slightmodiﬁcations.First,incaseofpaired-endreads,eachnode willcorrespondtoareadpair.Second,inadditiontosufﬁcient over-lapbetweentworeads(orreadpairs),anedgeisdrawnbetween

twonodesifthecorrespondingreadsarelikelytostemfromthe sameviralstrain.Thechancethattworeadsoriginatefromthe samehaplotypeisevaluatedbasedontwocriteria:(i)sequence similarityinthepresenceoftechnicalerrors,and(ii) compatibil-ityoftheinsertsizes.Theinsertsizecriterionallowstoidentify structuralvariants.Relativelylongindels aredetectedbasedon deviationsfromtheexpectedinsertsizeforreadpairsinaclique. Therefore,ifthereareindicationsthattheviruspopulationposes suchstructuralvariants,HaploCliquewouldbeasuitablechoice ofsoftware.Viralhaplotypesarereconstructediterativelyby ﬁnd-ingmax-cliquesandmergingthemintosuper-reads.Asuper-read istheconsensussequenceofallreadsinamax-clique.This itera-tiveschemeisusedtoextendlocallyreconstructedhaplotypesinto full-lengthhaplotypes,providedthatthedegreeofgeneticdiversity oftheviruspopulationissufﬁcientlyhigh.Ifthereisnoevidence onhowtoextendasuper-read,thealgorithmterminates.A pos-sibledownsideofthismethodisthattheruntimeisexponential inthereadcoverage.Nevertheless,HaploCliquewasobservedto outperformothermethodsintermsofruntime.

Acomplementaryvariantoftheread-graph,theconflictgraph, wasinitiallyproposedandimplementedinthesoftwareQColors (Huangetal.,2011).Intheconflictgraph,theverticesrepresent reads(orreadpairs)andedgesaredrawnbetweenconflictingpairs of vertices,i.e.,edges connectreads thatdo not agree ontheir overlap.Reconstructingviralhaplotypeshasbeenaddressedina parsimoniousfashionbyfindingtheminimumnumberof max-imally independent sets of non-conflictingreads. This problem is equivalenttofinding theminimumnumber of labels or col-orsrequiredforcoloringtheverticesoftheconflictgraph,such thatnoedgeconnectsverticeswithidenticalcolors(Huangetal.,

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2011).Morerecently,thisproblemhasbeenre-formulatedasa Max-Cut problem and it has been solved using a top-down approach.Theconﬂictgraphisrecursivelypartitionedaccordingto itsmaximumcut,untilcomponentsbecomeindependent(Mangul etal.,2014).Relativefrequenciesofthehaplotypesareestimated usingan expectation-maximization(EM)algorithm in a similar fashion as in the ShoRAH model (Eriksson et al., 2008).Reads areassumed tobesampledfromtheunderlyingdistributionof viralstrains,buthereapriorprobabilityfortheviralhaplotypes isused.Thus,insteadofmaximizingthelikelihood,theposterior probabilityis maximized.This computationalmethodhasbeen implementedinthesoftwareVGA,whichstandsforViralGenome Assembler(Manguletal.,2014).

Asmentioned earlierin thissection, errorcorrectioncanbe incorporatedasastepbeforebuildingthereadgraph.Suchisthe caseforthesoftwareShoRAH(Zagordietal.,2010,2010,2011) and QuRe(Prosperiand Salemi, 2012).Othermethods, suchas AmpMCF,QColorsandVGA,assumereadshavebeencorrectedfor technicalerrors,eitherusingcomputationalmethodsforerror cor-rection(Zagordietal.,2010;Skumsetal.,2012;Heoetal.,2014)or sequencingprotocolsbasedonprimerIDs(Kindeetal.,2011;Lou etal.,2013;Seifertetal.,2016)(cf.Table3).Alternatively, tech-nicalerrorscanbetreatedinaprobabilisticfashionasisdonein softwareViSpA(Astrovskayaetal.,2011)andHaploClique(Töpfer etal.,2014).

4.3.2. Probabilisticmethodsforhaplotypereconstruction

In many approaches described in the previous section, the readgraphisconstructedfromsequencingreadswhichhavebeen previouslycorrectedforsequencingerrors.Instead,the stochas-ticprocessunderlyingthegenerationofsequencingreadscanbe modeledexplicitly.Methodsfallinginthiscategoryhavebeen for-mulatedasprobabilisticmodelsofeitherthesequencingprocess (Jojic etal.,2008)ortogetherwithagenerativeprocessforthe viralhaplotypes(Töpferetal.,2013;Prabhakaranetal.,2014).The formerapproachhasbeenproposedbyJojicetal.(2008),whereas thelatter havebeenimplementedin softwarepackages Predic-tHaplo(Prabhakaranetal.,2014)andQuasiRecomb(Töpferetal., 2013)(cf.Table4).

InthemodelproposedbyJojicetal.(2008),observedreadsare assumedtoconstituteasamplefromafixednumberofviralstrains, butanoisysampleasreadsaresubjecttotechnicalnoise. Never-theless,thenumberofunderlyingviralstrains,whichisgenerally unknown,needstobespecifiedbeforehand.Tocircumvent this limitation,PredictHaploandQuasiRecombimplementmodel selec-tionstrategiesthatfindanoptimaltrade-offbetweensensitivityof inferringhaplotypesanddepthofthedata.

In PredictHaplo, viral haplotypes are modeled as the com-ponents of a multinomial mixturemodel, in which the mixing coefficientscorrespondtothehaplotypefrequencies.Multinomial distributionsareemployedtocapturethegeneticdiversityateach locus by meansof haplotype- and position-specific probability tables.Moreover,andinordertoavoidspecificationofthe num-berofcomponentsapriori,anon-parametricDirichletprocessis employedaspriorprobabilitydistribution,andhaplotypeinference isperformedinafashionsimilartothelocalreconstructionmodule ofShoRAH.Full-lengthhaplotypesarereconstructediterativelyby extendinglocallyreconstructedhaplotypes,startingfromthe win-dowofalignedreadswithhighestcoverage.Clusterassignment probabilitiesextractedfromthelocallyreconstructedhaplotypes areusedaspriorinformationtograduallyextendthelocal win-dow,andthisprocessiscarriedoutuntilthewindowspansthe entirelengthofthegenomeorgeneticregionofinterest.

Athirdgenerativemodelhasbeenproposedbasedonhidden Markovmodels(HMM)andhasbeenimplementedinthesoftware packageQuasiRecomb(Töpferetal.,2013).Inadditiontomodeling

mutations by position-speciﬁc probability tables, QuasiRecomb modelsrecombinationeventsexplicitly.Thisfeatureiskeywhen studyingsomeRNAviruses,suchasHIV,whererecombinationis animportantsourceofgeneticheterogeneity.AsinPredictHaplo, globalhaplotypereconstructionisseededonlocallyreconstructed haplotypes,andsolvedusingahierarchicalassemblystrategy(Di Giallonardoetal.,2014).

BothQuasiRecombandPredictHaplo wereinitiallytested on simulatedreadsmirroring454errorpatternsandreadlengths.The abilityofthesetoolstoreconstructfull-lengthhaplotypeswaslater validatedexperimentally usingreads fromdifferentsequencing platforms,namely454/Roche,IlluminaandPacBio(DiGiallonardo etal.,2014).

4.3.3. Denovoassemblyofviralhaplotypes

As mentioned earlier (cf. Section 3), biases induced by the readmappinghinderthereconstructionofviralhaplotypes. Meth-odsfordenovoquasispeciesassemblyrepresentanalternativeto reference-basedhaplotypereconstruction.Todate,two reference-freemethodologies,dubbedMutant-Bin(Prabhakaraetal.,2013) and MLEHaplo(Malhotraet al.,2016), have beenproposed (cf. Table5).Itisworthemphasizingthatassemblingasingleconsensus genomedenovoisnotequivalenttoassemblinganunknown num-berofcloselyrelatedviralhaplotypes.Therefore,genericdenovo assemblersarenotwellsuitedfortheviralquasispecies reconstruc-tiontask.

A computational framework for estimating the number of viral haplotypes and their frequencies has been implemented in the method Mutant-Bin (Prabhakara et al., 2013) and later reﬁned by Malhotraet al. (2013). This framework is based on theLander–Watermanmodelof sequencing,in whichreadsare assumed tofollow a Poisson distribution parameterizedbythe sequencingcoverage.Assuch,frequenciesofk-mers(i.e.,substrings oflength k)extractedfrom sequencingreadsare modeledas a mixtureofPoissondistributions.ExpectedvaluesofthePoisson distributions correspondtotheso-called composite frequencies, i.e.,frequencieswhichareobservedasthesumoftheabundances oftheunderlyinghaplotypessharingagivenk-mer.Thegoalis toinferthefrequenciesoftheunderlyinghaplotypes,whichare denotedasbasicfrequencies.Agreedystrategyisusedforﬁnding aminimalsetofbasicfrequenciesexplainingcomposite frequen-cies.ItinvolvestraversingthelistofPoissonmeansinincreasing order.Ineachiteration,anelementisregardedasthefrequency of an underlyinghaplotype if it cannot be obtainedby adding basicfrequenciesalreadypresentinthesolutionset.Limitations of this method include thelack of an errormodel, the depen-denceona uniformcoverageand theassumptionthatdifferent viralstrainsarepresentinthepopulationwithdistinct frequen-cies.Moreimportantly,genomicsequencesofviralstrainsarenot reconstructed.Ontheotherhand,anadvantageisthatitallowsto infer,withhighprecisionandrecall,thestructureofthe popula-tionwhenthegeneticdiversityislow(Malhotraetal.,2013).This isanotableadvantage,becausethereconstructionofviral haplo-typesusinganyotherapproachbecomesharderasthediversity ofthesampledecreases(Jayasundaraetal.,2015;Erikssonetal., 2008).

Morerecently,adenovoassemblyalgorithmbasedonthede Bruijngraph hasbeen proposedforestimating viralhaplotypes frompaired-endreads(Malhotraetal.,2016).ThedeBruijngraph isconstructedinasimilarfashiontothereadgraph.Thevertices ofthegraphcorrespondtok-mersgeneratedfromerror-corrected readsandtheedgesconnectoverlappingk-mers.However,the ori-entationofthereadsisunknown.Therefore,k-mersfromthereads aswellasfromtheirreversecomplementsarerepresentedinthe graph.Inthisframework,viralhaplotypereconstructionisdivided intotwophases.Intheﬁrstphase,aﬁxednumberoftop-scoring

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Table4

Probabilisticmodelsforhaplotypereconstruction.

Method Sequencing

mode

Approach Model

selection

Inference Avail. Ref. Jojicetal.,2008 Shotguna _{Probabilistic}_model

forgenerationof

sequencingreads

None EM No Jojicetal.

(2008) PredictHaplo PEb _Multinomial mixturemodel Dirichlet processasprior probability distribution MCMC Yesc _Prabhakaran etal.(2014)

QuasiRecomb PEb _Jumping_HMM _BIC _EM _Yesd _Töpfer_et_al.

(2013)

Inference,latentvariablesandunderlyingprobabilitydistributionsareestimatedfromthedatabymaximumlikelihoodestimationeitherusingtheexpectation-maximization

algorithm(EM)orMarkovchainMonteCarlo(MCMC).Avail,availability.Ref.,references.

a_Initially_tested_on₄₅₄_reads.

b_PE,_paired-end_reads._If_available_the_model_incorporates_information_from_paired-end_reads.

c _{http://bmda.cs.unibas.ch/HivHaploTyper/}_. d _{https://github.com/cbg-ethz/QuasiRecomb}_.

Table5

Othermethodsforhaplotypereconstruction.

Method Platform/sequencingmode Approach Errorhandling Avail. Ref.

Mutant-Bina _454/Shotgun _De_novo _Thresholding_of

low-frequentk-mers

No Prabhakaraetal.(2013)

MLEHaplo Illumina/PEb _De_novo _{Error-corrected}_readsc _Yesd _Malhotra_et_al.₍₂₀₁₆₎

Dilerniaetal.,2015 PacBio Hierarchicalclustering Binomialerrormodel No Dilerniaetal.(2015)

2SNV PacBio Hierarchicalclustering Binomialerrormodel Yese _Artyomenko_et_al.₍₂₀₁₆₎

Sequencingplatformsarespeciﬁedifsoftwarewastestedonrealdatasets,asreportedontheoriginalpublication.

Avail.,availability.Ref.,references.

a_Only_applicable_for_haplotype_frequency_estimation.

b_PE,_paired-end_reads._Paired-end_information_explicitly_taken_into_account.

c _Software_BLESS₍_Heo_et_al.,₂₀₁₄₎_was_used_for_error_correction.

d _{https://github.com/raunaq-m/MLEHaplo}_.

e_{http://alan.cs.gsu.edu/NGS/?q=content/2snv}_supplement_.

pathspervertexaregeneratedusingaheuristicalgorithm(named ViPRA).Thescoreofapathisbasedonthenumberofreadpairs coveredbysuchpathaswellasonthecompatibilityoftheirinsert sizes.In thesecondphase,thesetofcandidatepathsisreﬁned viabackwardelimination.Pathsareiterativelyremoveduntilthe likelihoodoftheremainingpathsstartstodecrease.Thisapproach hasbeenimplementedinthesoftwareMLEHaplo(Malhotraetal., 2016).

4.3.4. Hierarchicalclusteringoflongreadsforreconstruction viralhaplotypes

Recoveringthestructureofaviruspopulationfromshortreads (i.e.,readsshorterthantheviralgenomeorgenomicregionof inter-est)isfurtherhamperedbytheexistenceofrelativelylongregions, commontomanyviralstrains.Thisisbecauseconservedregions longerthanthereadlengthintroduceambiguitiesinthe recon-structionoffull-lengthviralgenomes,i.e.,thereexistsmorethan oneplausiblewaytoconnecttherelativelyshortreads(cf.Fig.4).In ordertobridgeconservedregions,somealgorithmseitherexploit thelinkageinformationprovidedbypaired-endreads(Töpferetal., 2014)orusetherelativefrequenciesasevidencetoresolve ambi-guities(Manguletal.,2014;ProsperiandSalemi,2012;Jojicetal., 2008;Prosperietal.,2011).However,thesestrategieshavesevere limitations.Intheformercase,pairinginformationislimitedby thelengthoftheinsertsizeandreliesonthelocationofatleastone ofthepairsonaheterogeneousregion.Inthelattercase, ampli-ﬁcationandsequencingbiasescanleadtoanon-uniformsample, resultingindeviationsfromthetrueunderlyingfrequenciesofthe viralstrains.ThisissuecanbecircumventedbyusingPaciﬁc Bio-scienceorOxfordNanoporetechnologieswhichnowadaysoffer readlengthsthatarecomparabletothesizeofthegenomeofmany RNAviruses.

Twomethodsusinghierarchicalclusteringoflongreadshave beenproposedforelucidatingthestructureofviruspopulations (Dilerniaetal.,2015;Artyomenkoetal.,2016)(cf.Table5).Usinga topdownapproach,readsarerecursivelypartitionedintoclusters onthebasisofcommonSNVs,untiltherearenogroups contain-ingconflictingSNVs.Resultingclustersareassumedtocorrespond toviralstrainsand,consequently,haplotypesarereconstructedas thegeneticconsensusofeachcluster.Thecomputational work-flowproposedbyDilerniaetal.(2015)employsabinomialerror modelforcallingSNVsandthepairwisedistancebetweenreadsis computedasthepercentageofSNVsinwhichthereadsdiffer.In theframeworkproposedbyArtyomenkoetal.(2016),called2SNV, errorsarealsoassumedtofollowabinomialdistribution,but2SNV useslinkageinformationbetweenSNVs.Themainlimitationofthe 2SNVmodelisrelianceontheexistenceoflinkagedisequilibrium. Readsarerecursivelypartitionedintoclusterswhenaread clus-terexhibitsatleasttwosignificantsegregatinglociwithrespect toanothercluster.Nonetheless, identifyingviralmutant strains thatdifferinasinglelocusisahardtask(Jayasundaraetal.,2015; Erikssonetal.,2008).Thesoftware2SNVhasbeentestedonamixed sampleobtainedbyerror-pronePCRontheInfluenzaAvirusPB2 segment(approx.2kblong).Theapplicabilityof2SNVtolonger genomicregionshasnotbeenevaluated,anditmightbeanother limitingfactorastheruntimescalesquadraticallywithrespectto thenumberofsitesevaluated.

These hierarchicalclustering approaches canbe regardedas local haplotypereconstructionmethods, in the sensethat they cannot linkvariantsover distances largerthantheread length. However,sinceviralgenomescanbesequencedina singlerun using Paciﬁc Bioscienceor Oxford Nanopore technologies, they offer the possibility to reconstruct full-length genomes. Other methods,suchastheDirichletprocessmixtureimplementedin

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ShoRAH(Zagordietal.,2010)andPredictHaplo(Prabhakaranetal., 2014)areinprincipleapplicabletoreconstructviralhaplotypes fromlongreads,however,thesemethodshavenotbeenrigorously tested.

Otherproof-of-conceptapplicationsusinglongreadshavebeen alsoproposedtoelucidatethestructureofviruspopulations.For instance,thetag-basedprotocolproposedbyHuangetal.(2016) reliesonknownmutantlocifortheidentiﬁcationofviralstrains andavoidsphasinghaplotypes.Thismethodologyhasbeenapplied toanalyzethelinkageofHIV-1drugresistancemutationsatthe haplotypelevel.Inadditiontohaplotypereconstruction applica-tions,alignmentoflongreadsseemstobeanotheremergingarea ofresearch.Themajorobstacleinaligninglongreadsisthatdue tohigher error rates of, e.g., PacBioplatforms and longerread lengths,previousreadmappersperformpoorly.Severalread map-perstailoredtolongreadshavebeenproposedandimplemented insoftwarepackagesBWA-MEM(Li,2013),BLASR(Chaissonand Tesler,2012),rHAT(Liuet al.,2016)andProbAlign(Zengetal., 2014).

4.3.5. Choiceofsoftware

Whenitcomestochoosingatoolforanalyzingamixedsample fromaviruspopulation,thewealthofhaplotypereconstruction toolsisoverwhelming,especiallyforinexperiencedusers.A num-berof review articles which were publisheda few years back, mayproveusefulwhenselectingapropertoolforagiven appli-cation(PanditanddeBoer,2014;Prosperietal.,2013;Schirmer etal.,2014).However,atthetimethesestudieswereconducted, thenumberoftoolsavailablewasscarce,andbenchmarkswere limitedto evaluation ofShoRAH, QuReand PredictHaplo. From thesestudies,thegeneralobservationisthatShoRAHandQuRe tendto over-estimatethe number of haplotypes,while Predic-tHaplotendstounder-estimateit.Notsurprisingly,PredictHaplo consistentlyreportsthelowestnumberoffalsepositives,resulting inhighprecisionoftentimesatthecostoflowrecall.

Othercomparativeassessmentshavebeenincludedin publica-tionsofthelatestmethods.Usually,thesestudiesemphasizehow theauthors’softwareimprovesoverprevioustools,andalthough subjectivity may be questionable, the main difﬁculty is a lack ofstandardization.Henceforth,wesummarizethemostgeneral ﬁndings.

Factors influencing reliability of viral haplotype reconstruc-tionincludetheratiobetweenthereadlengthandthegenome size,thedepthofcoverage,technicalerrorrates,abundancesof viralstrainsandtheunderlyinggeneticheterogeneityofthevirus population. Thefirst three factorsare partof theexperimental designand,therefore,canbecontrolled,whilethelatterare intrin-sictotheviruspopulation.Ingeneral,thelongerthereads,the higherthecoverage,themoreabundanttheviralstrainandthe largerthedegreeofdiversity,thebetteronecanexpectanygiven methodtoperform(Manguletal.,2014;Jayasundaraetal.,2015; Malhotraetal.,2016;PanditanddeBoer,2014;Eriksson etal., 2008;Prabhakaranetal.,2014;Töpferetal.,2014;Skumsetal., 2013;Prosperietal.,2013;Schirmeretal.,2014;Zagordietal., 2012).Coverageinfluencestheminimumfrequencyatwhicharare mutantcanbeidentified,whereasthereadlengthandthegenetic diversityaffectthecapabilityofbridginggapsbetweenconserved regionsindifferenthaplotypes.Additionally,mostabundant hap-lotypesarebetterrepresentedinthesamplethanlowabundant counterparts,thus,areoftentimesreconstructedmoreaccurately.

Althoughsome of theaforementioned factors can be modi-ﬁedaspartoftheexperimentaldesign,therearesometechnical limitationswhenchoosingasoftwareforanalyzingthedata.For instance,independentstudieshaveindicatedthatQuReaborted execution,amongotherreasons,duetothelargevolumeofinput reads(Jayasundaraetal.,2015;Prabhakaranetal.,2014;Töpfer

et al., 2014; Schirmer et al.,2014). In order toease the selec-tionprocess,wehavelistedsomeaspectsreportedintheoriginal publications(cf.SupplementaryTableS2).Thesedataareintended toillustrateinwhichrangesof,e.g.,readlengthsorvolumesofinput reads,performanceofagiventoolhasbeenstudied.AHaplotype reconstructiontoolmaywellrunoutsidetheseranges.

Intermsofruntimes,andaggregatingresultsfromdifferent benchmarks, it hasbeenobserved that latestread-graphbased algorithms,suchasViQuaSandHaploCliquearefasterthan Pre-dictHaplo,whichinturnisfasterthanShoRAH,ViSpAandQuRe (Jayasundaraetal., 2015;Astrovskayaet al.,2011;Prabhakaran etal.,2014;Töpferetal.,2014;Schirmeretal.,2014).

Tothebestofourknowledge,allsoftwarepackagesdeveloped todatehavebeendevelopedforresearchpurposes.Unfortunately, usability,portabilityandmaintainabilityarenotprioritiesinthis setting.Most,ifnotall,softwarearedistributedascommandline tools(cf.SupplementaryTableS2)andthefewavailablepipelines lackintegrationintoscientiﬁcworkﬂowsystems.Therefore,basic toadvancedcomputationalskillsareapre-requisitefromtheuser.

5. Conclusionsandfuturedirections

HTStechnologieshaveopenedupnewavenuesforstudying geneticheterogeneityofviruspopulationsatan unprecedented level of detail. However,since reads are error-proneand typi-cally shorter than the targeted genomic region, HTS platforms provideanincompleteandimperfectsampleofthevirus popula-tion.Biasesanderrorsintroducedduringlibrarypreparationsteps, ampliﬁcationandactualsequencingcanbeamelioratedusing sam-plecontrolsandsuperiorexperimentalprotocols(e.g.,primerIDs, CirSeq).Ontheotherhand,referencebiasesinducedbytheread alignmentremainchallenging,andcurrentalignersleavealotof roomforimprovement.

SeveralmethodsforSNVcallinghavebeenproposedand imple-mentedinthepastﬁveyears.Nowadays,itispossibletodetect variantsinthepopulationatrelativefrequenciesbelow1%. Infor-mationonlow-frequencymutationsisofrelevanceforantiviral treatment and thus we foresee applications aimed at routine practiceinclinicalvirology,substitutingdiagnosisbasedonSanger sequencing.

Manystrategieshavebeenproposedassolutionsfortheviral quasispecies reconstructionproblem. However,it is difficultto comparativelyassesstheirperformance.Thisislargelydueto(i) several factors influencing the accuracy of methods for haplo-type reconstruction,aswellas(ii)lack ofstandardized metrics or(iii)validationstandards.Firstly,therearemanyfactors influ-encingreliabilityofhaplotypereconstructionalgorithms,including aspectsrelated to thesequencingplatform ofchoice (e.g.,read length,coverage,error rates)and intrinsic tothevirus popula-tion(e.g.,geneticdiversity,strainprevalence).Secondly,itwould bedesirabletohaveawidelyacceptedperformancemetricwhich quantifiestheabilityofreconstructingviralhaplotypesaccounting foraforementionedfactorsorwithrespecttotheoreticallimits.The lattercanbeestimated,e.g.,usingtheLander–Watermanmodel. Undertheassumptionofuniformcoverage,theLander–Waterman modelprovidesatheoreticalboundontherelativefrequencyat which viral strains can beidentified (Jayasundara et al., 2015; Erikssonetal.,2008),but,inadditiontoseveralsimplifying assump-tions,ignoresthecombinatorialproblemthatariseswhilemerging short readsinto full-length haplotypes. Lastly, from a practical perspective,many software packageshave beentested only on simulateddatasets,wherefactorssuchasfaithfulnessof simu-latederrorprofilesandassumptionsonthestructureofthevirus populationmaybequestionable.Furthermore,whenthe perfor-manceofhaplotypereconstructiontoolsisevaluatedonrealdata sets,reconstructionaccuracyremainsanissue(PanditanddeBoer,