m01Fig3Bmcrit023AlthoughthesegeneralpatternsareconsistentwiththepredictionsofYeamanandWhitlock28theeffectofthestrengthofselectionontherateofgenomeevolutionisnotaccountedforbyEqs2or4likelyinpartbecaus ID: 891326
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1 evolutiontoclusteredarchitecturesissomew
evolutiontoclusteredarchitecturesissomewhatreduced(e.g., m =0.1,Fig.3 B ; m crit =0.23).Althoughthesegeneralpatterns areconsistentwiththepredictionsofYeamanandWhitlock (28),theeffectofthestrengthofselectionontherateofgenome evolutionisnotaccountedforbyEqs. 2 or 4 ,likelyinpartbe- causetheseapproximationsignorerearrangementsthatyield clustersoflociwith r � 0( Methods ).When r � 0,theamountof linkagedisequilibriumbetweenloci,andthereforethe tness bene tsoflinkage,shouldscalewiththestrengthofselection (19,53),suchthatunderstrongerselectionthereiseffectively alargertargetregion( L )overwhichrearrangementscanyield clustersoflociwith tnessbene tsowingtolinkage. Therateofevolutionofclusteringisalsostronglydeterminedby boththepopulationsize( N )andtherateofoccurrenceofrear- rangements( ).Clusteringevolvesmuchmorerapidlywhen N = 10 4 thanwhen N =10 3 ,butif isincreasedbyanorderofmag- nitudefor N =10 3 ,therateofevolutionofclusteringisquite similartowhen N =10 4 (Fig.3 C ).Thisshowsthattherateof architectureevolutiondependsheavilyonthepopulation-level rateofoccurrenceofrearrangements( N ),aspredictedbyEq. 2 . Clusteredgenomicarchitecturesalsoevolvewhenenviron- mentsarebothspatiallyandtemporallyheterogeneous(Fig.4 A ) andwhenpopulationsgothroughalternatingperiodsofspatial heterogeneityandhomogeneity(Fig.4 C ).Fig.4 A showsthe evolutionofgenomicarchitecturewhenpopulationsinhabit aspatiallyheterogeneousenvironment(localoptimaare+1/ 1) thatalso uctuatesovertime(asshowninFig.4 B ).Whenthe periodoftemporal uctuationsisshort( T =1,000,Fig.4 A ), clusteringevolvesmoreslowlyandstabilizesatanintermediate level.Theamountofclusteringattheendofthesimulations variesnonmonotonicallyasafunctionof T ,withthemostclus- teringseenwhen T =5,000(Fig.4 A ).Whentheperiodisvery long( T =10 5 ),genomicarchitectureevolvestowardhighly clusteredarchitecturesbut uctuatesduetotransientincreases inthenumberofunclusteredselectedloci( SIText and Fig.S2 ). Whenpopulationsinhabitanenvironmentthatperiodically alternatesbetweenspatiallyhomogeneousandspatiallyhetero- geneous(asshowninFig.4 D ),clusteredgenomicarchitectures stillevolve,althoughtherateofevolutionisslowerforsmaller T (Fig.4 C ).Inthesesimulations,geneticdivergenceoftencollap- sescompletelyduringtheintervalsofhomogeneityandany islandsofallelicdivergencearelost,butclusteredgenomic architecturespersistandcanrapidlygiverisetonewislandsof allelicdivergencewhenheterogeneousenvironmentsarerees- tablished.Clusteredarchitecturesstillevolvewhentheenviron- mentishomogeneousformoretimethanitisheterogeneous, butataslowerrate( SIText and Fig.S3 ). Fromtheaboveresults,itisclearthattherateofrearrangement isanimportantdriverofarchitectureevolution,butistherealsoan effectofthetypeofrearrangement?Therearenumerousmech- anismsthatcangiverisetotherearrangementofsmallfragments ofthegenome:( a )nonhomologousorectopicrecombinationin- volvingtwocloselyspacedcrossovers(54,55),( b )repairfollowing multipledouble-strandedbreaks(56 58),( c )intrachromosomal recombinationformingcircularDNAthatreinsertselsewherein thegenome(59),( d )excisionandreinsertionmediatedby anking transposons(60,61),( e )transposon-mediatedtransduplication [e.g.,byhelitrons(62)o rPack-MULEs(63)],and( f )reverse transcriptionandretrotranspos itionofmRNA,whichresultsin thelossofintronsinthedaughtercopy(64).Ofthese,someresult inthemovementofagenefromoneplacetoanother(e.g., a d ), whereasothersresultinthecreationofaduplicatecopyinanew location(e.g., e and f ).Unfortunately,thereisstilllittlein- formationontherelativefreque ncyofthesedifferentmecha- nismsindifferentspecies.Alth oughalloftheabovesimulations wererunusingacut-and-pastemodelofrearrangementsimilar tomechanisms a d ( Methods ),therateofevolutiontowardclus- teredarchitectureswasnotsubstantiallychangedwhenadupli- cationmodelsimilartomechanisms e and f wasusedinstead( Fig. S4 ).However,unlikethecut-and-pastemodel,alowrateofgene deletion( )wasnecessaryforsigni cantclusteringtoevolvein theduplicationmodel,becauseotherwisetherewasnomecha- nismthroughwhichthelessclusteredparentalcopyofalocus couldbelost( Fig.S4 ). Inthesesimulations,geneduplication,genedeletion,andre- combinationbetweenrearrangedandancestralhaplotypescanall resultinchangesinthenumberofcopiesofagivenlocusthatare passedfromparenttooffspring.Empiricalstudieshavefoundthat changesingenecopynumberofteninvolvephenotypicchangesor tnesscosts,likelybecausechangesinthedosageofsomegenes upsettheoverallbalanceofexpression(65 67).Alloftheabove simulationswererunundertheassumptionofrelativelyweakse- lectionagainstcopynumbervariants(CNV; Methods ).Therateof evolutiontowardclusteredarchitecturestendedtodecreasewith increasingstrengthofselectionagainstCNV( Fig.S5 ),suggesting thatclusteredarchitecturesaremorelikelytoinvolvegenesthat haveonlyminimal tnesseffectsduetochangesincopynumber (i.e.,lesspotentialtoupsetthebalanceofexpression;refs.65 67). Whensimulationswererunexcluding tnesscostsforCNV, clusteredarchitecturesstillevolvedatratescomparabletothose showninFig.3,providingtherateofgenedeletionwasatleast ashighastherateofrearrangement( Fig.S4 ). Discussion ImplicationsforGenomicIslandsofDivergence. Therehasbeen considerabledebateabouttheimportanceofdivergencehitch- hikingfortheevolutionofgenomicislandsofdivergence(16,20, 26),withrecentworknotingthattheeffectofdivergencehitch- hikingonestablishmentprobabilitymayoftenbequitelimited relativetotheeffectofselectionactingdirectlyonbene cial Spatially homogeneous Time ( g enerations x1000) Map position (cM) 0250500 0 10 20 30 40 50 Spatially heterogeneous Time ( g enerations x1000) 0250500 A B Fig.2. Thedistributionofselectedlocialonga singlechromosomeover500,000generationsof evolutionwhentheenvironmentisspatiallyhomo- geneous( A ;optimaare =+1and+1)andspatially heterogeneous( B ;optimaare =+1and 1).Pop- ulationsareoftenpolymorphicforarrangements, withselectedandneutrallocibothpresentindif- ferentindividualsatthesamechromosomallocation. Foragivenchromosomalpositionatagivenpointin time,blueindicatesthatmostindividualsinboth populationshaveaselectedlocus,redindicatesthat mostindividualsinonepatchhaveaselectedlocus whereasmostindividualsintheotherlocushave aneutrallocus,andwhiteindicatesthatmostindi- vidualsinbothpopulationshaveaneutrallocus; m =0.01, =0.75, N =10 4 , =10 6 . E1746 | www.pnas.org/cgi/doi/10.1073/pnas.1219381110 Yeaman 26.ViaS(2012)Divergencehitchhikingandthespr eadofgenomicisolationduringecological speciation-with-gene- ow. PhilosTransRSocLondBBiolSci 367(1587):451 460. 27.BartonNH,HewittGM(1989)Adapt ation,speciationandhybridzones. 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Yeaman PNAS | PublishedonlineApril22,2013 | E1751 EVOLUTION PNASPLUS exceptionstothispatternoccuroververynarrowrangesofmi- grationratefallingjustbelowthecriticalthresholdabovewhich noadaptivedivergenceoccurs(Fig.1,grayshading).Inthese cases,thedivergencehitchhikingadvantageishighbecausethe establishmentprobabilityofsmallunlinkedmutationsiscloseto0. Undertheassumptionthatthelocithatcanpotentiallycon- tributetolocaladaptationareuniformlydistributedthroughout thegenome,theratio linked / unlinked willbeafunctionofthe fractionofthegenomethatoccurswithin50cMoneithersideof thefocallocus(i.e.,theregionoverwhichthedivergence hitchhikingadvantageiscalculatedinFig.1),relativetothe fractionofthegenomethatisunlinked.Todevelopasimple heuristicunderassumptionsmostfavorabletothedivergence hitchhikinghypothesis,thisratiocanbeapproximatedas clustered / unlinked =1/2/( k 1/2)=1/(2 k 1),where k isthe numberofchromosomes,assumingchromosomesareallof equivalentsize,andtheregionmaintainedasaclusterspans50% ofasinglechromosome.Ifweassumethedivergencehitchhiking advantage, EP clustered / EP unlinked 3(fromFig.1)and k =21(as inthethreespinestickleback),thenusingEq. 1 ,wewouldexpect atleast13unlinkedallelestoestablishforeveryclusteredallele thatestablishes.Notethatinmostcasesthisratiowouldbeeven larger,becausetheadvantageofdivergencehitchhikingissel- domashighasthreefold(Fig.1),andtheregionmaintainedas aclusterinmostempiricalcontextsistypicallymuchsmallerthan 50%ofachromosome. Basedontheaboveheuristic,veryfewoftheallelesthat contributetolocaladaptationareexpectedtoresideinagiven islandofdivergenceexceptunderverylimitedregionsofpa- rameterspace.Itmaybearguedthatashortcomingofthis heuristicisthatitconsidersonlytheformationofagenomic islandaroundasinglefocallocus,buttherecouldbemanysuch focallociindifferentlocationsthroughoutthegenome,eachof whichcouldformagenomicisland(effectivelyincreasingthe mutationaltargetand clustered ).However,thisissueisunlikelyto beimportantbecauseboththeincreaseinestablishmentprob- abilityandthesizeofthegenomicislandthatcanbeformedby divergencehitchhikingareproportionaltothestrengthofse- lectiononthefocaldivergentlocus.Ifmanysuchfocallociexist throughoutthegenome,thenthemaximumstrengthofselection ateachfocallocuswilltypicallybelower,therebyreducingboth thepotentialsizeofthecluster[dueto s vs. r (19,53)]andthe divergencehitchhikingadvantageforanylinkedmutations. Thus,divergencehitchhikingisunlikelytobeabroadlyimpor- tantexplanationfortheexistenceofislandsofdivergencewith- outsomegenomicmechanismthatdramaticallyreducestherate ofrecombinationaroundtheinitiallydivergentlocus,suchas alargeinversion(24,32)ormodi erscreatingarecombination coldspot.Alternatively,ifgenomicrearrangementsbringto- getherthelocithatcontributetolocaladaptation(therebycre- atingagenomicisland),thiswouldeffectivelyincreasetheratio of clustered / unlinked ,andcouldfacilitatedivergencehitchhikingin subsequentboutsoflocaladaptation(iftheallelesformingthe genomicislandhappenedtobelostowingtogenetichomoge- nizationamongpopulations). RearrangementsLeadtoClusteringofLocallyAdaptiveLoci. Clusters oflocallyadaptivelocimightbeexpectedtoevolveundermi- gration selectionbalancethroughthespreadofgenomicrear- rangements,providedtherateofrearrangementsandtheir probabilityof xationarebothsuf cientlyhigh.Ifthelocithat contributetolocaladaptationareinitiallyrandomlydistributed throughoutthegenome,thenthetimerequiredtoevolveacon- gurationwheretheselociareorganizedinasingletightlylinked clustercanbeapproximatedbyaccountingfortherateofoc- currenceofsuitablerearrangementsandtheirprobabilityof xation[basedonamodelbyKirkpatrickandBarton(32)].If L isthenumberofbasepairsoverwhich r 0, G isthenumberof basepairsinthegenome, istherateofrearrangementper locus,pergeneration, N p isthetotalmetapopulationcensussize, and m isthemigrationrate,thenthetime(ingenerations)to evolveaclusteredarchitecturecanbeapproximatedas t G = N p mL [2] ( Methods givesthederivation).Thiscoarseapproximationwill rangeovermanyordersofmagnitude,dependingontheparam- eters,andprovidessomeintuitionabouttheirrelativeimpor- tance.Itisinsensitivetothenumberoflociinvolvedinlocal adaptation( n ),becausewhen n increases,thelongertimere- quiredtorearrangealargernumberoflociisoffsetbyincreases intherealizedrateofrearrangement,becausetherearemore locithatcanpotentiallyberearrangedintoacl
4 uster.However, thetimerequiredtoevolveap
uster.However, thetimerequiredtoevolveapartiallyclusteredarchitecture(by Eq. 4 )maybeseveralordersofmagnitudelessthanthetimeto evolveafullyclusteredarchitecture(byEq. 2 ; Fig.S1 ).These equationscanbeusedtoprovidecoarsepredictionsofwhether clusteringofgenomicarchitecturemightbeexpectedinagiven taxon.Forexample,if N p =10 5 , L =10 5 , G =10 9 ,and m = 0.001,thencompleteclusteringmightbeseenatbiologicallyre- alistictimescalesif � 10 5 (as t 10 7 ,byEq. 2 ),andpartial clusteringof n x =5outof n =50locimightoccurif � 10 7 (as t 2 × 10 7 ,byEq. 4 ).Thismodelillustrateshowslightvariations insomeparameterscanyieldlargeeffectsontherateofgenome evolution,butasameansofmakingquantitativepredictionsit shouldbeseenasacoarseapproximation,owingtotheassump- tionsinvolvedinitsderivation(detailsaregivenin Methods ). Toexploretheevolutionofgenomearchitecturemoreex- plicitly,withfewersimplifyingassumptionsabouttheevolu- tionarydynamics,Iusedindividual-basedsimulationsofatwo- patchmodelundermigration selectionbalancesimilartothat usedinref.28.Thesesimulationsareinitializedwith10phe- notype-affecting(hereafter,selected)lociequallyspacedalong asinglechromosome,eachseparatedby49neutralloci.Geno- micrearrangementsoccurbymovingasingleselectedlocusto anewlocationaccordingtoeitheracut-and-pasteoraduplica- tionmodel( Methods ),ataper-locusrateof .Becauserear- rangementscanresultinchangesinthenumberofcopiesofeach locus,smalladditional tnesscostswereincurredforindividuals thatdidnothaveexactlytwocopiesofeachofthe10original selectedloci(detailsaregivenin Methods ). Whenbothpopulationsinhabitthesametypeofenvironment, thereisnobene ttohavingatightlylinkedgenomicarchitecture, andthedistributionofselectedlocionthesimulatedchromosome evolvesveryslowly,mainlyunderthein uenceofrandomgenetic drift(Fig.2 A ).Bycontrast,whenpopulationsinhabitdifferent environmentsandexperienceatensionbetweenmigrationand divergentselection,thearchitectureevolvesrapidlythroughthe successive xationofsingle-locusrearrangements,eventually leadingtoclustersoftightlylinkedselectedlocithatare xed acrossbothpopulations(Fig.2 B ).Inthiscase,populationsrapidly evolvegenotypicdivergencethroughtheestablishmentoflocally adaptedallelesateachlocus(usuallywithinseveralthousand generations).Oncegenotypicdivergenceisestablished,rear- rangementsthatmoveoneselectedlocuswithalocallyadapted alleleclosetoanothertendtoinvadeandreplacelesstightly clusteredarchitectures,becauseoftheadvantageofreducedre- combinationbetweenmoretightlylinkedloci.InFig.2 B ,anearly fullyclusteredarchitectureevolvesinanamountoftimesimilar tothatpredictedbyEq. 5 (for m =0.01, n =10, L =2, G =490, =10 6 , N p =20,000,then t =8.4 × 10 5 ). Inmostcases,therateofevolutiontowardclusteredarchi- tecturesincreaseswiththestrengthofdivergentselection(Fig. 3 A )andmigrationrate(Fig.3 B ).However,whenmigrationrates arehighandjustbelowthecriticalthreshold(24,52),therateof Yeaman PNAS | PublishedonlineApril22,2013 | E1745 EVOLUTION PNASPLUS sites (45,46).Studiesofgeneregulationhavefoundevidence thatneighboringgenessometimeshavehighlycorrelatedex- pressionpro les(72 75),ortendtobefunctionallyrelated(76, 77).Evolutionaryexplanationsforthesepatternshavebeenvar- iedbutareoftenrelatedtothebalancebetweenratesofrear- rangement,geneticdrift,andpurifyingselection(50,72).Where explanationsinvokepositiveselection,the tnessbene tsare typicallybasedonchangesthatareendogenoustotheorganism andenvironment-independent,suchasfacilitatedregulationof functionallyrelatedgenes(78)orreducedexpressionnoise(79). Thegeneralperspectivethatarisesfromthesestudiesisthat thearchitectureofthegenomeevolveswithlittleconnectionto theecologyofthespecies,beyondtheimpactofdemographyon geneticdrift(50,72).Lynchandcoworkers(49,80)havepre- sentedcompellingevidenceshowingthatspecieswithsmaller effectivepopulationsizestendtohavelargergenomes,duethe reducedef ciencyofnaturalselectiontoeliminateinsertionsthat increasetheglobalmutationhazard.Beyondthislinktoecology throughdemography,inmostcases,thepatternsthathavebeen studiedincomparativegenomicsaretestablewithoutgoingout intonaturetostudytheecologyofthespecies.Bycontrast,the mechanismofgenomeevolutiondescribedinthisstudyisex- plicitlytiedtotheecologyofthespecies.Thismechanismcanbe seenasanextensionoftheinversion-basedmechanismsoflocal adaptationandspeciationthathavereceivedconsiderablestudy inrecentyears(30 32)andmodelsfortheevolutionofsuper- genes(81),whichbothhavemuchincommonwithprevious studiesontheevolutionofrecombination(82 86).Thismecha- nismisalsosimilarinmanywaystomodelsfortheevolutionof sexchromosomes;CharlesworthandCharlesworth(87)showed thatrearrangementsmovingautosomallocitosexchromosomes wouldbefavoredwhendifferentalleleswerefavoredineachsex. Bycontrast,inthemechanismdiscussedhere,rearrangementsare favoredbecausetheyreducerecombinationbetweenlociwith allelesthatareadaptedtodifferentenvironments.Although earliermodelsofchromosomeevolutionalsonotedthatpositive selectionduetolinkagecouldresultinthespreadofrearrange- ments,theytypicallyfocusedontheeffectofdriftandpopulation structureonthespreadoflargerearrangementswithdeleterious effectsintheheterokaryotype(e.g.,88,89). Becausetherearrangement-basedmechanismdiscussedhereis explicitlytiedtoecology,studyingitmayrequireadifferentap- proachthanistypicallyusedincomparativegenomics.Inmany cases,localadaptationinvolvesgenesfromnumerouspathways. Forexample,adaptationtofreshwaterinthreespinesticklebacks includesresponsestonovelwaterchemistry,temperatureregimes, visualenvironments,predatorcommunities,andforageavailability (89 93).Therefore,analysesofclusteringbasedongeneontology (e.g.,77)mayfailtodetectclustersoflociiftheyinvolvegeneswith suchdifferentproximatefunctions.Also,clustersthatevolvein responsetoadaptationwithgene owmightspanphysicaldis- tancesmuchlargerthanthosecommonlyanalyzedinthecoex- pressionclusterstudies,whichtypicallyexamineslidingwindowsof 2to15genes(e.g.,73 75).Forexample,agenomicislandspanning � 10cMhasbeenobservedinpeaaphidsadaptingtodifferent hosts(5),whichpresumablyincludestenstohundredsofgenes. OneintriguingcomparativegenomicstudyofamniotesbyLarkin etal.(93)foundthatrearrangementbreakpointstendedtocluster inregionscontaininggeneswithgeneontologytermsrelatingto in ammationandmuscularcontraction,whereasconservedre- gionswithfewbreakpointstendedtoincludegenesfordevel- opment.Theysuggestedthatbecausein ammationandmuscular contractiongenesaremoredirectlyinvolvedininteractionswith theenvironment,evolutionmayhavefavoredthespreadofrear- rangementsinresponsetonovelenvironmentalchallenges.Simi- larly,Freelingetal.(61)foundthatgeneswithproductsthat interactmoredirectlywithrapidlychangingbioticandabiotic environments(e.g.,diseaseresistanceor owering)hadhigher Average distance between selected loci (cM) 0 10 20 30 40 Time (generations x1000) 0 250 500 Time (generations x1000) 0250 500 0 10 20 30 40 Local optimum -2 -1 0 1 2 period ( T ) Time interval period ( T ) Local optimum -2 -1 0 1 2 Time AB CD Fig.4. Evolutionofclusteredarchitecturesunderspatialandtemporalheterogeneity( A ,as
5 shownin B andspatialheterogeneitypunctua
shownin B andspatialheterogeneitypunctuatedwithperiodsof homogeneity( C ,asshownin D ).InC,theintervallasts1,000generations,duringwhich m =0.5;theblacklineshowstheamountofclusteringforaconstant spatiallyheterogeneousenvironmentwithnoperiodsofhomogeneity.AllotherparametersaresetasinFig.3. E1748 | www.pnas.org/cgi/doi/10.1073/pnas.1219381110 Yeaman areunlinkedtoanarchitecturewhere n x oftheselociarearrangedin asingleclustercanbeapproximatedas t ¼ 4 N p m L = G n n 1 1 þ n x 1 i ¼ 2 4 N p m L = G n i 1 : [4] If n x = n ,thisreducesto t ¼ 4 N p mL = G 1 n 2 i ¼ 1 i 1 þ 1 = n n 1 ¼ G ð H n þ 1 = ð n ð n 1 ÞÞÞ 4 N p mL ; [5] where H n isthe( n 2) th harmonicnumber(if n =2, H n =0).Because1 H n 10formostbiologicallyrealisticvaluesof n ,thiscanbeapproximatedtoan orderofmagnitudeas t G /( N p mL ).Giventheassumptionsinvolvedin applyingthemodelfromKirkpatrickandBarton(32),parameterizingthis modelrequiresthat L representthenumberofbasepairssurroundingeach locusoverwhich r 0.Notethat N p representsthetotalsizeofthemeta- population,becauserearrangementswouldbefavoredwithinwhichever patchtheyoccurandwouldlikelyeventually xthroughthemetapopulation (again,thedynamicsinvolvedhereareoversimpli ed).Becausethismodel ignoresthecontributionsofrearrangementsthatyieldless-tightlylinked clusters(with0 r 0.5),itwilltendtooverestimatethetimerequiredto evolveaclusteredarchitecture.Amor ecomplexmodelbyBürgerandAkerman (24)suggeststhattheKirkpatrickandBarton(32)modelmayunderestimate theinvasionrate,furtherindicatingthatEqs. 4 and 5 shouldtendtoover- estimatethetimerequiredfortheevolutionofclusteredarchitectures. Individual-BasedSimulations. SimulationswererunusingtheversionofNemo (101)thatwasmodi edforref.28(sourcecodedepositedinSourceforge). Twopopulationsexchangingmigrantsatrate m experiencedivergentse- lection,wherethe tnessofanindividualwithagivenphenotype( Z )is afunctionofthelocaloptimum( = ± 1),strengthofselection( ),andthe curvatureofthe tnessfunction( =2): w ¼ 1 ðj Z j = j 2 jÞ (backward andforwardmigrationratesareequal,giventheconstantdensities). Unlessotherwiseindicated, N =10 4 , =0.75, m =0.01,andtheperlocus mutationrate =10 4 .Unlikeinref.28,mutationsfollowahouse-of-cards model(102),withthenewvalueofamutationreplacinganyexistingvalue. Thismutationmodelwasusedsothatnoallelesoflargeeffectcouldbuild upthroughmultiplemutationsatasinglelocus.Mutationeffectsizesare drawnfromaGaussiandistributionwithmean=0andSD=0.05andare truncatedsothatallmutationsizeswere | 0.05 | .Thephenotypeiscalcu- latedbyaddingthemutationeffectsacrossallselectedloci,sothatalocally optimalphenotypeinthepatchwith =1couldbebuiltwith10homozy- gousmutationsof0.05. Genomicarchitectureismodeledbyinterspersingeachof n =10locithat affectthephenotype(selectedloci)with49neutrallocialongasingle chromosome(foratotalof500loci)andsettingtherecombinationrate betweenadjacentlocito0.002,suchthatonaveragetherewouldbeone recombinationeventperindividualpergeneration.Genomicrearrange- mentsoccuratrate perlocus(setto10 6 unlessotherwisenoted), accordingtooneoftwomodelsofrearrangement.Forthecut-and-paste model,rearrangementsoccurredbymovingasingleselectedlocustoanew locationoccupiedbyaneutrallocus;theselectedlocusreplacestheneutral locusinitsnewlocationandisreplacedbyanewneutrallocusinitsoriginal location,tomaintainchromosomesize(thisprocesswasconstrainedsothat oneselectedlocusneverreplacedanotherselectedlocus).Fortheduplica- tionmodel,theprocesswasidenticaltothecut-and-pastemodel,exceptthe parent locusretaineditsstateasaselectedlocus.Selectedlocicouldbe lost(i.e.,converttoneutralloci)ataper-locusrateof ,whichrepresentsthe processofpseudogenizationorgenedeletion.Unlessotherwisenoted,all simulationswererunusingthecut-and-pastemodelwith =0. Torepresentthe tnesscostsarisingfromCNV,anadditional tnesscost ( s c )wascalculatedforeachindividualbasedonaGaussianfunctionwith s c ¼ n i ¼ 1 ð 1 exp ½ ð 2 c i Þ 2 = V c Þ ,summedacrosscontributionsfrom n loci, with c i representingthenumberofcopiesofthe i th locus.Whenthewidthof thisfunction, V c ,issmall,selectionagainstCNVisstrong(e.g.,for V c =50and c =3atonelocus, s c =0.0198);when V c islarge,selectionisweak(e.g.,for V c =5,000and c =3atonelocus, s c =0.0002);for V c = ,thereisnoselection againstCNV.Thisapproachissimilartoamorecomplexmodelproposedby Goutetal.(103),whichalsoassumesthat tnessdecreaseswithincreasing deviationsfromoptimallevelsofgeneexpression,whichinturnoccurdue tochangesingenecopynumber.Thecompletedeletionofagenewill sometimes,butnotalways,resultinlethality(104,105);forsimplicity,inall simulationsanyindividualwith c =0foranylocuswasgivena tnessof 0(irrespectiveof V c ).Unlessotherwisestated,thesimulationsinthispaper wererunusing V c =5,000. Unlessotherwiseindicated,simulationswererunfor500,000generations, withstatisticscalculatedevery500generations,basedonatleast20replicates foreachparametercombination.Theenvironmental uctuationsshownin Fig.4 A weremodeledusingasinewavewithamplitude=2andperiod T , andthese uctuationswereaddedontothelocaloptimaineachpopulation (i.e.,+1/ 1;asshowninFig.4 B ).Theenvironmental uctuationsshownin Fig.4 C weremodeledbychangingthelocaloptimafrom+1/ 1to0/0and themigrationratefrom0.01to0.5for1,000generations,every T gen- erations(asshowninFig.4 D ).ForallothersimulationsshowninFig.4, migrationratewasheldconstantat m =0.01. ACKNOWLEDGMENTS. IthankMikeWhitlockandSallyOttoforworking withmeontheprojectsthatprecededthismanuscriptandprovidinghelpful feedbackandsuggestionsthroughout.DiscussionswithL.Rieseberg, S.Aitken,J.Mee,D.Schluter,F.Guillaume,J.Mell,theAitken,Rieseberg, andWhitlocklaboratorygroup,andtheEvolutionofGenomicandGenetic Architecturejournalclubalsomadeveryimportantcontributionstothede- velopmentofthispaper;helpfulcommentsoftwoanonymousreviewersare alsoacknowledged.SpecialthankstoJ.Meefornotinganerrorinequation1 inref.28.ComputationswererunontheWestGridGlacierHighPerformance ComputingConsortium.ThisworkwassupportedbyGenomeCanadaand GenomeBCfundingtoAdapTree(co-ProjectleadersS.AitkenandA.Hamann). 1.AllenOrrH(2001)Thegeneticsofspeciesdifferences. TrendsEcolEvol 16(7):343 350. 2.BartonNH,KeightleyPD(2002)Understandingquantitativegeneticvariation. Nat RevGenet 3(1):11 21. 3.EhrenreichIM,PuruggananMD(2006)Themoleculargeneticbasisofplant adaptation. AmJBot 93(7):953 962. 4.TurnerTL,HahnMW,NuzhdinSV(2005)Genomicislandsofspeciationin Anopheles gambiae . PLoSBiol 3(9):e285. 5.ViaS,WestJ(2008)Thegeneticmosaicsuggestsanewroleforhitchhikingin ecologicalspeciation. MolEcol 17(19):4334 4345. 6.NosilP,FunkDJ,Ortiz-BarrientosD(2009)Divergentselectionandheterogeneous genomicdivergence. MolEcol 18(3):375 402. 7.NadeauNJ,etal.(2012)Genomicislandsofdivergenceinhybridizing Heliconius butter iesidenti edbylarge-scaletargetedsequencing. PhilosTransRSocLondB BiolSci 367(1587):343 353. 8.RenautS,etal.(2012)Genome-widepattern
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sofdivergenceduringspeciation:the lakewhite shcasestudy. PhilosTransRSocLondBBiolSci 367(1587):354 363. 9.SmadjaCM,etal.(2012)Large-scalecandidategenescanrevealstheroleof chemoreceptorgenesinhostplantspecializationandspeciationinthepeaaphid. Evolution 66(9):2723 2738. 10.FederJL,EganSP,NosilP(2012)Thegenomicsofspeciation-with-gene- ow. Trends Genet 28(7):342 350. 11.RogersS,BowlesW,MeeJA(2013)Theconsequencesofgenomicarchitectureon ecologicalspeciationinpostglacial shes. CurrentZoology 59(1):53 71. 12.StrasburgJL,etal.(2012)Whatcanpatternsofdifferentiationacrossplantgenomestellus aboutadaptationandspeciation? PhilosTransRSocLondBBiolSci 367(1587):364 373. 13.SmithJM,HaighJ(1974)Thehitch- hikingeffectofafavourablegene. Genet Res 23(1):23 35. 14.HermissonJ,PenningsPS(2005)Softsweeps:Molecularpopulationgeneticsof adaptationfromstandinggeneticvariation. Genetics 169(4):2335 2352. 15.PrzeworskiM,CoopG,WallJD(2005)Thesignatureofpositiveselectiononstanding geneticvariation. Evolution 59(11):2312 2323. 16.NoorMAF,BennettSM(2009)Islandsofspeciationormiragesinthedesert? Examiningtheroleofrestrictedrecombinationinmaintainingspecies. Heredity (Edinb) 103(6):439 444. 17.NachmanMW,PayseurBA(2012)Recombinationratevariationandspeciation: Theoreticalpredictionsandempiricalresultsfromrabbitsandmice. PhilosTransR SocLondBBiolSci 367(1587):409 421. 18.PetryD(1983)Theeffectonneutralgene owofselectionatalinkedlocus. Theor PopulBiol 23(3):300 313. 19.BartonN,BengtssonBO(1986)Thebarriertogeneticexchangebetweenhybridizing populations. Heredity 56:357 376. 20.FederJL,NosilP(2010)Theef cacyofdivergencehitchhikingingeneratinggenomic islandsduringecologicalspeciation. Evolution 64(6):1729 1747. 21.CharlesworthD,CharlesworthB(1979)Selectiononrecombinationinclines. Genetics 91(3):581 589. 22.PylkovKV,ZhivotovskyLA,FeldmanMW(1998)Migrationversusmutationinthe evolutionofrecombinationundermultilocusselection. GenetRes 71(3):247 256. 23.LenormandT,OttoSP(2000)Theevolutionofrecombinationinaheterogeneous environment. Genetics 156(1):423 438. 24.BürgerR,AkermanA(2011)Theeffectsoflinkageandgene owonlocal adaptation:Atwo-locuscontinent-islandmodel. TheorPopulBiol 80(4):272 288. 25.FederJL,GejjiR,YeamanS,NosilP(2012)Establishmentofnewmutationsunder divergenceandgenomehitchhiking. PhilosTransRSocLondBBiolSci 367(1587): 461 474. E1750 | www.pnas.org/cgi/doi/10.1073/pnas.1219381110 Yeaman exclusive.Veryfewstudieshavebeenabletoidentifywhetherloci withsignaturesofdivergenceareinfactcontributingtolocal adaptationorjustneutralalleles alongfortheride. Several empiricalstudieshaveidenti edmultiplesignaturesofdiver- gencethatmaptochromosomalinversions(34 37),butothers havefoundthatinversionswereonlyweaklyimplicatedin adaptivedivergence(e.g.,ref.38).Beyondunderstandingthe originsandmaintenanceoflocaladaptation,determiningthe importanceofthesevariousmechanismsalsohasimplications forunderstandingthenatureofgenomeevolution.Ifislandsof divergenceareactivelybuiltbythe xationofgenomicrearrange- ments(mechanism iv ),thenadaptation-with-gene owcouldbe animportantandunderappreciateddriverofevolutionof genomicarchitecture. This competitionamonggenomicarchitectures mechanism couldprovideapartialexplanationforthedramaticvariationin theratesatwhichrearrangementsaccumulateinthegenomesof differenttaxa.Ratesofcoarse-scalechromosomalrearrangement aremorethanthreeordersofmagnitudehigherin Drosophila thaninmammals(39).Althoughrelativelylowratesofchangein geneorderhavebeenfoundinLepidopteransbasedoncoarse- scalemappingdata(40), ne-scalegenomicanalyseshaveshown ratesofrearrangementashighasorhigherthanthosein Dro- sophila ,largelyduetonumeroussmall-scaletranspositionsand inversions(41,42).However,genomicanalysesofbirdsreveal ratesofgene-orderevolutionevenlowerthanthoseinmammals atboththemicro-andmacroscale(43,44).Ratesofrearrange- mentaccumulationalsovaryacrossthegenome;somehighly conservedregionshaveverylowratesofaccumulation,relativeto so-calledfragileregionsthatexperiencehigherratesofaccumu- lation(45,46).Explanationsforthisdramaticvariationinratesof genomeevolutionhavelargelyfocusedonnonadaptiveargu- mentsbasedonrearrangementrate,theactivityoftransposable elements,ordemographicdrift-basedmechanismsthatmodify theef cacyofpurifyingselectiontopurgemildlydeleterious rearrangements(39,47 50).Ifrearrangementstendtobein- volvedinlocaladaptation,thenecologicallymediatedpositive selectionmayplayaroleindrivingsomeofthesedifferencesin ratesandpatternsofgenomeevolution. Here,Ijointlyconsidertheevolutionoflocaladaptationand genomearchitectureinpopulationsinhabitingheterogeneous environments.Idevelopaheuristicbasedonpreviouslyestab- lishedanalyticalmethodstoexplorethelikelihoodofgenomic islandsofdivergenceevolvingunderthestandarddivergence hitchhikinghypothesis(mechanism i ).Usingthisheuristic,I showthatincreasesinestablishmentprobabilityduetodi- vergencehitchhikingshouldrarelybelargeenoughtoexpect strongstatisticalsignaturesofislandsofdivergence.Ithenusean analyticalapproximationandindividual-basedsimulationsto explorethepotentialimportanceofsmallgenomicrearrange- mentsasawaytocreateclustersoflocallyadaptiveloci,which maybefavoredowingtoreducedratesrecombinationbetween loci(mechanism iv ).I ndthatclusteringoflocallyadaptiveloci evolvesreadilyunderawiderangeofparameterspace,sug- gestingthatsmall-scalegenomicrearrangementsmayplayan importantroleintheevolutionofislandsofgenomicdivergence. Results LikelihoodofIslandFormationbyDivergenceHitchhiking. Ifgenomic islandsofdivergencecommonlyevolvebydivergencehitchhik- ing,thenwewouldexpectastatisticalenrichmentofthenumber oflocallyadaptedallelesthatoccurinclusters,relativetothe numberofunlinkedlocallyadaptedallelesscatteredthroughout thegenome.Asimpleexpressionforthisratiocanbeapproxi- matedby n clustered n unlinked ¼ EP clustered EP unlinked clustered unlinked ; [1] where n clustered and n unlinked representthenumberoflocallyadap- tedallelesthatestablishinaclusterextendingto50cMoneither sideofthefocallocus(i.e., r =0.5)vs.anywhereintherestofthe genome, EP clustered and EP unlinked representtheaverageestablish- mentprobabilitiesforclusteredandunlinkedmutations,and clustered and unlinked representthegenomicmutationratesaver- agedoverallclusteredandunlinkedloci.Theestablishment probabilities, EP clustered and EP unlinked ,canbeestimatedbyusing thecontinent-islandmodelofBürgerandAckerman(24)to calculatetherelative tnessoflinkedandunlinkedmutations, andsplicingthisintoKimura s(51)equationfor xationproba- bility,asshownbyYeamanandOtto(52).Thisapproach assumesthatagenomicislandbeginsasasingledifferentiated allele(ata focallocus )andexpandsasotherlinkedlocally adaptedmutationsestablish(detailsaregivenin Methods ). Althoughtheadvantageduetodivergencehitchhikingmaybe quitelargeformutationsthathappentobeverytightlylinkedto theinitiallydivergedfocallocus,mostgenomesareverylarge, andthechancethatamutationwouldoccurfortuitouslyintight linkageisquitesmall,relativetothechanceofamutationoc- curringelsewhereinthegenome.Ifweassumethatthelocithat couldpotentiallycontributetolocalad
7 aptationarerandomly distributedthroughou
aptationarerandomly distributedthroughoutthegenome,thenrelativelyfewofthese lociwouldbefoundintightlinkagetothefocallocus.Thetotal advantageduetodivergencehitchhikingcanbequanti edby averagingtheratio EP clustered / EP unlinked overallpossiblelinked sites(from r =0.5to r 0,aroundthefocallocus).Asshown inFig.1,forthismodeltheaveragedivergencehitchhikingad- vantageisrarelyhigherthanthreefold(andusuallymuchlower) overawiderangeofbiologicallyrealisticparameters.Theonly 0246 8 10 Migration rate Divergence hitchiking advantage 0.0010.010.10.5 = 0.001 = 0.01 = 0.1 Fig.1. Onaverage,mutationslinkedtoalocuswithanestablishedlocally adaptedallelehaveonlyaslightadvantageoverunlinkedmutationsin termsofincreasedestablishmentprobabilityduetodivergencehitchhiking, (divergencehitchhikingadvantage= EP clustered / EP unlinked ),exceptatvery highmigrationrates,justbelowthecriticalthresholdforthemaintenanceof localadaptation(grayshading).Curvesshowthedivergencehitchhiking advantageforthreestrengthsofselectiononthenewmutation( ),aver- agedovermutationsoccurringatarangeofdistancesfromtheinitialdi- vergentlocus,from0.001cMto50cM,usingEq. 3 .Inallcases,selectionon theestablishedalleleis =0.9;similarresultsarefoundforlowervaluesof , butpeakstendtobenarrower. E1744 | www.pnas.org/cgi/doi/10.1073/pnas.1219381110 Yeaman mutations(25).Here,Ipresentaheuristicmodelthatexplicitly quanti estheeffectofdivergencehitchhikingonestablishment probability(Fig.1)andshowthatitisunlikelytoyieldstrong signaturesofislandsofdivergenceundertheassumptionthat thelocithatcancontributetolocaladaptationarerandomly scatteredthroughoutthegenom e.Instead,foreachlocally adaptedallelethatestablishesinagenomicislandduetodi- vergencehitchhiking,therewilllikelybemanyallelesthates- tablishatrandomlocationsthroughoutthegenome.Thisoccurs becausethemutationaltargetthatresideswithinapotential genomicislandisverylimitedrelativetothemutationaltarget acrossthewholegenome,the tnessadvantageforbeingtightly linkedissmall,andunlinkedmutationsstillhaverelativelyhigh probabilitiesof xation. Althoughthe tnessadvantageofbeingtightlylinkedmay usuallybetoosmalltohavemucheffectontheevolutionofge- nomicislandsontheshorttimescaleofasingleboutoflocalad- aptation,thesimulationresultsIpresentshowthatcompetition amonggenomicarchitecturescanhavepronouncedeffectsover longerevolutionarytimescales.Highlyclusteredgenomicarchi- tecturesevolvereadilygivensuf cientlylargepopulations,rear- rangementrates,strengthsofselectionandratesofmigration(Fig. 3).Withinthiscontext,themutationaltargetitselfisrearranged, whichwouldincreasetheproportionofclusteredrelativetoun- linkedmutationsthatcouldestablishinanysubsequentbouts ofadaptation. Divergencehitchhikingcouldpotentiallyplayanimportant roleinforminggenomicislandsofdivergenceinconjunction withthisrearrangementmechanism,ifaspeciesexperiences temporalenvironmentalordemographic uctuationsthatresult inrepeatedepisodesofdivergentselectionandadaptivere- sponsefollowedbyhomogenization.Thecyclingofglacialand interglacialperiodsovermillionsofyearsprovidesanempirical exampleofonesuchsourceofenvironmental uctuation,which haslikelyaffectedadaptationinnumerousspecies(68).Here,I foundthatclusteredgenomicarchitecturesevolveunderarange ofscenarioswithenvironmental uctuations(Fig.4 A ),andthese clusteredarchitecturespersistthroughperiodsofhomogeniza- tionamongpopulations(Fig.4 C ),unliketheclusteredallelic architecturesdescribedbyYeamanandWhitlock(28).The amountofclusteringtendedtovarywiththeperiodoftemporal uctuations(Fig.4 A ),suggestingthatglacialcyclesmighthave quitedifferenteffectsonthegenomicsofadaptationinlong- livedspeciessuchasforesttreescomparedwithshort-lived speciessuchasannualplants.Giventhecyclicalnatureofcli- matic uctuationsandaccompanyingrangeshifts,itseemspos- siblethatforeveryspeciationeventinthehistoryofsomegenera therehavebeenmultipleepisodesofdivergenceandhomoge- nization.Althoughtheprocessofecologicalspeciationmaybe conceptualizedasacontinuumfromearlystagesofdivergenceto good specieswithcompletereproductiveisolation(10),move- mentalongthiscontinuumisnotunidirectional.Thevagariesof historymayresultinrepeatedtransitionsbackandforthalong thiscontinuum,increasingthewindowofopportunityforcom- petitionamongarchitecturesanddivergencehitchhikingtoplay aroleinadaptionand,eventually,speciation. Studiesofthegeneticsoflocaladaptationandecologicalspe- ciationthat ndevidenceofgenomicislandsshouldstrivetotest whetherthelociinvolvedhavebeenbroughttogetherbyrear- rangements.Thiscouldbeachievedbycomparinghoworthologs associatedwithlocaladaptationaredistributedalongchromo- somesinanumberofsisterspeciesspanningincreasingtaxonomic distances.Numerousstudieshavefoundevidencethatsegregating inversionsareofteninvolvedinadaptivegeneticdivergence(36, 69,70),butlessfocushasbeenplacedonothertypesofrear- rangements.Itisworthnotingthatfortheinversion-basedmech- anismofadaptationproposedbyKirkpatrickandBarton(32), inversionsmustbesegregatingtoreducerecombination,whereas rearrangementsdiscussedinthispaperreducerecombinationby changingthepositionoflocionchromosomes,andthereforetend to xacrosspopulations.Anotherimportantpredictionfromthis workisthatislandsofdivergencewithmultipleselectedalleles couldbeexpectedtoforminallopatry,providedthespecieshad aprevioushistoryofadaptationwithgene ow(duringwhichtime clustersoflocicouldhaveevolvedthroughrearrangements).In- deed,thiscouldprovidepartialexplanationforthesimilarityin sizeandnumberofgenomicislandsfoundinsympatricvs.allo- patricpairsofpopulationsof Helianthus (71). ImplicationsfortheEvolutionofGenomeArchitecture. Withcurrent advancesingenomesequencingtechnologies,considerablere- searchhasfocusedon ndingpatternsintheorganizationof genesonchromosomes.Comparativegenomicstudieshavefound thatthedistributionofrearrangementbreakpointstendstobe nonrandomthroughoutthegenome,withhighernumbersof rearrangementsat fragilesites andlowernumbersat solid 0 10 20 30 40 Average distance between selected loci (cM) 0 10 20 30 40 0 Time (generations x1000) 0250500 10 20 30 40 A B C Fig.3. Theaveragepairwisedistancebetweenselectedlocidecreasesover timeatdifferentrates,givendifferentstrengthsofphenotypicselection( A ), migrationrates( B ),andpopulationsizesandrearrangementrates( C ).Un- lessotherwisespeci ed, m =0.01, =0.75, N =10 4 , =10 6 ,andallother parametersareasdescribedin Methods . Yeaman PNAS | PublishedonlineApril22,2013 | E1747 EVOLUTION PNASPLUS likelihoodsoftranspositionin Arabidopsis .Althoughratherspec- ulative,theseinterpretationsofthedataareconsistentwiththe predictionsforthespreadofrearrangementsduetolocaladap- tationdiscussedhere,soitwouldbeinterestingtotestforsimilar patternsinothertaxa. Therateofrearrangementoccurrenceisoneofthemostim- portantfactorsdeterminingwhetherclusteredarchitectures evolve(Eq. 2 andFig.3 C ),butverylittleisknownaboutthe magnitudeof fordifferentrearrangementmechanisms,despite mountingevidencethatnumeroussmall-scalerearrangements haveaccumulatedwithinsomelineagesovertime(42,61).For example,in Arabidopsisthaliana ,itisestimatedthat21 27
8 %of allgeneshavebeenrearrangedsincetheco
%of allgeneshavebeenrearrangedsincethecommonancestorwith Papaya,almostallofwhichoccurredassingle-generearrange- ments(61,94).Whereasmanyofthesewerelikelycausedbyret- rotransposition(94),othermechanismsareimplicatedinatleast 55%oftherearrangementsthatoccurredsincethe A.thaliana Arabidopsislyrata split(59).Althoughhighlyspeculative,itis possiblethatthe3Dorganizationofchromosomesinthenucleus couldfacilitatetheevolutionofclustering.Spatialproximityof genesinthenucleushasbeenshowntoin uencebothgenereg- ulation(95)andratesofrearrangement(96),soifgenesthattend tobeinvolvedinlocaladaptationarealsobroughtintoclose proximityinthenucleustofacilitatecoregulation,theymightmore readilyberearrangedontothesamechromosome.Furtherre- searchwillhelpidentifyhowcommonlythevariousrearrangement mechanismsoccur,andhowthisvariesamongspecies. Itisimportanttonotethatwhereasspatialenvironmentalhet- erogeneitywilltendtofavortightclusteringofthelociinvolvedin localadaptation,someformsoftemporalheterogeneitymayfavor lessclustering.Whenapopulationevolvestowardanewoptimum bythe xationofnovelbene cialmutations,tightlinkagebetween selectedlociwilltendtoslowtheresponsetoselection,duetothe slowerrateatwhichbene cialmutationsondifferentchro- mosomesarebroughttogetherbyrecombination[i.e.,theHill Robertsoneffect(86,97,98)].Similarly,currentlybene cial combinationsofallelesmightbecomedetrimentalfollowingan environmentalchange,favoringincreasedrecombinationbetween thelociinvolvedinlocaladaptation(23,86,99,100).Theresultsin Fig.4 A showthattherelationshipbetweenperiodlength( T )and amountofclusteringisnonmonotonic,suggestingthatfurtherre- searchisneededtodeterminehowthesedifferentformsofselec- tionwillinteractandwhethersomeintermediaterecombination ratemaybeoptimalundercertaintypesofenvironmentalvariation. Moregenerally,anyadvantageofreducedrecombinationbetween locallyadaptedlocimaybecounteredbyarangeoffactorsthat favorincreasedratesofrecombination(86).Thisbringsusbackto Turner(85),whoasked, Whydoesthegenotypenotcongeal? and suggestedthatclustersoflocimightevolveduetolocus-speci c bene tsoftighterlinkage,despiteglobalbene tsofrecombination. Itseemslikelysomeintermediateamountofclusteringwouldyield ratesofrecombinationlowenoughtomaintainlinkagedisequi- libriumbetweencombinationsoflocallyadaptedalleles,buthigh enoughtofacilitatethepurgingofdeleteriousallelesandthe spreadofnewbene cialmutationsintimesofenvironmental change.Giventheimportanceofmigrationratesfordetermining theadvantageoflinkage(32),andmutationratesfordetermining thedeleteriouseffectsoflinkage(86),itseemslikelythattheop- timalamountofclusteringwillbedeterminedtosomeextentbythe ratioofmutationtomigration.Regardlessofwhicharrangementof adaptivelociisselectivelyoptimal,driftandlimitedrearrangement ratesmightpreventtherealizationofsuchcon gurations.Com- parativegenomicstudiesofecologicaladaptationwillprovide much-neededdatatoevaluatetherelativeimportanceofselective andstochasticprocessesinshapingthearchitectureofthegenome. Methods AnalyticalApproximationsofEstablishmentProbability. Theestablishment probabilitiesofnewlinked( EP clustered )andunlinked( EP unlinked )mutations canbeapproximatedusingthesplicingapproachdescribedbyYeamanand Otto(52)withthetwo-locuscontinent-islandmodelofBürgerandAkerman (24).Considerapopulationexperiencingnaturalselectionandimmigration, withtwoloci( A and B )thatrecombineatrate r .Ifthereisastablepoly- morphismsegregatingatlocus B ( B 1 and B 2 experienceselectionof+ and , respectively),andamaladaptedalleleatlocus A ( A 2 experiencesselection of ),thenanewlocallyadaptedallele, A 1 (experiencingselectionof+ ), willestablishwhentheratesofrecombinationandimmigrationofthe maladaptedgenotype( m ; A 2 B 2 )aresuf cientlylow(24).Basedonthe derivationsdescribedbyBürgeran dAkerman(24),therateatwhichthis allelewillinvadecanbeapproximatedbyevaluatingtheJacobianmatrixfor theirequation2atfrequenciesof A 1 B 1 =0, A 2 B 1 =0, A 1 B 2 =1 ( m / ),and A 2 B 2 = m / (equilibriafromequation3.9inref.24).AsshownbyYeaman andOtto(52),theleadingeigenvalueofthismatrixcanbeusedtoap- proximatethenetstrengthofselectionfavoringtheinvasionoftheallele A 1 ,andcanbesubstitutedfor s inpopulationgeneticapproximationsfor xationprobability.Becausethe xationprobabilityofanewmutationis 2 s inlargepopulations, A 1 willestablishwithprobability EP ¼ 2 r þ 2 þ 2 r 4 mr þ r 2 q : [3] Therefore,theadvantageduetodivergencehitchhikingforanewmutation linkedatsomerecombinationrate r = x canthenbequanti edastheratioof EP r = x / EP r =0.5 . ToparameterizethisequationforFig.1,theaveragevalueof EP clustered wascalculatedacross50,000loci,withrecombinationratesranginglinearly from0.001cMto50cMinincrementsof0.001cM(i.e.,numericalin- tegration).Thisapproachassumesthatgenedensityandrecombination ratesareuniformacrossthegenomeandisintendedasameansofap- proximating EP clustered / EP unlinked toparameterizeEq. 1 ,ratherthananat- tempttomakehighlyaccuratepredictions.Althoughtheaverageof EP clustered / EP unlinked wouldbehigherifcalculatedoverasmallerrangeof recombinationrates,thiswouldalsoimplyasmallermutationaltarget(and therefore clustered ),leadingultimatelytoalowervaluefor n clustered . EvolutionofClusteredGenomicArchitectures. Ifall n locithatcontributeto localadaptationbegininanunlinkedcon gurationdistributedrandomly throughoutthegenome,thetimerequiredtorearrange n x oftheselociinto asingletightlylinkedclustercanbeestimatedasfollows.Iftheper-locusrate ofrearrangementis andtheprobabilityofinsertionnearaspeci clocusis L / G (where L isthesizeoftheregionaroundthelocusand G isthesizeofthe genome),thenrearrangementsyieldinga rstpairofclusteredlociwilloccur atprobabilityof2 N p ( L / G ) n ( n 1)pergenerationinametapopulationofsize N p ,becausethereare n possiblelocithatcouldmoveintotightlinkagewith anyofthe( n 1)otherloci.Followingthis rststep,theprobabilityofrear- rangementsmovingoneoftheremaininglociintotightlinkagewiththis rstclusterwouldbe2 N p ( L / G )( n i ),forthe i th locusaddedtothecluster, where i rangesfrom2to( n x 1). Itissomewhatlessstraightforwardtoestimatetheprobabilitythatany suitablerearrangementswouldspreadthroughthepopulation,butthiscan beapproximatedbyconsideringonlythoserearrangementsthatresultin extremelytightlinkage,reducingtherateofrecombinationto 0.For amodeloflocaladaptationwithimmigration(atrate m ),Kirkpatrickand Barton(32)showedthatifanewchromosomalinversioncapturestwolo- callyadaptedloci,reducingtherateofrecombinationfrom r =0.5to r =0,it shouldspreadatarateof m .Importantly,thisrateisindependentofthe strengthofselectiononthelociwithintheinversion,soitshouldgeneralize toanyrearrangementsthatreducerecombinationtonearly0betweentwo previouslyunlinkedloci,regardlessoftheeffectofsizesoftheallelesin- volved(althoughathighmigrationrates,alleleswithsmall s wouldbelost). Thisapproachneglectsan
9 ydirect tnesscostscausedbytherearra
ydirect tnesscostscausedbytherearrangement itselfowingtodisruptedexpression,problemswithrecombination,orim- balancedgenenumber,so shouldbeinterpretedastherateofrear- rangementsthatdonotinvolvesigni cant tnesscosts.FollowingYeaman andOtto(52),theprobabilityof xationofsuchrearrangementsshouldbe 2 m ,andtheexpectedtimebeforetheoccurrenceofarearrangementthat xestoyieldthe rstpairofclusteredlociisthereciprocalofthesecom- binedprobabilities: t 1 ¼ð 2 m × 2 N p ð L = G Þ n ð n 1 ÞÞ 1 .Ignoringrearrange- mentsthatreduceclusteringonceithasevolved,becausethesewillbe disfavored,theexpectedtimetoevolvefromanarchitecturewhereall n loci Yeaman PNAS | PublishedonlineApril22,2013 | E1749 EVOLUTION PNASPLUS Genomicrearrangementsandtheevolutionofclusters oflocallyadaptiveloci SamYeaman a,b,1 a DepartmentofForestandConservationSciencesand b BiodiversityResearchCentre,UniversityofBritishColumbia,Vancouver,BC,CanadaV6T1Z4 EditedbyMichaelLynch,IndianaUniversity,Bloomington,IN,andapprovedApril1,2013(receivedforreviewNovember8,2012) Numerousstudiesofecologicalgeneticshavefoundthatalleles contributingtolocaladaptationsometimesclustertogether,form- ing genomicislandsofdivergence. Divergencehitchhikingtheory positsthattheseclustersevolvebythepreferentialestablishmentof tightlylinkedlocallyadaptedmutations,becausesuchlinkage reducestheratethatrecombinationbreaksuplocallyfavorable combinationsofalleles.Here,Iusecalculationsbasedonpreviously developedanalyticalmodelsofdivergencehitchhikingtoshowthat veryfewclusteredmutationsshouldbeexpectedinasingleboutof adaptation,relativetothenumberofunlinkedmutations,suggest- ingthatdivergencehitchhikingtheoryalonemayoftenbeinsuf - cienttoexplainempiricalobservations.Usingindividual-based simulationsthatallowforthetranspositionofasinglegeneticlocus fromonepositiononachromosometoanother,Ithenshowthat tightclusteringofthelociinvolvedinlocaladaptationtendsto evolveonbiologicallyrealistictimescales.Theseresultssuggestthat genomicrearrangementsmayoftenbeanimportantcomponentof localadaptationandtheevolutionofgenomicislandsofdivergence. Moregenerally,theseresultssuggestthatgenomicarchitectureand functionalneighborhoodsofgenesmaybeactivelyshapedbynat- uralselectioninheterogeneousenvironments.Becausesmall-scale changesingeneorderarerelativelycommoninsometaxa,compar- ativegenomicstudiescouldbecoupledwithstudiesofadaptation toexplorehowcommonlysuchrearrangementsareinvolvedin localadaptation. chromosomalrearrangement | geneticarchitecture | migration selectionbalance | synteny U nderstandingthegeneticbasisofadaptationisacentral problemofevolutionarybiology.Inlightofarapidlygrowing bodyofempiricaldata,therehasbeenconsiderableinterestin howmanygenescontributetolocaladaptation,thedistributionof theireffectsizes,andwheretheyarelocatedinthegenome(1 3). Numerousstudieshavefoundevidencethatthelocithataremost stronglydifferentiatedbetweenpopulationsaresometimesclus- teredtogether(i.e.,inclosephysicallinkage),inwhathavebeen termed genomicislandsofdivergence (4 11).However,other studieshavefoundlittleornoevidenceofdivergentallelesclus- teringinlargegenomicislands(6,10,12).Inlightofthesecon- ictingpatterns,furtherresearchisnecessarytoclarifywhenand howgenomicislandsshouldbeexpectedtoevolve. Genomicislandsmayevolveasabyproductofnaturalselection orasdirectresponsetonaturalselection(orsomecombinationof thetwo).Inthebyproductcase,selectionincreasesthefrequencyof afocalallele,causingallelesatlinkedneutrallocitoalsoincreasein frequency(13 17).Thisyieldsasignatureofdivergenceatadjacent locithatdecreaseswithincreasingratesofrecombination(i.e., distancefromtheselectedsite),andwillgraduallydisappearfol- lowingtheinitialselectivesweepinpopulationsthatdivergedin allopatry.Ifdivergentselectionoccursinthefaceofcontinuedgene ow,geneticdivergenceatlinkedneutrallociwilltendtopersist, owingtoareductionintheeffectiverateofmigration(18,19), whichisalimited neutral formofdivergencehitchhiking(20). Genomicislandscanalsoevolveasadirectadaptiveresponse todivergentselectionwithgene ow.Ifadaptationtoagiven environmentisbasedonchangesinallelefrequencyatmultiple loci,thenrecombinationbetweenthechromosomesofalocally adaptedparentandamaladaptedimmigrantwilltendtobreak upcombinationsofalleleswithhigh tnessthathavebeen establishedbyselection(21 24).Aslongasmigrationratesare lowenoughthatthedescendentsofalocallyadaptedallele spendalargeproportionoftheirtimeinthepatchwherethey are ttest,thenitisbene cialtobetightlylinkedtootheralleles thatarealsolocallyadapted. Thereareatleastfourdifferentmechanismsfortheevolutionof genomicislandsasadirectresponsetoselection,basedonthe generaladvantageofreducedrecombinationbetweenlocally adaptedalleles:( i )increasedestablishmentprobabilityoflinked locallyadaptedalleles[divergencehitchhiking(5,25,26)],( ii ) increasedpersistencetimeoflinkedlocallyadaptedallelesfol- lowingsecondarycontact(6,27),( iii )competitionamongcombi- nationsofalleleswithsimilarphenotypiceffectsbutdifferent linkagerelationships[competitionamonggeneticarchitectures (28)],and( iv )the xationofgenomicrearrangementsthatmove locallyadaptedlociintoclosegeneticlinkage[competitionamong genomicarchitectures(28)].Forallfourofthesemechanisms,the tnessbene tsduetolinkagetendtodecreasewithincreasing ratesofrecombinationbetweenlocallyadaptedalleles(21,24,25, 28,29).Asaresult,genomicislandsaremorelikelytoevolvein areasofthegenomewithlowratesofrecombination,suchas coldspotsorregionswithsegregatinginversions(17,30 33).It shouldbenoted,however,thattheseregionsarealsomorelikelyto havehighlevelsofdivergenceduetothebyproductmechanism discussedabove(17). Unfortunately,itisoftenverydif culttoevaluatewhichof thesemechanismsmaybeinvolvedinbuildinggenomicislandsof divergence,especiallybecausetheyarenotnecessarilymutually Signi cance Genomescansoften ndthatthelociinvolvedinlocaladap- tationtendtoclustertogetheronchromosomes.Aleading explanationsuggeststhatclustersevolvebecausetheproba- bilityofanewmutationestablishingishigherwhenoccurring nearanotherlocallyadaptedmutation,becausesucharchi- tecturesareseldomdisruptedbyrecombination.Ishowthat thistheoryisunlikelytoexplainempiricallyobservedclusters. Instead,simulationsshowthatclustersaremorelikelytoform throughgenomicrearrangementsthatbringcoadaptedloci closetogether.Thissuggeststhatecologicalselectionmayplay animportantroleinshapinggenomearchitecture,incontrast tomanynonadaptiveexplanations. Authorcontributions:S.Y.designedresearch,performedresearch,contributednewre- agents/analytictools,analyzeddata,andwrotethepaper. Theauthordeclaresnocon ictofinterest. ThisarticleisaPNASDirectSubmission. FreelyavailableonlinethroughthePNASopenaccessoption. Datadeposition:ThesourcecodeforthesimulationshasbeendepositedintheSource- forgeRepository, https://sourceforge.net/projects/nemorearrange/ . 1 E-mail:yeaman@zoology.ubc.ca. Thisarticlecontainssupportinginformationonlineat www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1219381110/-/DCSupplemental . www.pnas.org/cgi/doi/10.1073/pnas.1219381110PNAS | PublishedonlineApril22,2013 | E1743 E1751 EVOLUTION PNASPL