Evolving inversions

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Evolving inversions

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Faria, R., Johannesson, K., Butlin, R.K. orcid.org/0000-0003-4736-0954 et al. (1 more

author) (2019) Evolving inversions. Trends in Ecology & Evolution, 34 (3). pp. 239-248.

ISSN 0169-5347

https://doi.org/10.1016/j.tree.2018.12.005

[email protected]

https://eprints.whiterose.ac.uk/

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Opinion

Evolving

Inversions

Rui

Faria,

Kerstin

Johannesson

,

* Roger

K.

Butlin,

and

Anja

M.

Westram

Empiricaldatasuggestthatinversionsinmanyspeciescontaingenes impor-tantforintraspecificdivergenceandspeciation,yetmechanismsofevolution remainunclear.Whilegenesinsideaninversionaretightlylinked,inversionsare notstaticbutevolveseparatelyfromtherestofthegenomebynewmutations, recombination within arrangements, and gene flux between arrangements. Inversionpolymorphismsaremaintainedbydifferentprocesses,forexample, divergentorbalancingselection,oramixofmultipleprocesses.Moreover,the relativerolesofselection,drift,mutation,andrecombinationwillchangeover the lifetime of an inversion and within its area of distribution. We believe inversions are central to the evolution of many species, but we need many moredataandnewmodelstounderstandthecomplexmechanismsinvolved.

TheParadoxofInversionsandFelsenstein_’sDilemma

Early studies of inversions were restricted to species with easily visualisedchromosomes (e.g.,flies).Today,inferringthepresenceofinversionsistechnicallypossibleinmanyspeciesas referencegenomes,geneticmaps,andextensivesequencingdatabecomeavailable.Classical work hassuggestedthat inversionsare important inlocal adaptationandspeciation[1,2], and later studies have emphasised that they offer a potential solution to Felsenstein’s

dilemma[3](seeGlossary).Suppressedrecombination among genesinsidethe inversion,

inheterokaryotypeindividuals,resultsinlargelyindependentgenomeevolutionofderived

andancestralarrangementsandopportunities fordivergence andspeciation[4–9].Yet,

inversionsarecommonlypolymorphicwithinpopulations[10].Thisisaparadoxthatcurrent modelscannotresolve,becausebalancingselection(whichmaintainspolymorphismwithin populations)typicallyopposesdivergence(neededforspeciation).However,theevolutionof inversionsismultifacetedandvariableoverspaceandtime.Usingalife-historyframeworkthat describes the possible fates of new inversions, we highlight the need for a deeper understandingof the evolutionof inversions bymaking connectionsamong existingideas andidentifyinggapsinourknowledge.

ALife-HistoryPerspectiveon Inversions

Manyauthorshaveconsideredtheconditionsfortheinitialspreadofanewinversion[4,8,11], whilethesubsequentevolutionoftheinversionhasbeenstudiedless,especiallythechanging alleliccontents of the ancestral andderived arrangements. Thelife history of an inversion embracesevolutionarychangefromitsappearancebymutationofasingle,flippedhaplotype, toitslossorfixation.Importantly,anewderivedarrangementhasnogeneticvariationatthe start, whilethe ancestral arrangementis variable (incommonwith collinear regions ofthe genome).Overtime,thederivedarrangementtendstobecomeincreasinglyvariable(unless selective sweeps are frequent), and recombination among haplotypes increases as

homokaryotypic individuals become more common. Thus, the dynamics of inversion

polymorphisms changeover time, and there are also manypossibleinteractions between thederivedandtheancestralarrangementwithimplicationsforthefateoftheinversionandits roleintheevolutionofthepopulation(Box1).

Highlights

Empiricaldatasuggestthatmany inver-sionsaremaintainedpolymorphicwithin populationsbybalancingselection,which impedesdivergenceandspeciation.

Contrary to earlier beliefs, we here argue that balancing and divergent selection may act together shaping the frequencies ofinversions, main-taining many of them polymorphic, andhaving importantconsequences foradaptationandspeciation.

Inversionsarenotstaticbutthederived andancestralarrangementsofan inver-sioncontinuetoevolve,partlyseparately fromeachotherandfromthecollinear genome,untillostorfixed.However,the evolutionofinversionsaftertheir estab-lishmentisoftenneglected.

Newmodellingapproachesanddata from additional taxa are needed to understandhowinversionsevolveover timeandspace,andwhatrolesthey play in adaptation, divergence, and speciation.

1_{DepartmentofAnimalandPlant}

Sciences,UniversityofSheffield, Sheffield,UK

2_{DepartmentofMarineSciences,}

Tjärnö,UniversityofGothenburg, Strömstad,Sweden

3_{ISTAustria,AmCampus1,3400}

Klosterneuburg,Austria

4_{Theseauthorscontributedequally}

*Correspondence: [email protected] (K.Johannesson).

Theratesoforiginofnewinversionsornewmutationsinsideinversionsarerarelyrecorded,but mostnew,derivedarrangementsarelostbygeneticdriftsoonaftertheyappear,astheinitial frequency is low (1/2N). Deleterious effects at breakpoints or fitness reduction in heterokaryotypesduetotheeliminationofrecombinantgametesincreasetheprobabilityof rapidloss[4].Incontrast,inversionswithpositivefitnesseffectsinheterokaryotypesoccurless frequentlybutaremorelikelytobecomeestablished,thatis,tobemaintainedlongenoughin thepopulationforotherevolutionaryprocessestoinfluencetheirfate.Rarely,anewinversion mightcaptureauniversallyfavouredhaplotype,forexample,onewithalowloadofdeleterious mutations[12]orfavouredbymeioticdrive[13],andspreadrapidlytofixation.

Aninversionpolymorphismcanestablishinoneoftwoways.Thederivedarrangementmight spreadtofixationbydriftorselectioninsomepopulationswhilebeingabsentorlostinothers, potentiallywithsomelocalpolymorphismmaintainedbygeneflow(werefertothisasTypeI inversionpolymorphism).Alternatively,abalancedpolymorphismcanbesupportedwithinoneor morepopulations,forexample,byoverdominanceorfrequencydependence(TypeIIinversion polymorphism) (Figure 1). Several different mechanisms influence these alternatives. Geneticdriftinsmallandisolatedpopulationscanfixanewarrangementlocally,evenwithsome

underdominance[1],leadingtoTypeIpolymorphisms.Selectionforlocaladaptation,eveninthe

presenceofgeneflow[6],canalsogenerateTypeIpolymorphisms.However,balancingselection isneededtomaintainTypeIIpolymorphisms.Thiscanarisefromepistaticinteractionsamong allelesatdifferentloci[14],fromassociativeoverdominance[15]or,onrareoccasions,when theinversioncapturesalocusthatis,itself,underbalancingselection(Box1).

Localadaptationwithgeneflowiscommon,andhasbeensuggestedasalikelydriverforthe establishment of new inversions [6]. If locally fit alleles at two or more loci on the same chromosomearecapturedbyaninversion,theirassociationisconservedforextensiveperiods of time and the haplotype within the inversion is favoured over recombining haplotypes. Importantly,therateofspreadoftheinversionisproportionaltothemigrationratebetween populations[6],andlargerinversionsthatcapturemorelocallyadaptedallelesaremorelikelyto spread.Furthermore,populationsthatcyclebetweenstagesofisolationandmigrationpromote thespreadofinversionsunderevenbroadersetsofconditions[16].

Critically,thetypesofallelesthatdrivetheseprocessescontinuetoarisebymutation,onboth theancestralandderivedarrangements,withpotentiallyprofoundconsequencesforthelife historyoftheinversion.

TheEvolutionaryProcessesFollowing Establishment

Therelativerolesofselection,drift,mutation,andrecombinationchange overthelifetimeofan inversion.Forexample,thederivedandancestralarrangementsdivergebynewmutations,but convergebyoccasionalgeneflux(seeFigureIinBox1).Asthecontentsofboththeancestraland derivedarrangementschangeovertime,theopportunitiesforselectionalsochange.Recombination isinfrequentinalow-frequencyarrangement,becausehomokaryotypesarerare,andthisalso shifts the balancebetween drift and selection towards drift[5]. Furtherinversion mutations in the same genomicregionmightreducegenefluxorextendthegenomicregionofsuppressedrecombination [17].Theresultcanbeacomplexandchangingpatternofdifferentiationbetweenarrangements,as seeninthePayneinversioninthevinegarflyDrosophilamelanogaster[18],analogoustothepatterns ofdifferentiationamongpopulationsgeneratedbyselection–migrationbalance.

TomaintainaTypeII(balanced)inversionpolymorphismrequireseitherheterosisornegative frequency-dependentselection(includingselectionintemporallyorspatiallyheterogeneous

Glossary

Associativeoverdominance:

overdominancecausedbyrecessive deleteriousallelesordominant advantageousalleleseachpresentin onlyoneinversionarrangementsuch thathomokaryotypesforthe inversionsufferreducedfitnessbut heterokaryotypesdonot.

Balancingselection:selection favouringthemaintenanceof polymorphism,fortwoormore allelesatalocusorarrangementsin thecaseofinversions.

Breakpointeffects:positiveor negativeeffectsofthedisruptionof thegenomecausedbythebreak andlaterrepairwhenaninversion arises.

Coadaptation:adaptationattwoor morelocitothesameenvironment. Coadaptationcaninvolve,butdoes notrequireepistaticinteraction betweenloci(seebelow).

Collineargenome:thepartofthe genomethatisoutsideregions polymorphicforinversions.

Derivedandancestral arrangements:respectively,the reversedandoriginalgeneorderfor thepartofthegenomethatcontains aninversion(seeFigure2FigureIin Box1).

Dobzhansky–Müller

incompatibilities:negativeepistatic interactionsbetweenalleleswhen broughttogetherinthesame individualfollowingtheirindependent evolutionaryorigin.Dobzhansky–

Müllerincompatibilityisthoughttobe amajorsourceofbarrierstogene flowbetweencloselyrelatedspecies.

Epistaticinteractions:positiveor negativeinteractionsbetweenalleles attwodifferentlociaffectingfitness.

Felsenstein’sdilemma:that recombinationfacilitatesadaptive evolutionbutbreaksupassociations amongcoadaptedgenesandinthis waycounteractsdivergenceand speciation.Felsenstein[4]considered thisamajorreasonwhyspeciationis notmorefrequent.

Geneflux:theexchangeofgenes betweentwoinversionarrangements inaheterokaryotypebydouble crossoverandgeneconversion. Genefluxislesslikelythanexchange betweenhaplotypesdueto recombinationinthecollinear genomeorininversion homokaryotypes.

Haplotype:asetofalleles,uptothe sizeofthewholehaploidgenome, thatisinheritedtogetheruntil disruptedbyrecombinationor mutation.Genomesequences belongingtothesamehaplotypeare geneticallyidentical.Amutation causinganinversionwillproducea derivedarrangement(thereversed geneorder)whichinitiallyonlyoccurs asasinglehaplotype(see

Figure2FigureIinBox1).

Heterokaryotype:anindividual carryingonecopyofeachofthetwo arrangements(theancestralandthe derived)ofaninversion.

Heterosis:classicallyhybridvigour; usedhereforselectionfavouring heterokaryotypesfortheinversion duetoassociativeoverdominance, overdominanceatindividuallocior epistaticinteractions.

Homokaryotype:anindividual carryingtwocopiesofthesame arrangementofaninversion.Note thattheseindividualsmightbe heterozygousatindividuallociwithin theinversion,thatis,theycarrytwo distincthaplotypesinthisregion.

Introgression:mixingofgenomes oftwoearlierseparatedlineages(e. g.,species,subspecies,or ecotypes).Introgressionisoftena resultofsecondarycontactbetween lineagesthathaveearlierbeen separatedinallopatry.

Overdominance:selectionfavouring heterozygoteindividualsover homozygoteindividuals.

Recessivedeleteriousmutations:

mutationscausingdeleteriouseffects inhomozygotesbutnot

heterozygotes.

Reinforcement:evolutionof increasedbarrierstogeneexchange duetoselectionagainsthybrids.

Supergene:asinglelocus, containinggenesinheritedtogether whichinfluencesmultiplephenotypic traits.

Underdominance:selection favouringhomozygoteindividuals overheterozygoteindividuals. environments),whiledivergent selectionmaintainsType Ipolymorphism.Ineithercase,the

alternativearrangementsreceivedifferenttypesofmutations(seeFigureIIinBox1).Atthe sametime,thefatesofthesemutationsdependonthestateoftheinversionpolymorphism.For example,in the absence of homokaryotypes, recessive deleterious mutations are not exposedto selectionandtendto accumulateontherarerarrangement(initiallythederived arrangement).Importantly, recentmodelling(Berdanetal.personalcommunication)shows thattheancestralarrangementalsoaccumulatesdeleteriousrecessiveallelesslowly,butata higherratethanthecollineargenome.Thisisbecausethereisalsoalowerrecombinationrate intheancestralarrangementcomparedtothecollineargenome.Theseprocessesmightresult in fitness loss in both homokaryotypes and increased heterokaryotype advantage due to associativeoverdominance(seeFigureIIinBox1).Thisaccumulationofdeleteriousrecessive alleles is more likely under Type II polymorphism than Type I polymorphism where each arrangementhasalargelocaleffectivepopulationsize(Figure1).

In contrast, inversions that differentiate populations are likely to accumulate further locally adaptedallelesandcanalso acquireallelesthatpromoteassortativemating.However,the advantageprovidedbysuppressed recombination is availableonly in populationsthat are influencedbygeneflow.Divergentselectioncanalsocreateandmaintainamong-population variationforunderdominantinversions[6],whicharelesslikely topersistwithinpopulations (althoughthisispossiblewithsomeformsoffrequencydependence[19]).

Dobzhansky–Müllerincompatibilitiesaremostlikelytobecomeassociatedwithinversions

that are fixed different between isolated populations, due to the independent spread of mutationsunderdriftorselection.Theseincompatibilitiesmightbeexpressedonsecondary contactandbeimportantinmaintainingreproductivebarriers[20].Theycanalsoaccumulate withininversionsinthepresenceofgeneflow[21].However,itisunlikelythatallelescausing incompatibilitiescould spread within inversions that are maintained as balanced polymor-phisms within populations (Type II inversion polymorphisms), unless the same alleles are advantageouswithintheirowngenomicbackground.

Generally,theconditionsforinversionpolymorphismsseembroaderthanthosefor single-locusbalancedpolymorphisms.Thisisforthesimplereasonthataninversioncontainsmany, potentiallyinteractinglociresultinginmanypossibleallelecombinationsthatcoulddrivethe balance.Forexample,anewinversionthatcapturesbothlocallyfavouredorepistaticalleles anddeleteriousrecessivealleleswillincreaseinfrequency butrarelyreachfixationas the homokaryotypeforthe inversionexpressesthedeleteriousallelesandisselectedagainst. However,acentralpointhereisthatthemechanismsmaintaininginversionpolymorphisms are not static. If an inversion polymorphism is initially established by, for example, one overdominantlocus insidethe inversionor byfrequency-dependent selection, overtime, increasing stability might evolve by the accumulation of different recessive deleterious mutationsinthederivedandancestralarrangementsbuildingupassociativeoverdominance. Alternatively, increasingdivergence betweenpopulations might occur as locallyadapted alleles and, later, Dobzhansky–Müller incompatibilities accumulate within the inversion. Frequency-dependentselectionorheterosis couldmaintain bothbalancedpolymorphism anddivergencebetweenpopulationsatthesametime.Equilibriumfrequenciesof arrange-mentsdifferbetweenpopulationseitherbecausethe samesetsof allelesconfer different fitness,orbecausethesamearrangementscarrydifferentallelesineachlocalpopulation,as observed in D. melanogaster [22,23]. Thus the end point need not be either among-populationdivergence(TypeI)orbalancedpolymorphism(TypeII);itcanbeacombination ofboth(Box2).

Box1.ConceptsandMechanisms

Whenachromosomalmutationformsaninversion,thederivedarrangementhasnovariation(FigureI)butaccumulatesnewgeneticvariationovertimebymutation, orbyraregeneflux(doublecrossoversandgeneconversion,[44])inheterozygotesfortheinversion(heterokaryotypes).Withinthepoolofderivedhaplotypes, recombinationispossibleinhomozygotesfortheinversion(homokaryotypes).Ifthederivedarrangementisfavourableandfinallyfixed,itbecomesthenewcollinear regionandisonlydistinguishablebycomparingthesequenceorderwithotherpopulationsorspecies(FigureI).

Collinear genome (genecally variable with

many haplotypes)

Derived arrangement (no genec variaon) Ancestral arrangement

(genecally variable with many haplotypes)

Inversion

Older derived arrangement (genecally variable with

many haplotypes) Ancestral arrangement

(if lower fitness compared to new arrangement)

In

v

e

rsio

n po

lym

o

rphism

New collinear genome (inversion fixed in the species)

Time

Gene flux

FigureI.SimplifiedLifeHistoryofanInversion.Amutationgeneratinganewinversionresultsinonederivedandoneancestralarrangement; theformerinitiallywithoutvariation.Overtime,pointmutationsandgene_fluxaddnewvariation,andselectionanddriftreducevariationin botharrangements.Eventually,oneofthearrangements(inthisillustrationtheancestralone)mightbelostandtheremainingarrangement (here thederived one)is thenew collinear genome inthisgenomic position.Notethat thesingle gene fluxevent shown goesinone directionandwhilegeneconversionisunidirectional,doublecrossovergoesinbothdirections.

Theinitialstagesinthelifehistoryofaninversionaregovernedbyitsdirecteffects(positiveornegativebreakpointeffects),itsalleliccontent,and/oritseffectson neighbouringgenes.Meioticproblems,includingthelossofunbalancedrecombinantgametes,mightcauseunderdominance[1](FigureIIA1,2).Underdominance usuallycauseslossofthederivedarrangement,unlessdriftorotherfitnesseffectsbringittohighfrequency.

Theinversionmightcapturedifferenttypesofallelesthatincreaseordecreasethefitnessofthederivedarrangementand,critically,mutationssubsequentlyintroduce newvariationatrandomintothederivedandancestralarrangements.Someofthesemutationstendtowardsfixingonearrangementlocally,thusgenerating divergenceamongpopulationsandprogresstowardsspeciation(FigureIIB).Otherstendtopromotepolymorphismwithinpopulationsbygeneratingbalancing selection(FigureIIC).

Multipleandlocallyadvantageousalleleswithintheinvertedregion,inthepresenceofgeneflow,canfavourestablishmentofthederivedarrangement[6],andfurther locallyadvantageousallelescanaccumulatesubsequently(FigureIIB3).Dobzhansky–Müllerincompatibilitiesmightaccumulatewithintheinvertedregion[21],and theinversionhelpstomaintainthemfollowingsecondarycontact[20](FigureIIB4).Highlinkagedisequilibriumwithintheinversionfavoursthespreadofalleles causingnonrandommatinginresponsetolowfitnessofheterokaryotypes(i.e.,reinforcement[27])(FigureIIB5).

Individuallociwithintheinversionmightshowoverdominanceorbeundernegativefrequency-dependentselection(includingfrequencydependencedueto environmentalheterogeneity;e.g.,[19]),generatingbalancingselectionwithinpopulations(FigureIIC6).Overdominancefortheinversioncanresultfromepistatic interactionsamongallelesatdifferentloci[14],andnewallelesthatcontributetothiscoadaptationaresubsequentlyfavoured[2](FigureIIC7).Finally,associations maintainedbysuppressedrecombinationbetweenrecessivedeleteriousallelesatdifferentloci,dominantadvantageousallelesatdifferentloci,orboth,canmakethe heterokaryotypemorefitthaneitherhomokaryotype(associativeoverdominance[15])(FigureIIC8,9).

(C) Alleles favouring balanced polymorphism

6. Individual overdominant loci, frequency dependent loci or both

7. Overdominance or frequency dependence due to epistasis

8. Associave overdominance due to recessive deleterious alleles

9. Associave overdominance due to dominant advantageous alleles

A b C D*

d C b A

A b C d

d c B a

A b c d

d C b a

A b C D

d C B A

(B) Alleles favouring divergence

3. Locally advantageous alleles favour inial spread, accumulate subsequently, or both

4. Dobzhansky–Müller incompabilies accumulate in allopatry (or perhaps with gene flow)

5. Reinforcement by spread of assortment alleles under linkage disequilibrium

A b C d

d c B A

A b C D

d C B A

A b C d

D c B A (A) Direct inversion effects

1. Breakpoint disruptsgene or modifies expression (’posion effect’)

2. Underdominance due to problems in meiosis or loss of unbalanced gametes

FigureII.EvolutionaryEffectsofInversionsandtheLociwithinThem.Thegeneticmechanismsofdirect(A)andindirect(B,C)effectsofaninversionare illustrated,includingthosegeneratingdivergence(B)andpolymorphism(C).Ancestralallelesareinblack,uppercaseindicatesdominance,derivedallelesaregreenif advantageous,redifdeleterious,andblueifneutralbutgeneratingassortment.Anallelethatcausesoverdominanceisindicatedbyanasterisk.Arrowsindicate epistaticinteractions.

Establishmentofaninversionpolymorphismisalsoafirststepfromwhichthereareseveral possiblescenariosforfurtherevolutionalongothertrajectories.Forexample,theearlystagesof evolutionofsexchromosomesandsupergenesofteninvolveinversions[24,25].Inallcases, theinitialmechanismspreadingasuppressorofrecombinationislatercombinedwithother processesthatcancometodominatesubsequentevolution.

InversionPolymorphisms andSpeciation

ForaTypeIinversionpolymorphismestablishedbydivergentselectionandmigration, recom-binationintheheterokaryotypeisstronglyreduced[6].Althoughlimitedtoapartofthegenome, thissituationissimilartoallopatrywhereaphysicalbarrierimpedesgeneflow.Underthese conditions,locallyfavourableallelesaretrappedinthedifferentarrangementsand,if incom-patible underepistatic interactions, heterokaryotypesare selectedagainstina way thatis similartohybridsbetweenpopulationsinaclassicalDobzhansky–Müllermechanism[21,26]. Thismight promotereinforcementbyevolutionofprematingmechanisms,andeventually

New inversion by mutaon (local, low frequency,

heterokaryotype)

Supported by:

-overdominance

-frequency dependence -epistasis/coadaptaon -associave overdominance

Type II polymorphism

Nm Type I polymorphism

Supported by:

- underdominance

-locally advantageous alleles -DM incompabilies -reinforcement

Nm

Divergence

Balanced polymorphism

Nm ≈ 0

Speci

aon

Inial fil

ter

Fina

l fil

ter

D

C

A

B

Nm

Fixaon of one

arrangement

E

Universally lost (dri, negave selecon)

Rapid universal fixaon

(dri, posive

selecon)

Figure1.LifetimeEvolutionofanInversion.Initialfilteringremovesamajorityofallnewinversions(A),whilesomefixthroughoutthespeciesrange(B).Thefewthat remainpolymorphicarepolymorphicamongpopulationsduetodivergentselectionandmigration(TypeIpolymorphism)orwithinpopulationsduetobalancing selection(TypeIIpolymorphism).InteractionsbetweenprocessesfavouringTypeIandIIpolymorphismseitherpromotecontinuedbalancedpolymorphism,or continueddivergence,orboth(C),andpotentiallyleadtospeciation(D)throughanarrayofdifferentmechanisms.Alternatively,oneofthearrangementswilleventually befixedthroughoutthespecies(E).Shadesofgreyinpopulations(circles)representdifferentfrequenciesoftheancestralandderivedarrangementsfromfixationofone (white)tofixationoftheother(black).Abbreviation:DM,Dobzhansky–Müller.

completion of speciation [27,28]. Thus, suppression of recombination by inversions can promotetheevolutionofspeciesbarriersinthepresenceofgeneflow[29].If thebarrieris completed,thetwoincipientspecieswillbefixedfordifferentchromosomalarrangements.

However,speciationisnotaninevitableoutcome.If,forexample,habitatchoiceor assorta-tivematingreducesgeneflowatan earlystageintheprocess(asaconsequenceoflocal adaptation),themechanismsthatpromoteestablishmentofaninversionareweakened.That is,withlittlegeneflowandthusalowrateofeffectiverecombination,theselectiveadvantage oftheinversionisstronglyreduced[6,9].Inasimilarway,thespatialpatternofpopulations acrossanenvironmentalclineisimportantasitaffectsmigration,andtheimpactisgreaterfor demesclosetothehabitattransitionthanforthosefurtheraway.Consequentlytheeffective recombinationrateamonglociunderlyinglocaladaptationisreducedandselectionfavouring aninversionlessstrong.Multidememodelsthat extendtheclassicaltwo-dememodelsto clines are needed to sort out the more specific conditions under which inversions are establishedandformstrongbarrierstogeneflow.

Polymorphicinversionsmightalsohinderspeciationifheterosisorotherprocessesprevent fixation.Indeed,empiricalexamplesshowthatthederivedandancestralarrangementscanbe farfromfixationinthehabitatwheretheyarepositivelyselected[30–35].Thisisnotwhatwe expectfromcurrentmodels.Overtime,accumulationofDobzhansky–Müllerincompatibilitiesis

Box2.WhatHappensWhenBalancingSelectionandLocalAdaptationBothIn_fluenceInversion Frequencies?

Weconstructedasimplesimulationmodeltoshowhowbalancingselectioninteractswithdivergentselectionwhenthey bothimpactonthesameinversion.Wesimulatedalinearchainof150demes,eachofwidth1,withahabitattransition afterdeme75andwithdispersalof1.5.Randommatingwasfollowedbyviabilityselection,dispersalandthendrift (demesize20).Theallelefrequencywasinitiallyequalforalldemesinoneenvironmentbutdifferentbetweenthetwo environments(randomlychosenfromtherange0–1foreachenvironmentindependently),treatingtheinversionasa singlelocus,andsimulationswererunfor1000generations.

Weconsideredthreeformsofselection:divergentonly,divergentwithheterosis,andfrequency-dependentwith differentequilibriainthetwohabitats.FitnessisindicatedinTableI.

Asexpected,wefindthatdivergentselectionalonegeneratesclinesthatapproachfixationinpopulationsdistantfrom thehabitattransition(FigureI).Whendivergentselectionisweak,clinesarewideandnoisy.Incontrast,balancing selectioncanresultindifferentequilibriumfrequenciesinthetwohabitats,withsteepclinesclosetothehabitat transition.

TableI.FitnessoftheThreeKaryotypesinEachofTwoHabitats(LeftandRight)forThreeDifferentModel Simulations

Lefthabitat Righthabitat

Divergentonly

Ancestralhomokaryotype 1–2sleft 1 Heterokaryotype 1–sleft 1–sright

Derivedhomokaryotype 1 1–2sright

Divergentplusheterosis

Ancestralhomokaryotype 1–2sleft 1 Heterokaryotype 1–sleft+h 1–sright+h

Derivedhomokaryotype 1 1–2sright

Frequencydependenta

Dominantphenotype aleft+bP aright+bP

Recessivephenotype 1 1

a_{PhenotypefrequencyP=p}

D2+2pDpA,wherepAistheancestralarrangementfrequencyandpDisthederived arrangementfrequency.

expected to decrease fitness of the heterokaryotypes [21], and new adaptive mutations increaselocalfitnessofhomokaryotypes[6].Alongwithreinforcementmechanisms[27],this wouldtendto pushthelocally beneficial arrangementstowardsfixationateach endofan environmental gradient. This paradox suggests that some counteracting force, such as heterosisorfrequency-dependentselection,is maintainingthesebalancedpolymorphisms, inlinewithourgeneralargumentthatmultipleprocessesarelikelytocontributeoverthelifetime ofinversions(Figure1).Combiningdivergentselectionwithamechanismofbalanced poly-morphism(heterosisorfrequencydependence)canexplaininversionsthatremainpolymorphic atclineendsundervariousconditions(Box2).Indeed,earlyempiricaldatapromotedheterosis asamodeltoexplaininversionpolymorphismsinD.melanogaster[2,36],andarecentreview suggeststhatitiswidespreadamongtaxa[10].Amodelwithheterosisisattractivebecause underthesameenvironmentalconditions,thestrengthofheterosisincreasesbythe continu-ous accumulation of new deleterious recessive alleles. A similar effect is achieved with accumulation of universally advantageous alleles in each arrangement, or alleles advantageousinthebackgroundofeacharrangementthatwill beexpressedjointlyonly in theheterokaryotype[5].

(A)

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FigureI.SimulationsofDifferentFormsofSelectionacrossanEnvironmentalTransition.(A)Theresultofdivergentselectiononly,withsleft=0.04, sright=0.07. (B) Weak divergent selection only,with sleft=0.004,sright=0.007. (C) Divergent selection andheterosis, with h=0.1,sleft=0.04,sright=0.07. (D)Frequency-dependentselectiontowardsdifferentequilibria,withaleft=1.3,aright=1.8,b= 1.Pinklinesare100replicateruns(redisthemean).

ParallelEvolutionofEcotypes

Importantly,abalancedinversionpolymorphismcontainingallelesdifferentiallyadaptedtolocal environmentsprovidesanoperational poolofstandinggeneticvariationallowingrapid and repeatedcolonisationandestablishmentofdifferentecotypesorsubspeciesina heteroge-neouslandscape.Rapidandrepeatedestablishmentoffreshwaterpopulationsofthree-spined stickleback(Gasterosteusaculeatus)frommarinefoundersinvolvinginversionsimportantfor freshwateradaptation[30,37] isafamous example,although it remainsuncertainhowthe inversionspersistinmarinepopulations.Similarprocessesofparallelecotypeformationare alsofound in,for example,themonkeyflowerMimulusguttatus[38],andthemarine snail

Littorinasaxatilis[34,39,40].Theseexamplesalsoillustratethefactthatinversionsmightbeold andconsiderablypredatemorerecentecotypedivergenceevents.Wespeculatethatanold inversioncanpromotelocaladaptationinseveraldifferentways.First,anancestralinversion polymorphismthatisolderthanthesplitinlocallyadaptedecotypesprovidesusefulgenetic variationthatseedsthesystemfromthestart[41].Second,anoldandwidespreadinversionis alsoaplatformthatallowsaccumulationoflocallyadaptedallelesspecificforageographic area. Finally, the inversion might bethe ‘ready-to-use kit’ that contributes to the genetic variationneededforlocaladaptationwithinspecies,inparticular,ifitisintroducedby

intro-gressionfromarelatedspecies[42,43].However,weemphasisethatoldinversionsarealso

variable,withinbotharrangements.Moreempiricaldatacoveringvariationamongarrangement haplotypesindifferentgeographicareas,andcomparativestudiesthattracetheancestryof inversions,areneededtodistinguishbetweenthesealternatives.

ConcludingRemarks

Whenanewinversionhasbecomeestablishedinanearlypolymorphicstate,itmightalreadyhave captured eithercoadaptedorepistaticallelesthatareuniversallyfavourableforonephenotypeofa polymorphicspecies,orallelesthatarelocallyfavourableinaspecifichabitat,oramixofthese possibilities.Whicheveristhestrongesteffectonfitnessofindividualsislikelytodrivetheroleofthe inversioninfurtherevolution.Iftheinversionevolvestowardsapolymorphismwithalternative rearrangementsfavouredindifferentenvironments,itwillapproachasecondcrossroads.Here, thenew pathis determinedbythe opposingforces ofDobzhansky–Müller incompatibilities selectingagainstheterokaryotypeindividualsandrecessivedeleteriousallelesfavouringthem. Aninversionthatstayspolymorphiceverywherecontributestostandingvariationandpotentially parallelecotypeformationbutnotspeciation.Incontrast,whereincompatibilitiesdominateover localadaptationorheterosis, polymorphismisonlypresentinanarrowhybridzoneandthe inversionmostlycontributestothefinalstagesofspeciation.Couplingbetweenearlyandlate inversionlifetimeevents,inversionandcollineargenomerelationships,andpotentialinteractions withotherinversionsareamongtheissuesthatneedtobeaddressed(seeOutstanding Ques-tions).Furthermore,therolesofgenefluxbetweenarrangementsandreinforcementofbarriers (includingadditionofnewinversions)needconsideration.Thus,manydifferentprocessesappear entangled,someinsynergy,othersinopposition,andthelong-termoutcomeiscurrentlydifficult topredict.Weconcludethatthereisplentyofroomfornewmodellinginitiativesandmanymore empiricaldatatosolvethemanyambiguitiesofinversionevolution.

Acknowledgements

WewouldliketothankHernanMoralesandMarinaRafajlovicforfruitfuldiscussionsonthistopic;EmmaBerdan,Claudia

Bank,andAlexandreBlanckaertforsharingunpublishedmodellingresults;andtworeviewersforhelpfulcommentsonan earlierversion.TheworkwasfundedbytheNaturalEnvironmentResearchCouncil,theEuropeanResearchCouncil,and theSwedishResearchCouncilsVRandFormas(throughaLinnaeusgranttotheCentreforMarineEvolutionaryBiology).

R.F.andA.M.W.werefundedbytheEuropeanUnion’sHorizon2020researchandinnovationprogrammeundertheMarie Sklodowska-CuriegrantagreementNo706376andNo754411,respectively.

OutstandingQuestions Howcan we distinguishamong the potential mechanisms maintaining inversionpolymorphisms,bothwithin andbetweenpopulations?

Howcanweidentifytheroleof indi-viduallociwithininversionsthat con-tribute to polymorphism (within or betweenpopulations)?

Whatistherelativeimportanceof over-dominance(e.g.,duetorecessive del-eteriousalleles)andunderdominance (e.g., due to Dobzhansky–Müller incompatibilities)underdifferent con-ditions,andhowdothetwointeract? Howdoesthisaffecttheprobabilityof speciation?

Are there evolutionary paths more probablethanothers duringthe life-timeofaninversion,andtowhatextent isthisaffectedbythealleliccontent whentheinversionfirstemerged?

Howimportant aregene conversion anddoublecrossoverindetermining evolutionofaninversion?

What interactions occur between inversions, and between inversions andcollinearpartsofthegenome?

Howimportantareinversionsin pro-motingparallelevolution,comparedto collinearregionsofthegenome?

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