Different Evolutionary Paths to Complexity for Small and Large Populations of Digital Organisms

19 Pages·2016·1.44 MB·English

RESEARCHARTICLE
Different Evolutionary Paths to Complexity for
Small and Large Populations of Digital
Organisms
ThomasLaBar1,2,3*,ChristophAdami1,2,3,4
1DepartmentofMicrobiologyandMolecularGenetics,MichiganStateUniversity,EastLansing,Michigan,
UnitedStatesofAmerica,2Ecology,EvolutionaryBiology,andBehaviorProgram,EastLansing,Michigan,
UnitedStatesofAmerica,3BEACONCenterfortheStudyofEvolutioninAction,MichiganStateUniversity,
EastLansing,Michigan,UnitedStatesofAmerica,4DepartmentofPhysicsandAstronomy,MichiganState
University,EastLansing,Michigan,UnitedStatesofAmerica
a11111
*[email protected]
Abstract
Amajoraimofevolutionarybiologyistoexplaintherespectiverolesofadaptiveversusnon-
adaptivechangesintheevolutionofcomplexity.Whileselectioniscertainlyresponsiblefor
OPENACCESS
thespreadandmaintenanceofcomplexphenotypes,thisdoesnotautomaticallyimplythat
Citation:LaBarT,AdamiC(2016)Different
strongselectionenhancesthechancefortheemergenceofnoveltraits,thatis,theorigina-
EvolutionaryPathstoComplexityforSmalland
LargePopulationsofDigitalOrganisms.PLoS tionofcomplexity.Populationsizeisoneparameterthatalterstherelativeimportanceof
ComputBiol12(12):e1005066.doi:10.1371/ adaptiveandnon-adaptiveprocesses:aspopulationsizedecreases,selectionweakens
journal.pcbi.1005066
andgeneticdriftgrowsinimportance.Becauseofthisrelationship,manytheoriesinvokea
Editor:SergeiMaslov,UniversityofIllinoisat roleforpopulationsizeintheevolutionofcomplexity.Suchtheoriesaredifficulttotest
Urbana-Champaign,UNITEDSTATES
empiricallybecauseofthetimerequiredfortheevolutionofcomplexityinbiologicalpopula-
Received:April20,2016 tions.Here,weuseddigitalexperimentalevolutiontotestwhetherlargeorsmallasexual
Accepted:July18,2016 populationstendtoevolvegreatercomplexity.Wefindthatbothsmallandlarge—butnot
intermediate-sized—populationsarefavoredtoevolvelargergenomes,whichprovidesthe
Published:December6,2016
opportunityforsubsequentincreasesinphenotypiccomplexity.However,smallandlarge
Copyright:©2016LaBar,Adami.Thisisanopen
populationsfolloweddifferentevolutionarypathstowardsthesenoveltraits.Smallpopula-
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,which tionsevolvedlargergenomesbyfixingslightlydeleteriousinsertions,whilelargepopulations
permitsunrestricteduse,distribution,and fixedrarebeneficialinsertionsthatincreasedgenomesize.Theseresultsdemonstratethat
reproductioninanymedium,providedtheoriginal
geneticdriftcanleadtotheevolutionofcomplexityinsmallpopulationsandthatpurifying
authorandsourcearecredited.
selectionisnotpowerfulenoughtopreventtheevolutionofcomplexityinlargepopulations.
DataAvailabilityStatement:AllAvida
configurationfiles,dataanalysisscripts,andAvida
dataareavailableintheDryadrepository:http://dx.
doi.org/10.5061/dryad.3h5kv.
AuthorSummary
Funding:ThisworkwassupportedbyaMichigan
StateUniversityDistinguishedFellowshiptoTL, Sincetheearlydaysoftheoreticalpopulationgenetics.scientistshavedebatedtheroleof
andbytheNationalScienceFoundation’sBEACON
populationsizeinshapingevolutionarydynamics.Dolargepopulationspossessanevolu-
CenterfortheStudyofEvolutioninAction,under
tionaryadvantagetowardscomplexityduetothestrengthofnaturalselectioninthese
contractNo.DBI-0939454.Thefundershadnorole
populations?Ordosmallpopulationshavetheadvantage,asgeneticdriftallowssmall
instudydesign,datacollectionandanalysis,
decisiontopublish,orpreparationofthe populationstocrossfitnessvalleysthatlargepopulationsareunlikelytotraverse?There
manuscript.
PLOSComputationalBiology|DOI:10.1371/journal.pcbi.1005066 December6,2016 1/19
PathstoComplexityforSmallandLargePopulations
CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. aremanytheoriesthatpredictwhetherlargeorsmallpopulations–thosewithstrongselec-
tionorthosewithstrongdrift–shouldevolvethegreatestcomplexity.Here,weusedigital
experimentalevolutiontoexaminetheinterplaybetweenpopulationsizeandtheevolu-
tionofcomplexity.Wefoundthatgeneticdriftcouldleadtoincreasedgenomesizeand
phenotypiccomplexityinverysmallpopulations.However,largepopulationsalsoevolved
largegenomesandphenotypiccomplexity.Smallpopulationsevolvedlargergenomes
throughthefixationofslightlydeleteriousinsertions,whilelargepopulationsusedrare
beneficialinsertions.Ourresultssuggestthatbothstrongdriftandstrongselectioncan
allowpopulationstoevolvesimilarcomplexity,butthroughdifferentevolutionary
trajectories.
Introduction
Therelativeimportanceofadaptive(i.e.,selection)versusnon-adaptive(i.e.,drift)mecha-
nismsinshapingtheevolutionofcomplexityisstillamatterofcontentionamongevolutionary
biologists[1–6].Inmolecularevolution,theroleofnon-adaptiveevolutionaryprocessessuch
asgeneticdriftandgeneticdraftarewell-established[7–9].Theoreticalpopulation-genetic
principlesarguethatneutralevolution,notnaturalselection,drovetheevolutionoflarge,pri-
marilynon-functional,genomes[10–12].Meanwhile,thereexistsabundantexperimentalevi-
dencethatnaturalselectionisthemaincauseofevolutionarychange[13–15],includingthe
spreadofnoveladaptivephenotypes[16,17]inexperimentalpopulations.However,itisstill
possiblethatnon-adaptiveprocessesplayasignificantroleintheevolutionofcomplexity.For
instance,geneticdrift(orrelaxedselection)mayallowfortheaccumulationofmutationsthat
canlaterleadtotheevolutionofnovelcomplexity[4,18].Muchoftheworkdemonstrating
theroleofselectionindrivingtheevolutionofnovelcomplextraitsisbasedonexperiments
withlargepopulationsandstrongselection[19].Inmuchsmallerpopulations(i.e.,thosewith
fewerthan104individuals),selectionisweaker,andgeneticdriftbeginstoalterevolutionary
dynamics[15,20].Therefore,toexplaintheroleofadaptivevs.non-adaptiveprocessinthe
evolutionofcomplexity,onemustexploretheroleofpopulationsizeintheevolutionof
complexity.
Boththeoreticalmodelingandexperimentssuggestmanypossibilitiesfortherelationship
betweenpopulationsizeandtheevolutionofcomplexity.Therearetwoclassesofevolutionary
trajectoriesthatwouldfavorlargepopulationsintheevolutionofcomplexity.First,popula-
tionscouldperformanadaptivewalk(thefixationofasequenceofbeneficialmutations)
towardstheevolutionofanovelcomplextrait[21].Ifthiswasthecase,thenlargerpopulations
wouldfollowthistrajectoryfasterthansmallpopulationsduetotheirlargermutationsupply.
Experimentswithmicroorganismssupportthepossibleexistenceofadaptivetrajectories
towardscomplexity,asthereisstrongevidencethatthemutationsleadinguptoaphenotypic
innovationinbothEscherichiacoli[22]andphageλ[23]wereunderpositiveselection.How-
ever,itisunclearwhetheradaptivemutationsgenerallyprecedetheevolutionofcomplextraits
orwhethertheselargemicrobialpopulationscanonlytakeadaptivewalksduetotheintensity
ofselectioninlargepopulations.Thesecondtypeoftrajectorythatfavorslargepopulationsis
theneutralwalk(thefixationofasequenceofneutralmutations).Whileanyindividualneutral
mutationhasalowprobabilityoffixation,alargepopulationwouldbeabletoaccumulate
manyneutralmutationsatanygiventimeallowingfortheexplorationofitsfitnesslandscape.
WorkbyWagnerandcolleaguessuggeststhatmanyphenotypictraitsareconnectedtoeach
otherbysequencesofphenotypicallyneutralmutations[18,24].
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PathstoComplexityforSmallandLargePopulations
Iftheevolutionofcomplexityrequiresthefixationofdeleteriousmutations(forexample,via
valley-crossing),thentheeliminationofdeleteriousmutationsbypurifyingselectionmaylimit
theevolutionaryadvantagelargepopulationsmayhave.Wrightwasthefirsttoproposeanevo-
lutionaryadvantageofsmallpopulationsduetovalley-crossing[25].Morerecently,scientists
haveexploredunderwhichconditionssmallpopulationshaveanevolutionaryadvantageover
largepopulations[26,27].Aprominenttheorythatpredictsthatsmall(butnotlarge)popula-
tionsshouldevolvethegreatestgenomiccomplexity(andsubsequentlyorganismalcomplexity)
istheMutationalBurden(orMutationalHazard)hypothesis,proposedbyLynchandcol-
leagues[4,28,29].Thishypothesisarguesthatgenomesizeshouldbeinverselycorrelatedwith
theproductoftheeffectivepopulationsizeandthemutationrate[3,28].Strongpurifyingselec-
tionagainstexcessivegenomesizestreamlinesthegenomesinlargepopulations[30–32].
Meanwhile,weakenedpurifyingselectionandincreasedgeneticdriftinsmallpopulations
resultsintheaccumulationofslightlydeleteriousexcessgenomecontent[3,29].Atalatertime,
thisslightlydeleteriousgenomecontentmaybemutatedintonovelbeneficialtraits[4,33].
However,recentworkonvalley-crossinginasexualpopulations(andsexualpopulationswitha
lowrecombinationrate)showedthatbothsmallandlargepopulationscrossvalleysmorethan
intermediate-sizedpopulations[34–36].Therefore,itisnotclearwhetherlargeorsmallpopula-
tionsareexpectedtoevolvethegreatestcomplexitywhendeleteriousmutationsarerequired.
Thelongtimescalesrequiredtoobservetheemergenceofnoveltyandevolutionofcom-
plexitymakebiologicalexperimentstodistinguishbetweenthesetheoriesdifficulttoperform.
Toovercomethisdifficulty,weuseddigitalexperimentalevolution[37]totesttheroleofpop-
ulationsizeontheevolutionofgenomesizeandphenotypiccomplexityinasexualorganisms.
Digitalevolutionhasalonghistoryofaddressingmacroevolutionaryquestions(suchasthe
evolutionofnoveltraits)experimentally[38,39].Digitalpopulationscanbemanipulatedin
waysthatbiochemicalorganismscannot,makingitpossibletostudyaspectsoftheevolution-
aryprocessthatareordinarilytoodifficulttotest[40].Inthisregard,digitalexperimentalevo-
lutionhasthesamegoalsasmicrobialexperimentalevolution:touseawell-controlledmodel
systemthatisassimpleaspossible,tostudy“evolutioninaction”[41].Andwhiledigitalevolu-
tionstudiescannottesthypothesesthatdependonparticularbiochemicalprocessesinvolved
incellularlife,digitalpopulationsdoundergoselection,drift,andmutation,allowingfortheir
useintestinghypothesesderivedfromtheoreticalpopulationgenetics.Thus,digitalexperi-
mentalevolutionrepresentsawell-suitedmodelsystemtotestthepopulationgenetics-based
theoriesconcerningtheroleofpopulationsizeintheevolutionofcomplexity.
Here,weevolvedpopulationsranginginsizefrom10to104individuals,startingwitha
minimal-genomeancestor.Wefoundthatsmallpopulationsdoevolvegreatergenomesizes
andphenotypiccomplexity(numberofphenotypictraits)thanintermediate-sizedpopula-
tions.Thesesmallpopulationsevolvelargergenomesprimarilythroughincreasedfixationof
slightlydeleteriousinsertions.However,thesmallpopulationsizesthatenhancetheevolution
ofphenotypiccomplexityalsoenhancethelikelihoodofpopulationextinction.Wealsofound
thatthelargestpopulationsevolvedsimilarcomplexitytothesmallestpopulations.Largepop-
ulationsevolvedlongergenomesandgreaterphenotypiccomplexitythroughthefixationof
rarebeneficialinsertionsinstead.Largepopulationswereabletodiscovertheserarebeneficial
mutationsduetoanincreasedmutationsupply.Finally,wefoundthatastrongdeletionbias
canpreventtheevolutionofgreatercomplexityinsmall,butnotinlarge,populations.
Results
Toexploretheeffectofpopulationsizeontheevolutionofgenomesizeandphenotypiccom-
plexity,weusedtheAvidadigitalevolutionsystem[42].Avidaisaplatformthatallows
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PathstoComplexityforSmallandLargePopulations
researcherstoperformevolutionexperimentsinsideofacomputer,asthegeneticcodethat
evolvesareactualcomputerprogramsofvariablelength.Ithasbeenusedextensivelyin
researchinevolutionarybiology[37,43,44],andisdescribedindetailinMethods.
Weevolvedonehundredreplicatepopulationsacrossarangeofpopulationsizes(10−104
individuals)for2.5×105generations.Manyofthesmallestpopulations(thosewithtenindi-
viduals)didnotsurvivetheentireexperiment.Therefore,weevolvedonehundredadditional
smallpopulationsrangingfromtwentyindividualstoninetyindividualsinordertoexamine
howtheprobabilityofextinctionwasrelatedtotheevolutionofcomplexity.Allpopulations
withatleastthirtyindividualssurvivedfortheentireexperiment.Forty-sevenofthepopula-
tionswithtenindividualswentextinct,whileonlyoneofonehundredpopulationsunderwent
extinctioninthepopulationswithtwentyindividuals.Extinctionwasaconsequenceofpopu-
lationsevolvinglargegenomesthataccumulateddeleteriousmutationsandledtotheproduc-
tionofonlynon-viableoffspring.Theseextinctpopulationswerenotincludedinthestatistics
describedbelow.
GenomeSizeEvolution
Ofthesurvivingpopulations,wefirstexaminedhowgenomesizechangesfromtheancestral
valueoffifteeninstructions.Thesizeofthegenomefromeverypopulationsizeincreased,on
average(seeFig1andpanelAinS1Fig).However,boththesmallestandthelargestpopula-
tionsevolvedthelargestgenomes.Populationswithtenindividualsevolvedamediangenome
sizeof35instructions,whilepopulationswithtenthousandindividualsevolvedamedian
genomesizeof36instructions.Themedianfinalgenomesizedecreasedaspopulationsize
increasedforpopulationswithbetweentenandfiftyindividuals.However,frompopulations
Fig1.Finalgenomesizeasafunctionofpopulationsize.Redlinesarethemedianvaluesforeach
populationsize.Theupperandlowerlimitsofeachboxdenotethethirdandfirstquartile,respectively.
Whiskersare1.5timestherelevantquartilevalue.Plussignsdenotethosedatapointsbeyondthewhiskers.
Datarepresentonlythosepopulationsthatdidnotgoextinct.
doi:10.1371/journal.pcbi.1005066.g001
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PathstoComplexityforSmallandLargePopulations
Fig2.Proportionofslightly-deleteriousinsertionsasafunctionofpopulationsize.Redlinesarethe
medianvaluesforeachpopulationsize.Theupperandlowerlimitsofeachboxdenotethethirdandfirst
quartile,respectively.Whiskersare1.5timestherelevantquartilevalue.Plussignsdenotethosedatapoints
beyondthewhiskers.Datarepresentonlythosepopulationsthatdidnotgoextinct.
doi:10.1371/journal.pcbi.1005066.g002
withfiftyindividualstopopulationswithtenthousandindividuals,themedianfinalgenome
sizeincreasedaspopulationsizeincreased.
Next,weexaminedthedynamicsoffixationofinsertionmutations(insertions,forshort)to
explainwhyboththesmallestandthelargestpopulationsevolvedthelargestgenomes.For
eachexperimentalpopulation,wecountedeveryinsertionthatoccurredonthefittestgeno-
type’sancestrallineagethatwentbacktotheancestralgenotype(the“lineofdescent”,see
Methods).Themediannumberofinsertionsfixedfollowsthesametrendastheevolutionof
genomesize(S2Fig).Alargefractionofthesefixedinsertionsareslightlydeleteriousinpopu-
lationswithfewerthanonehundredindividuals(seeFig2andpanelBinS1Fig).However,no
insertionsareslightlydeleterious,onaverage,inlargepopulationswithmorethanonehun-
dredindividuals.Theoppositetrendholdsforbeneficialinsertions.Thefractionofinsertions
thatareunderpositiveselectionincreaseswithincreasingpopulationsize,withthelargestpop-
ulationsusuallyfixingonlybeneficialinsertions(Fig3andpanelCinS1Fig).Thesedatadem-
onstratethatsmallpopulationsevolvelargergenomesthroughthefixationofslightly
deleteriousinsertions.However,largepopulationscanevolvesimilarlylargegenomesthrough
thefixationofrarebeneficialinsertions.
EvolutionofPhenotypicComplexity
Next,wefocusontheroleofpopulationsizeintheevolutionofphenotypiccomplexity
(definedasthenumberofphenotypictraits).InAvida,aphenotypictraitisaprogram’sability
toperformacertainmathematicaloperationonbinarynumbers(seeMethods).Theevolution
ofphenotypiccomplexityfollowsthesametrendastheevolutionofgenomesize(seeFig4and
panelDinS1Fig).Populationswithtenindividualsevolvedamedianoffourtraits,while
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Fig3.Proportionofinsertionsunderpositiveselectionasafunctionofpopulationsize.Redlinesare
themedianvaluesforeachpopulationsize.Theupperandlowerlimitsofeachboxdenotethethirdandfirst
quartile,respectively.Whiskersare1.5timestherelevantquartilevalue.Plussignsdenotethosedatapoints
beyondthewhiskers.Datarepresentonlythosepopulationsthatdidnotgoextinct.
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Fig4.Finalnumberofevolvedphenotypictraitsasafunctionofpopulationsize.Redlinesarethe
medianvaluesforeachpopulationsize.Theupperandlowerlimitsofeachboxdenotethethirdandfirst
quartile,respectively.Whiskersare1.5timestherelevantquartilevalue.Plussignsdenotethosedatapoints
beyondthewhiskers.Datarepresentonlythosepopulationsthatdidnotgoextinct.
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PathstoComplexityforSmallandLargePopulations
Fig5.Correlationbetweenthefinalgenomesizeandthefinalnumberofevolvedtraits.Blackcircles
representthecombineddatafrompopulationswith10,100,1000,and10000individuals.Onlyreplicatesthat
survivedall2.5×105generationswereincluded.
doi:10.1371/journal.pcbi.1005066.g005
populationswithonethousandandtenthousandindividualsevolvedamedianofonetrait.
Therestofthepopulationsizesevolvedamedianofzerotraits.Asanavidian’sfitnessispri-
marilydeterminedbyitsphenotypictraitsintheAvidaenvironmentusedhere,theevolution
offitnessshowedasimilartrendtotheevolutionofphenotypiccomplexity(S3Fig).
Thatthetrendingenomesizeevolutionandinphenotypiccomplexityevolutionaremir-
roredsuggeststhattheevolutionoflargergenomesenablestheevolutionofincreasedpheno-
typiccomplexity.Toestablishalinkbetweenthetwo,weperformedtwotests.First,we
examinedthecorrelationbetweengenomesizeandphenotypiccomplexityacrossallpopula-
tions.Phenotypiccomplexityispositivelycorrelatedwithgenomesize(Fig5,Spearman’s
ρ(cid:25)0.72;p<2.3x10−57),suggestingthatitwastheincreasedgenomesizethatallowedforthe
evolutionofincreasedphenotypiccomplexity.However,therearetwopotentialmechanisms
thatcouldcauseanincreasedgenomesizetoresultinincreasedphenotypiccomplexity.On
theonehandanincreasedgenomesizecouldsimplyallowmore“room”fornovelfunctional
content.Ontheotherhand,itcouldbethattheincreasedgenomesizeleadstoafasterrateof
evolutionduetotheincreasedgenomicmutationrate.Toexaminetheroleofanincreased
mutationrateindrivingtheevolutionofphenotypiccomplexity,weevolvedafurtherone
hundredpopulationsoftenindividualswithafixedgenomicmutationrateof1.5×10−1(i.e.,
theancestralgenomicmutationrate).Underthiscondition,nopopulationwentextinct(as
opposedtoforty-seveninthevariablemutationratetreatment).Thefixedgenomicmutation
ratepopulationsevolvedamedianof2phenotypictraitscomparedtothevariablegenomic
mutationratepopulationsthathadevolvedamedianof4phenotypictraits(S4Fig).These
datademonstratethattheincreasedgenomicmutationratethatfollowsfromlargergenomes
doesincreasetheevolutionofphenotypiccomplexity.However,evenwithafixedgenomic
mutationrate,thesmallestpopulationsstillevolvedagreatermediannumberoftraits(on
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PathstoComplexityforSmallandLargePopulations
average2traits)thaneveryotherpopulationsize.Thus,whileanincreasedgenomicmutation
rate(duetoincreasedsequencelength)indeedenhancestheevolutionofphenotypiccomplex-
ity,smallpopulationsstillpossessanevolutionaryadvantageduetodrift-drivenincreasesin
genomesizeonly.
Non-functionalInsertions
Inthepreviousexperiments,largepopulationsevolvedlargergenomesandgreaterphenotypic
complexitybecausetheyfixedrarebeneficialinsertions.Next,wemorecloselyexaminethe
findingthatbeneficialinsertionsarenecessaryfortheevolutionofcomplexityinlargepopula-
tions.Werepeatedtheexperimentswiththesamepopulationsizesandmutationrates,except
wechangedhowinsertionsworked.Insteadofinsertingoneofthetwenty-sixinstructionsthat
composetheAvidainstructionset,weinserted“blank”instructionsintothegenome(see
Methodsfordetails).Theseblankinstructionscannotbebeneficial(ontheirownorincombi-
nationwithexistinginstructions)andwouldhavetobefurthermutatedtoleadtotheevolu-
tionofphenotypiccomplexity.Inthistreatment,greaterphenotypiccomplexityinlarge
populationswouldrequireatwo-stepmutationalprocess,asopposedtothesinglestepina
beneficialinsertion.
Wesawnoqualitativedifferenceinthetrendbetweentheseexperimentsandtheoriginal
experiments(S5Fig).Verysmallandlargepopulationsstillbothevolvedthelargestgenomes
andthegreatestphenotypiccomplexity.Populationsofallsizesevolvedlongergenomesand
morephenotypictraitsinthistreatment(S5Fig)thanintheoriginaltreatment(Figs1and4).
Thefractionoffixedinsertionsthatwereunderpositiveselectiondecreasedforeverypopula-
tionsizecomparedtotheoriginalexperiments,asexpectedfromtheinsertionofnon-func-
tionalinstructions(S6Fig).Weobservedanincreasedrateofextinctionintheverysmall
populations,withonly2populationswithtenindividualsand25populationswithtwentyindi-
vidualssurvivingtheexperiment.Populationextinctionwaslikelyenhancedbytheincreased
growthingenomesizeintheseexperimentsascomparedtotheoriginalexperiments.
DeletionBias
Finally,weperformedexperimentstotestwhethertheeffectofadeletionbias(ahigherfrac-
tionofdeletionsamongallindels)alterstherelationshipbetweenpopulationsizeandtheevo-
lutionofcomplexity.Abiasedratioofdeletiontoinsertionmutationsisfoundinbiological
organismsacrossthetreeoflife,especiallyinbacteria[45,46].Intheseexperimentswesetthe
ratioofdeletionstoinsertionsas9:1,butkeptthetotalindelmutationrateasintheoriginal
experiments.Inthistreatment,onlyonepopulationwithtenindividualswentextinct,as
opposedto47populationsintheoriginaltreatment.However,theadvantagetowardsevolving
complexitypreviouslyenjoyedbysmallpopulationsvanished(S7Fig).Themediangenome
sizeincreasedasthepopulationsizeincreasedforallpopulationssizes.Onlythelargestpopu-
lationsevolvedamediannumberofnovelphenotypictraitsgreaterthanzero.Theseresults
suggestthatitisnotonlytheroleofgeneticdrift,buttheequalfrequencyofinsertionsand
deletionsthatresultsintheincreasedgenomesizeandphenotypiccomplexityinsmall
populations.
Discussion
Theideathatsmallpopulationscouldhaveanevolutionaryadvantageoverlargepopulations
datesbacktoWrightandhisShiftingBalancetheory[25].Morerecently,apotentialsmall-
populationadvantagehasbeendemonstratedboththeoretically[27]andexperimentally[26],
butonlyinregardtoshort-termincreasesinfitness.TheMutationalBurdenhypothesis
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PathstoComplexityforSmallandLargePopulations
providesanevolutionarymechanismthatgivessmallpopulationsanadvantagetowards
increasedphenotypiccomplexity[4,33].However,anexperimentaldemonstrationofthis
advantageislacking.Ourstudyprovidesfurtherinsightintotheconditionsthatgivesmall
populationssuchanevolutionaryadvantage.Weconfirmedthatsmallpopulationsdoevolve
largergenomesduetotheincreasedfixationofslightlydeleteriousmutations,aspredicted
[28].Wealsoshowedhowsmallpopulationshaveanincreasedpotentialtolaterevolve
increasedphenotypiccomplexityinsmallpopulationsthroughthelargergenomesgenerated
byincreasedgeneticdrift[3,4].AsphenotypictraitsarestronglybeneficialintheAvidaenvi-
ronmentusedhere,thesesmallpopulationsusedslightlydeleteriousgenomeexpansionsto
crossfitnessvalleysandeventuallyreachnovelfitnesspeaks.
Ourworkalsoshowsthatthisevolutionaryadvantageofsmallpopulationsislimitedbyan
increasedrateofpopulationextinction.Suchatrendbetweentheevolutionoflargegenomes
andanincreasedrateofextinctionisseeninsomemulticellulareukaryoteclades[47,48].
Thesesmallpopulationsarestilllikelytohavealargerriskofextinctionbeyondthatcausedby
population-geneticriskssuchasMuller’sratchet[49]andmutationalmeltdowns[50,51].Eco-
logicalstressorsincreaseextinctionrisk[52]andsmallpopulationsarelessabletoadapttodet-
rimentalenvironmentalchanges[53].Ourresultsconcerningextinction,combinedwiththe
riskofotherfactorsnotexaminedhere,suggestthatthelikelihoodofasmallpopulationusing
geneticdrifttoevolvegreatercomplexitywithoutanincreasedriskofextinctionmaybelim-
ited.However,itispossiblethatmultiplesmallpopulationscouldreducetheriskofextinction
withoutreducingtheevolutionofcomplexity;futureworkshouldconsidertheinterplay
betweenpopulationsizeandtheevolutionofcomplexitywithinametapopulationofsmall
populations.
Largepopulationsalsoevolvedgreatergenomesizesandphenotypiccomplexity.Inour
originalexperiments,genomeevolutioninlargepopulationswasdrivenbythefixationofrare
beneficialinsertions(Fig4).Whileitislikelythatmanygeneduplicationsarenotunderposi-
tiveselectionandlostduetogeneticdriftandmutationaccumulation[54],some,especially
thoseresultingintheamplificationofgeneexpression,canbeimmediatelybeneficialandlater
leadtoincreasedphenotypiccomplexity[55–58].Duetotheincreasedmutationsupply,these
eventswouldoccuratagreaterfrequencyinlargepopulations[59]andpossiblyleadtoan
increasedprobabilityoftheevolutionofcomplexitythere.However,wealsofoundthatlarge
populationsdidnotrequirethislargesupplyofbeneficialinsertions.Evenwheninsertion
mutationsaddednon-functionalinstructionsandfurtherpointmutationswererequiredto
evolvefunctionaltraits,largepopulationsstillevolvedcomplexitysimilartothatevolvedin
smallpopulations.Theseresultssuggestthatpurifyingselectionmaynotlimittheevolutionof
complexityinlargepopulations.Finally,wefoundthatwhendeletionsoccuratamuchgreater
frequencythaninsertions,onlylargepopulationshaveanevolutionaryadvantagetowards
complexity.Asmanybacteriadohaveabiastowardsdeletions[60,61],thisresultsuggests
thatlargemicrobialpopulationscanhaveanevolutionaryadvantageoversmallmicrobialpop-
ulationsforevolvingnoveltraitsafterall.
Suchatrendwherebothlargeandsmall,butnotintermediate-sizedpopulationshavean
evolutionaryadvantagehasalreadybeentheoreticallyproposedelsewhere.Weissmanetal.
showedthatbothsmallandlargepopulationscrossfitnessvalleysmoreeasilythanintermedi-
ate-sizedpopulations[34].Smallpopulationsvalley-crossedduetogeneticdriftandlargepop-
ulationsdidsoduetoanincreasedsupplyofdoublemutants.OchsandDesaialsoshowedthat
intermediate-sizedpopulationsevolvedtoalowerfitnesspeakcomparedtosmallorlargepop-
ulationswhenvalley-crossingwasrequiredforreachingahigherpeak[36].Wefoundsimilar
results,butfromdifferentevolutionarymechanisms.Here,populationsneededtoincreasein
genomesizeinordertoevolvephenotypiccomplexity.Additionally,ourpopulationsevolved
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PathstoComplexityforSmallandLargePopulations
inacomplexfitnesslandscapewithmanydifferentpossiblepathstophenotypiccomplexity.
Whilesmallpopulationsdidfixdeleteriousinsertionstoincreasegenomesize,largepopula-
tionsevolvedonadifferentpath,eitherthroughbeneficialinsertions(Fig3)orneutralinser-
tions(S4Fig).Itispossiblethatevenlargerpopulationsthanthoseevolvedherewouldfix
moredeleteriousinsertions,asthelikelihoodofafurther,beneficialmutationarisingonthe
backgroundofasegregatingdeleteriousmutationincreasesaspopulationsizeincreases.How-
ever,ourresultsemphasizethatlargepopulationsmaynotbedependentonvalley-crossingin
somefitnesslandscapesifalternativeevolutionarytrajectoriesexist,evenifthesetrajectories
arerare.Whilethefirstmapsoffitnesslandscapessuggestedmutationalpathsaresmallin
number[62],morerecentworksuggeststhatmanyindirectevolutionarytrajectoriesexistin
largerfitnesslandscapes[63].
Thepopulationsizesthatledtotheevolutionofgreaterphenotypiccomplexityviadriftare
verysmall(10individuals).Asbiologicalpopulationsofthatsizeareunrealistic,wemaywon-
derwhethersuchpopulationscanactuallyevolvegreatercomplexityduetoincreasedgenetic
drift.However,therearereasonstobelievethattheseresultswouldgenerallyholdforbiologi-
calsystems.ThelimitedrangeofsmallpopulationsizesthatledtocomplexityisanAvida-spe-
cificresultduetotheseverefitnesseffectofinsertionmutationsinavidianswithsmall
sequencelength.Wefoundthatforthosesequences,mostinsertionsarelethal(about80%),
andtherestaresignificantlydetrimental,oftheorder10%to90%.Toovercomeadetrimental
effectof20%viadrift,populationsmustbeassmallasN=10.Insertionmutationsinbiological
genomesarenotnearlyasdetrimental,andthereforethecriticalpopulationsizetoseeevolu-
tionofcomplexityviadriftismuchlarger.InE.coli,forexample,thedeleteriouseffectof
insertionsisbetween1%and3%[64].Wecanthereforeexpecttoseetheeffectofincreased
complexityduetodriftinbiologicalpopulationsthataresmall,butnotunreasonablysmall.
Anotherpossibleavenueforfutureworksuggestedbythisstudyistouseasimplerpopula-
tiongeneticsmodeltoexplorethesamequestionsweattemptedtoanswerhere.Manyprevi-
oustheoreticalstudieshaveexaminedtherelevanceofvalley-crossingtotheevolutionof
complextraitsinsimplefitnesslandscapes[34–36].Onebenefitofasimplermodelisthatit
allowsforabroaderexplorationoftherelevantparametersinvolvedintheinterplaybetween
populationsize,genomesize,andtheevolutionofphenotypiccomplexity.Whilewewerenot
abletoperformlargeparametersearchesusingtheAvidasystem,ourworkhereestablishesa
possiblerelationshipbetweenthefactorsthatinfluencetheevolutionofcomplexityinafitness
landscapewithmanypossiblemutationaltrajectoriestonoveltraits[65].Theseresultsshould
drivefuturetheoreticalstudiesontheevolutionofgenomesizeandphenotypiccomplexity
usingpopulationgeneticsmodelswithsimplerfitnesslandscapes.
Herewestudiedtheevolutionofcomplexityinhaploidasexualdigitalorganismswithan
ancestralminimalgenomeonafrequency-independentfitnesslandscape.Whilebeyondthe
scopeofthiswork,itisworthconsideringhowadjustingthesegenotypecharacteristicswould
alterourresults.Itislikelythattheancestralminimalgenomesarearequirementforsmall
populationstoevolvethesamenumberofnoveltraitsaslargepopulations.Iftheancestor
organismhadasignificantamountofnon-functionalgenomecontent,themutationsupply
advantagethatlargepopulationshaveshouldresultinanacceleratedrateofphenotypicevolu-
tioninlargepopulations[66].Theorganismsusedhere,asinallAvidaexperiments,arehap-
loid.Itispossiblethatpolyploidywouldaltertheresultsfoundhere.However,the
implementationofaploidycycleinAvidaisnon-trivialduetothemechanisticstyleofreplica-
tion,andsopresentlyotherexperimentalsystemswouldhavetobeusedtoexploretheroleof
ploidyintheevolutionofphenotypiccomplexity.
Itisunclearhowsexual,insteadofasexual,reproductionwouldchangetheresults.While
sexualreproductioncanenhanceadaptationbycombiningbeneficialmutationsthatarisein
PLOSComputationalBiology|DOI:10.1371/journal.pcbi.1005066 December6,2016 10/19