ELUCIDATINGTHEEVOLUTIONARYORIGINSOFCOLLECTIVEANIMAL
BEHAVIOR
By
RandalS.Olson
ADISSERTATION
Submittedto
MichiganStateUniversity
inpartialentoftherequirements
forthedegreeof
ComputerScience-DoctorofPhilosophy
2015
ABSTRACT
ELUCIDATINGTHEEVOLUTIONARYORIGINSOFCOLLECTIVE
ANIMALBEHAVIOR
By
RandalS.Olson
Despiteoveracenturyofresearch,theevolutionaryoriginsofcollectiveanimalbehavior
remainunclear.Dozensofhypothesesexplainingtheevolutionofcollectivebehaviorhave
risenandfalleninthepastcentury,butuntilrecentlyithasbeenculttoperformcon-
trolledbehavioralevolutionexperimentstoisolatethesevarioushypothesesandtesttheir
individualInthisdissertation,Ioutlinearelativelynewmethodusingdigitalmod-
elsofevolutiontoperformcontrolledbehavioralevolutionexperiments.Inparticular,Iuse
thesemodelstodirectlyexploretheevolutionaryconsequenceoftheherd,predator
confusion,andthemanyeyeshypotheses,anddemonstratehowthemodelscanlendkey
insightsusefultobehavioralbiologists,computerscientists,androboticsresearchers.This
dissertationlaysthegroundworkfortheexperimentalstudyofthehypothesessurrounding
theevolutionofcollectiveanimalbehavior,andestablishesapathforfutureexperimentsto
exploreanddisentanglehowthevarioushypothesizedbofcollectivebehaviorinteract
overevolutionarytime.
TABLEOFCONTENTS
LISTOFTABLES
....................................
v
LISTOFFIGURES
...................................
vi
Chapter1Introduction
...............................
1
Chapter2BackgroundandRelatedWork
...................
4
2.1Hypothesesexplainingtheevolutionofcollectiveanimalbehavior......4
2.1.1herd................................5
2.1.2Predatorconfusion............................7
2.1.3Manyeyes.................................8
2.2Digitalmodelsofevolutionforcollectiveanimalbehavior...........9
2.3MarkovNetworks.................................10
2.3.1HowMarkovNetworksFunction.....................11
2.3.2GeneticEncodingofMarkovNetworks.................14
2.3.3VisualizationofMarkovNetworks....................16
2.4Particleswarmoptimizationandswarmrobotics................17
Chapter3HerdHypothesis
........................
19
3.1Modelofpredator-preyinteractions.......................19
3.2Predation................................23
3.2.1RandomAttacks.............................25
3.2.2RandomWalkAttacks..........................26
3.2.3OutsideAttacks..............................28
3.2.4Density-DependentPredation......................30
3.2.5High-DensityAreaAttacks........................31
3.3Predator-PreyCoevolution............................34
3.4EvolvedPreyMarkovNetworkAnalysis.....................37
3.5Discussion.....................................40
Chapter4PredatorConfusionHypothesis
...................
42
4.1Modelofpredator-preyinteractions.......................42
4.1.1Predatorandpreyagents.........................44
4.1.2Simulationenvironment.........................48
4.2ofpredatorconfusion...........................49
4.3Evolvedpredatorandpreybehavior.......................54
4.4Eco-evolutionarydynamics............................55
4.5Coevolutionbetweenpredatorvisualsystemsandpreybehavior.......57
4.6Discussion.....................................62
iii
Chapter5ManyEyesHypothesis
.........................
66
5.1Modelofpredator-preyinteractions.......................67
5.1.1Simulationofpredatorsandprey....................68
5.1.2Evolutionaryprocess...........................69
5.1.3Groupsize.................................70
5.1.4Geneticrelatedness............................70
5.1.5Reproductivestrategy..........................72
5.1.6Explicitcostofgrouping.........................73
5.2Forcedgrouping..................................73
5.3Optionalgrouping.................................77
5.4Tragedyofthecommonsinheterogeneousgroups...............78
5.5Explicitcostofgrouping.............................80
5.6Discussion.....................................81
Chapter6Conclusion
................................
85
References
.........................................
89
iv
LISTOFTABLES
Table2.1AnexampleMGthatcouldbeusedtocontrolapreyagentwhich
avoidsnearbypredatoragents.\PL"and\PR"correspondtothe
predatorsensorsjusttotheleftandrightoftheagent'sheading,
respectively,asshowninFigure3.2.ThecolumnslabeledP(
X
)in-
dicatetheprobabilityoftheMGdecidingonaction
X
giventhe
correspondinginputpair.MF=MoveForward;TR=TurnRight;
TL=TurnLeft;SS=StayStill.....................12
Table2.2TypicalmutationratesforexperimentsevolvingMarkovNetworks..15
Table3.1Possibleactionsencodedbytheagent'soutput.Eachoutputpair
encodesadiscreteactiontakenbytheagent.Theagent'sMNchanges
thevaluesstoredinoutputstatesLandRtoindicatetheactionit
hasdecidedtotakeinthenextsimulationtimestep..........22
Table3.2Geneticalgorithmandexperimentsettings...............23
Table3.3High-densityareaattack(HDAA)experimenttreatments.Thevalues
listedforeachtreatmentarethehandlingtimesforthecorresponding
predatorattackmode...........................31
v
LISTOFFIGURES
Figure2.1Example\domainsofdanger"(DODs)fromHamilton'sherd
hypothesis.Eachtrianglerepresentsapreyinthegroup,andthe
areaaroundeachtriangleisitsDOD.Preyontheinsideofthegroup
havesmallerDODs,whichmeares/theyarelesslikelytobetargeted
whenapredatorattacks.Asaconsequence,preythatmove
insidethegrouptominimizetheirDODwillhaveanevolutionary
advantage.................................6
Figure2.2AnexampleMarkovNetwork(MN)withfourinputstates(white
circleslabeled0-3),twohiddenstates(lightgreycircleslabeled4
and5),twooutputstates(darkgreycircleslabeled6and7),and
twoMarkovGates(MGs,whitesquareslabeled\Gate1"and\Gate
2").TheMNreceivesinputintotheinputstatesattimestep
t
,then
performsacomputationwithitsMGsuponactivation.Together,
theseMGsuseinformationabouttheenvironment,informationfrom
memory,andinformationabouttheMN'spreviousactiontodecide
wheretomovenext............................13
Figure2.3AzoomedinviewoftheMarkovGate(MG)labeled\Gate1"in
Figure2.2.Gate1hasthreebinaryinputsandtwobinaryoutputs,
andisthuscomposedofa2
3

2
2
probabilisticstatetransitiontable
whichencodesitslogic.Forexample,
p
52
intheprobabilisticstate
transitiontableistheprobabilityoftheinputset101(state0is1,
state2is0,state4is1)mappingtotheoutputset10(state6is1,
state4is0).Theprobabilitiesacrosseachrowmustsumto1.0...14
Figure2.4ExamplecircularbytestringsencodingthetwoMarkovGates(MGs)
inFigure2.2,denotedGene1andGene2.Thesequence(42,213)
representsthebeginningofanewMG(whiteblocks).Thenexttwo
bytesencodethenumberofinputandoutputstatesusedbytheMG
(lightgreyblocks),andthefollowingeightbytesencodewhichstates
areusedasinput(mediumgreyblocks)andoutput(darkergrey
blocks).Theremainingbytesinthestringencodetheprobabilities
oftheMG'slogictable(darkestgreyblocks)..............15
Figure2.5AcausalgraphofthenodeconnectionsfortheMarkovNetwork(MN)
inFigure2.2.Theonlystatesdisplayedarestatesthatprovideinput
toorreceiveoutputfromtheMarkovGatesoftheMN.Arrowsbe-
tweenthenodesindicatethewofbinaryinformationbetweenthe
states...................................17
vi
Figure3.1Adepictionofthesimulationenvironmentinwhichtheagentsin-
teract.Blackdotsarepreyagents,theblacktriangleisapredator
agent,andthelinesaroundthepredatoragentindicateitsof
view.Agentswraparoundtheedgesofthetoroidalsimulationenvi-
ronment..................................20
Figure3.2Anillustrationoftheagentsinthemodel.Lightgreytrianglesare
preyagentsandthedarkgreytrianglesarepredatoragents.The
agentshavea360

limited-distancevisualsystem(200virtualmeters)
toobservetheirsurroundingsanddetectthepresenceofotheragents.
Thecurrentheadingoftheagentisindicatedbyaboldarrow.Each
agenthasitsownMarkovNetwork,whichdecideswheretomove
nextbasedofacombinationofsensoryinputandmemory.The
leftandrightactuators(labeled\L"and\R")enabletheagentsto
moveforward,left,andrightindiscretesteps.............21
Figure3.3Anillustrationofthefourpredatorattackmodes.A)Ran-
domattacks,B)Randomwalkattacks,C)Outsideattacks,andD)
High-densityareaattacks........................25
Figure3.4Meanswarmdensityoverallreplicatesoverevolutionarytime,mea-
suredbythemeannumberofpreywithin30virtualmetersofeach
otheroveralifespanof1,000simulationtimesteps.Preyingroups
attackedrandomly(lightgreytriangles)tookmuchlongertoevolve
cohesiveswarmingbehaviorthanpreyingroupsattackedbyapreda-
torthatfollowsarandomwalk(darkgreycircles)oralwaysfromthe
outsideofthegroup(blacksquares).Whenpreyexperiencenoat-
tacks,theydonotevolveswarmingbehavioratall(lightgreystars).
Errorbarsindicatetwostandarderrorsover100replicates......27
Figure3.5Meanswarmdensityoverallreplicatesoverevolutionarytime,mea-
suredbythemeannumberofpreywithin30virtualmetersofeach
otheroveralifespanof1,000simulationtimesteps.Evenwhen
experiencingdensity-dependentpredation,preyingroupsattacked
randomly(lightgreytriangles)tookmuchlongertoevolveswarming
behaviorthanpreyingroupsattackedbyapersistentpreda-
tor(darkgreycircles)oralwaysfromtheoutsideofthegroup(black
squares).Errorbarsindicatetwostandarderrorsover100replicates.29
vii
Figure3.6Meanswarmdensityoverallreplicatesoverevolutionarytime,mea-
suredbythemeannumberofpreywithin30virtualmetersofeach
otheroveralifespanof1,000simulationtimesteps.Swarmdensity
wasmeasuredfromevolvedpopulationsthatwerenotexperiencing
predationduringmeasurement,eliminatinganypossibleofat-
tackmodesthatkillmorepreyfaster.Preyingroupsattackedonly
byoutsideattacks(lightgreytriangles)evolvedcohesiveswarming
behavior.Increasingtherelativefrequencyofhigh-densityareaat-
tacksfrominfrequent(darkgreycircles)tofrequent(blacksquares)
causedthepreytoevolveincreasinglydispersivebehavior.Errorbars
indicatetwostandarderrorsover100replicates............33
Figure3.7Meanswarmdensityoverallreplicatesoverevolutionarytime,mea-
suredbythemeannumberofpreywithin30virtualmetersofeach
otheroveralifespanof2,000simulationtimesteps.Preyingroups
experiencingdensity-dependentpredation(blackcircles)evolvedco-
hesiveswarmingbehavior,whereaspreyingroupsnotexperiencing
density-dependentpredation(lightgreytriangles)evolveddispersive
behavior.Errorbarsindicatetwostandarderrorsover100replicates.35
Figure3.8Numberofsensoryinputconnectionsfrom100evolvedpreyMarkov
Networksmappedontoapreyagent.Onlycausalconnectionsfrom
thesensoryinputstotheactuatorsareshown.Thearrowindicates
thefacingoftheagent.ThepreyMarkovNetworksevolvedastrong
preferenceforconnectingtopreysensorsinfrontandaslightprefer-
enceforsensorsbehindthepreyagent,buttendedtonotconnectto
thesensorsonthesides..........................38
Figure4.1Anillustrationofthepredatorandpreyagentsinthemodel.Light
greytrianglesarepreyagentsandthedarkgreytriangleisapreda-
toragent.Thepredatorandpreyagentshavea180

limited-distance
visualsystem(100virtualmetersforthepreyagents;200virtualme-
tersforthepredatoragent)toobservetheirsurroundingsanddetect
thepresenceofthepredatorandpreyagents.Eachagenthasits
ownMarkovNetwork,whichdecideswheretomovenextbased
ofacombinationofsensoryinputandmemory.Theleftandright
actuators(labeled\L"and\R")enabletheagentstomoveforward,
left,andrightindiscretesteps......................45
viii
Figure4.2Relationofpredatorattack(#successfulattacks/total#
attacks)tonumberofprey.Thesolidlinewithtrianglesindicates
simulatedpredatorattackasafunctionofthenumberof
preywithinthevisualofthepredator(
A
NV
).Similarly,the
dashedlinewitherrorbarsshowsthemeasuredsimulatedpredator
attackgiventhepredatorattacksagroupofswarmingprey
ofagivensize,usingthe
A
NV
curvetodeterminetheper-attack
predatorattacksuccessrate.Errorbarsindicatetwostandarderrors
over100replicateexperiments......................47
Figure4.3Screencapturesof(A)dispersedpreyinaswarmhuntedbyapreda-
torwithoutpredatorconfusion,(B)preyformingasingleelongated
swarmunderattackbyapredatorwithpredatorconfusion,and(C)
preyformingmultiplecohesiveswarmstodefendthemselvesfroma
predatorwithpredatorconfusionafter1,200generationsofevolution.
Blackdotsareprey,thetriangleisthepredator,thelinesprojecting
fromthepredatorrepresentthepredator'sfrontal180

visual
andthestardenoteswhereapreywasjustcaptured.........50
Figure4.4Meanswarmdensity(A),swarmdispersion(B),andsurvivorship
(C)withintheswarmoverallreplicatesoverevolutionarytime.The
swarmdensitywasmeasuredbythemeannumberofpreywithin30
virtualmetersofeachotheroveralifespanof2,000simulationtime
steps.Swarmdispersionwasmeasuredbythemeandistancetothe
nearestpreyforeverylivingpreyoveralifespanof2,000simula-
tiontimesteps.Survivorshipwithintheswarmwasmeasuredasthe
meannumberofsurvivingprey(outofaninitialtotalof50)atthe
endofthesimulationatagivengeneration.Preyhuntedbyapreda-
torwithpredatorconfusion(blackcircleswithafullline)evolved
tomaintaintlyhigherswarmdensityandtlyless
dispersedswarmingbehaviorthanpreyintheswarmshuntedbya
predatorwithoutpredatorconfusion(greytriangleswithadashed
line).Asaresult,tlymorepreysurvivedintheswarms
huntedbyapredatorwithpredatorconfusionthantheswarmshunted
byapredatorwithoutpredatorconfusion.Errorbarsindicatetwo
standarderrorsacross180replicateexperiments............53
Figure4.5Functionalresponsecurvesofcohesiveswarmshuntedbyapredator
withpredatorconfusion(blackcircleswithafullline)anddispersed
swarmshuntedbyapredatorwithoutpredatorconfusion(greytri-
angleswithadashedline).Theevolved,cohesiveswarmshunted
byapredatorwithpredatorconfusionresultinaTypeIIfunctional
responsewithaloweredplateau.Errorbarsindicatetwostandard
errorsacross180replicateexperiments.................56
ix
Figure4.6Meanswarmdensityatgeneration1,200asafunctionofpredator
viewangle.Swarmingtoconfusethepredatorwasanebe-
haviorifthepredator'svisualcoveredonlythefrontal60

or
less,duetothepredator'sfocusedvisualsystem.Asthepredator's
visualwasincrementallyincreasedtocoverthefrontal90

and
beyond,predatorconfusionviaswarmingagainbecameane
anti-predatorbehavior,asevidencedbytheswarmsexhibitingsignif-
icantlyhigherswarmdensityatgeneration1,200.Errorbarsindicate
twostandarderrorsacross180replicateexperiments.........58
Figure4.7SwarmdensityandpredatorviewanglefromtheLODofasingleco-
evolutionexperiment.Thepredatorandpreypopulationsappearto
continuallycyclebetweentstatesofviewanglesandbehaviors.59
Figure4.8Pearson's
r
betweenswarmdensityandpredatorviewanglefromthe
LODsof30coevolutionexperiments.Allcoevolutionexperiments
haveanegativecorrelationbetweenswarmdensityandpredatorview
angle,indicatingthatwhenswarmdensitygoesup,predatorview
anglegoesdownandviceversa.
P<
=0
:
001forallcorrelations...60
Figure4.9Numberofsimulationtimestepsthatpreyarepresentanywherein
anevolvedpredator'svisualsystemdependingonthepredator'sview
angle.Thepredatoriscompetedagainstdispersiveprey.Predators
withhigherviewanglesaremorelikelytohavepreyanywhereintheir
visualsystematagiventime.
P<
=0
:
001betweenallviewangles,
Kruskal-Wallismultiplecomparison...................61
Figure4.10Numberofsimulationtimestepsthatpreyarevisibleinaportionof
anevolvedpredator'svisualsystemthatitpaysattentionto,depend-
ingonthepredator'sviewangle.Thepredatoriscompetedagainst
dispersiveprey.Predatorswithhigherviewanglesaremorelikelyto
spotpreyatagiventime,whichincreasestheirforaging.
P<
=0
:
001betweenallviewanglesexcept180vs.210,Kruskal-
Wallismultiplecomparison........................61
Figure4.11Fitnessofanevolvedpredatorwhencompetedagainstdispersiveprey,
dependingonthepredator'sviewangle.Predatorswithhigherview
anglesforageforpreymoretly,thuscapturingmorepreyin
theirlifetimeandimprovingtheir
P<
=0
:
001betweenall
viewanglesexcept150vs.180and180vs.210,Kruskal-Wallis
multiplecomparison...........................62
Figure4.12Diagramdepictingtheobservedcoevolutionarycyclebetweenthe
predatorandpreyinthepresenceofthepredatorconfusion.64
x
Figure5.1
Depictionofthedisembodiedsimulation.
Preyseektoforage
asmuchaspossiblewhileavoidingbeingcapturedbythepredator.If
noneofthepreyinthegrouparevigilant,thetargetpreyiscaptured
100%ofthetime.............................67
Figure5.2
Treatmentcomparisonwhenpreyareforcedtoforagein
groups.
Bothgrouphomogeneityandasemelparousreproductive
strategyselectforhighlevelsofvigilance.However,onlyhomoge-
neousgroupsexperienceanincreaseinasgroupsizeincreases.
Incontrast,vigilancebehaviorbreaksdowninlarger,heterogeneous
groupsofsemelparousprey.Errorbarsindicatebootstrapped95%
intervalsover100replicates;someerrorbarsaretoosmall
tobevisible................................74
Figure5.3
Treatmentcomparisonwhenpreycanchoosetoforagein
groups.
Allowingpreytodecidewhethertheywishtobeinthegroup
producessimilarresultscomparedtowhentheyareforcedtogroup.
Inhomogeneousgroups,preychoosetospendmostoftheirtimein
thegroup.However,groupingbreaksdown(alongsidevigilance)in
heterogeneousgroupsofsemelparousprey.Thisoccursdespitethere
beingnodirectpenaltyassessedforchoosingtogroup.Errorbars
indicatebootstrapped95%intervalsover100replicates;
someerrorbarsaretoosmalltobevisible...............76
Figure5.4
Vigilanceinpreywithandwithouttheoptiontoforage
ingroups.
Inhomogeneousgroups,preywithforcedandoptional
groupingevolvesimilarvigilancebehaviors.Incontrast,individual-
istic(non-grouping)preyevolvevigilancebehaviorsthatmaximizein-
dividualMeanwhile,individualsinheterogeneous/semelparous
populationswiththeoptiontogroupevolvetobelessvigilantthan
eitheroftheothertwotreatments.Errorbarsindicatebootstrapped
95%intervalsover100replicates;someerrorbarsaretoo
smalltobevisible.............................79
Figure5.5
Fitnessforpreywithandwithouttheoptiontoforagein
groups.
Inheterogeneous/semelparousgroups,preywiththeop-
tiontogrouphavelowerthanpreythatareforcedtogroup.
Errorbarsindicatebootstrapped95%intervalsover100
replicates;someerrorbarsaretoosmalltobevisible.........79
xi
Figure5.6
Groupingbehaviorsinpreyexperiencinggroupingpenalties.
Evenwithasmallgroupingpenalty(
M
=1
:
0),alltreatmentsexcept
homogeneous/semelparousnolongerevolvegroupingbehavior.Prey
inthehomogeneous/semelparoustreatmentevolveonlyslightlylower
levelsofgroupingbehavior,evenwithextremepenaltiestoforaging
inagroup(
M
=1
;
000).Errorbarsindicatebootstrapped95%
intervalsover100replicates;someerrorbarsaretoosmall
tobevisible................................80
xii
Chapter1
Introduction
Overthepastcentury,researchershavedevotedconsiderableintostudyingcollective
animalbehaviorduetoitsimportantimplicationsforsocialintelligence,collectivecogni-
tion,andpotentialapplicationsinintelligence,swarmrobotics,anddistributed
systems[1].Indeed,collectivebehaviorsarepervasiveacrossallformsoflife.Forexample,
Europeanstarlings(
Sturnusvulgaris
)areknowntoformmurmurationsofmillionsofbirds
whileperformingawe-inspiringdisplaysofcoordinatedmovement[2,3].Westernhoneybees
(
Apismellifera
)communicatethelocationoffoodandnestsitestootherbeesintheirgroup
viaacomplexdancelanguage[4].Evenrelativelysimplebacteriaexhibitgroupingbehav-
ior,suchas
Escherichiacoli
formingwhichallowtheirgrouptosurviveinhostile
environments[5].
Despitetheabundanceofexamplesofcollectivebehaviorinnature,the
why
ofcollective
behaviorremainsdtoascertaintothisday[6].Whataretheadvantagesofworking
andlivingtogetherinagroup?Moreimportantly,whichoftheseadvantagesaretheunder-
lyingreasoncollectivebehaviorevolvedinthemultitudeofgroup-livingspeciesweobserve
today?Theobjectiveofthisdissertationistoidentifytheindividualhypothesesexplaining
howandwhycollectiveanimalbehaviorhasevolved,thendirectlyexplorethesehypotheses
inisolationtodeterminehow,when,and
if
eachofthehypothesizedbactuallyselects
fortheevolutionofcollectivebehavior.
Unfortunately,performinglong-termevolutionexperimentsisespeciallychallengingin
1
mostbiologicalsystemsbecausemanyspeciesthatexhibitcollectivebehaviortakemonths
orevenyearstoproduceTheselonggenerationtimesmakeitextremely
toexperimentallydeterminewhichoftheaforementionedbaresuttoselect
forcollectivebehaviorasanevolutionaryresponse,letalonestudythebehaviorsasthey
evolve[7,8].Tocomplicatemattersevenfurther,anystudiesattemptingtoisolateindividual
selectionpressuresinabiologicalsystemareoftenmuddledbythemultitudeofselection
pressurespresentinthesystem,makingitchallengingtoexperimentallyestablishadirect
relationshipbetweentheselectionpressureandtheevolvedbehavior.
Toovercomethesechallenges,inthisdissertationIusedigitalmodelsofevolutionto
exploretheevolutionaryofthevarioushypothesizedbofcollectivebehavior.In
thesemodels,Isimulateindividualpreyandtheinteractionsbetweenthemwithoutimposing
anyparticularmovementrulesonthem.Preythatsurvivelongerandforagemoretly
producemoreintothenextgeneration,allowingfortheevolutionofbehavior
inresponsetotheenvironment.Toobservetheoftheparticularhypothesisbeing
explored,Iintroduceanisolatedselectionpressuretothepreypopulation(e.g.,predation)
andmeasurethechangeinpreybehavioroverevolutionarytime.Digitalmodelsofevolution
thusprovideadecidedadvantageforexploringtheevolutionofanimalbehaviorinresponse
toisolatedselectionpressures,whichIwilldemonstratethroughoutthisdissertation.
ThesisStatement
Evolutionarycomputationandmulti-agentsystemscanbefruitfully
combinedtoelucidatetheevolutionaryoriginsofcollectiveanimalbehavior,whichproduces
testablehypothesesabouttheevolutionofcollectivebehavior.
Theremainderofthisdissertationproceedsasfollows.InSection2,Ioutlinetheseveral
hypothesesexplainingtheevolutionofcollectiveanimalbehavior,describethehistoryof
thedigitalmodelsofevolutionthatIusetoexplorethesehypotheses,anddiscussrelated
2
applicationsofcollectivebehaviorincomputerscienceandengineering.InSections3{5,
IprovidedetailsonseveralresearchprojectsIcompletedduringthecourseofmystudies
exploringtheherd,predatorconfusion,andmanyeyeshypotheses.Finally,Iprovide
concludingremarksaboutusingdigitalmodelsofevolutiontostudytheevolutionofcollective
animalbehaviorinSection6.
3
Chapter2
BackgroundandRelatedWork
Inthischapter,Ireviewtheliteraturesurroundingtheevolutionaryoriginsofcollective
animalbehavior.Ibeginthischapterbyoutliningthevarioushypothesesexplainingwhy
collectiveanimalbehaviorevolves.Next,Idescribethehistoryofthedigitalmodelsof
evolutionthatIusetoexploretheevolutionofcollectiveanimalbehavior.Finally,Idiscuss
relatedworkandpotentialapplicationsofthisthesisresearchintheofparticleswarm
optimizationandswarmrobotics.
2.1Hypothesesexplainingtheevolutionofcollective
animalbehavior
Aswithmanytraits,collectivebehaviorentailsavarietyofcosts,suchasincreased
predationrates[6],requisitesharingofresourceswithinthegroup[9],andheightenedcom-
petitionformates[10].Withthisfactinmind,thasbeendedicatedto
understandingthecompensatingbthatcollectivebehaviorprovides[6].Manysuch
bofcollectivebehaviorhavebeenproposed,forexample,itmayimprovematingsuc-
cess[11,12],increaseforaging[13,14,15,16,17],improvelocomotion[18],
orenablethegrouptosolveproblemsthatwouldbeimpossibletosolveindividually[1].
Furthermore,amajorcategoryofhypothesesproposethatcollectivebehaviorsprotect
4
groupmembersfrompredators.Forexample,collectivebehaviorcanimprovegroupvigi-
lance[19,20,21,22],reducethechanceofbeingencounteredbypredators[21,23],dilutean
individual'sriskofbeingattacked[24,25,26,27],enableanactivedefenseagainstpreda-
tors[28],orreducepredatorattackciencybyconfusingthepredator[7,29,30].
Withthemultitudeofpotentialcostsandbofcollectivebehavior,theneedforan
experimentalplatformtoexploreeachhypothesisinisolationbecomesabundantlyclear.In
thefollowingthreesections,Ireviewthreeofthehypothesizedbofcollective
behaviorthatIexploredindetailinthisdissertation.
2.1.1herd
,theherdhypothesisstatesthatpreyingroupsunderattackfromapredator
willseektoplaceotherpreyinbetweenthemselvesandthepredator,thusmaximizingtheir
chanceofsurvival.Asaconsequenceofthisbehavior,individualscontinuallymove
towardacentralpointinthegroup,whichgivesrisetotheappearanceofacohesiveswarm.
Hamilton'soriginalformulationoftheherdhypothesisintroducedtheconceptof
\domainsofdanger"(DODs,Figure2.1),whichservedasamethodtovisualizethelike-
lihoodofapreyinsideagrouptobeattackedbyapredator[27].Preyontheedgesof
thegroupwouldhavelargerDODsthanpreyontheinsideofthegroup;thus,preyonthe
edgesofthegroupwouldbeattackedmorefrequently.Moreover,Hamiltonproposedthat
preyontheedgesofthegroupwouldseektoreducetheirDODbymovinginsidethegroup,
thusplacingothergroupmembersbetweenthemselvesandthepredator.Furtherworkhas
expandedonthishypothesisbyaddingalimitedpredatorattackrange[31],investigating
theofpreyvigilance[32],consideringtheinitialspatialpositioningofpreywhenthe
groupisattacked[33],exploringtheroleofpreybodycharacteristicsinshapingherdchar-
5
Figure2.1Example\domainsofdanger"(DODs)fromHamilton'sherdhypothesis.
Eachtrianglerepresentsapreyinthegroup,andtheareaaroundeachtriangleisitsDOD.
PreyontheinsideofthegrouphavesmallerDODs,whichmeares/theyarelesslikelyto
betargetedwhenapredatorattacks.Asaconsequence,preythatmoveinsidethe
grouptominimizetheirDODwillhaveanevolutionaryadvantage.
acteristics[34,35],andevencorroboratingHamilton'spredictionsinbiologicalsystems[36].
Additionalstudieshavefocusedonthemovementrulesthatpreyinaherdfollow
tominimizetheirDOD[37].Thislineofworkbeganbydemonstratingthatthesimple
movementrulesproposedbyHamiltonreducepredationriskforpreyinsidethegroup[38],
thenopenedsomeparametersofthemovementrulestoevolutioninanattempttodiscover
amorebiologicallyplausiblesetofmovementrules[39,40].Importantly,thesestudies
demonstratedthatitispossibleforherdbehaviortoevolvebynaturalselection
onmovementrulesthatrelyononlylocalinformationforeachagent,ratherthanglobal
informationabouttheentiregroup.
However,itstillremainsanopenquestionofhowtheactionsofthepredator|forexam-
ple,whetherthepredatorcancoevolveandadapttotheherdbehavior|canimpact
6
theherdhypothesis.Thisdissertationbuildsonthispreviousworkbystudyingthe
ofcoevolvingpredatorsandpredatorattackmode(i.e.,howpredatorsselectaprey
inagrouptoattack)ontheevolutionoftheherd.
2.1.2Predatorconfusion
Inthepredatorconfusionhypothesis,thepresenceofmultipleindividualsmovinginaswarm
confusesapproachingpredators,makingitforpredatorstosuccessfullyexecutean
attack[29,7,30,41].Thisconfusionishypothesizedtoarisefromtheincreasedcog-
nitiveprocessingtimeneededtodecideonatargetamongmultipleprey.Inarecentreview
ofpredator-preysystemswithswarmingprey,JeschkeandTollriannotedthatpredators
appearedtobecomeconfusedbyswarmingbehaviorin16ofthe25systemsreviewed[7].
However,evidencethatpredatorconfusionisaseeminglywidespreadphenomenonstillleaves
openthequestionofhowivepredatorconfusioncouldbeasaselectiveforcefavoring
theevolutionofswarmingbehavior.Owingtotheyofdisentanglingtheindividual
ofhypothesessuchasthepredatorconfusionhypothesisinnaturalsystems,thereis
aneedtoexplorethepredatorconfusionhypothesisinisolationinadigitalmodel.
Predatorconfusionisbroadlyinterestingfortwoadditionalreasons.First,itprovides
anopportunitytostudyhowswarmingbehaviorcaninturnexertevolutionarypressureson
predators,especiallyontheperceptualconstraintsthatallowforpredatorconfusioninthe
place.Forexample,onceswarmingbehaviorevolvesinprey,predatorconfusionmay
inturnprovideaselectiveadvantageforpredatorsthatarenolongerconfusedbyswarms.
Second,predatorconfusionmaythe
functionalresponse
describingthepredator's
consumptionrateaspreydensityincreases[42],assuggestedinapreviousstudy[43].Un-
derstandinghowpervasivemechanismssuchaspredatorconfusiontfunctionalresponse
7
relationshipsiscriticalforaccuratelymodelingthedynamicsofpredator-preyinteractions
overecologicalandevolutionarytime[44].
Thisdissertationbuildsonpreviousworkonthepredatorconfusionhypothesisbyexplor-
ingallthreeoftheabovepossibilitiesinadigitalmodel,whereitispossibletoexperimentally
controltheofpredatorconfusion.
2.1.3Manyeyes
Finally,themanyeyeshypothesisconcernsthebetweenvigilance(e.g.,watching
foranincomingpredator)andforagingforfoodingroupsofprey.Firstproposedusing
amathematicalmodel[22]andexploredexperimentallyayearlater[15],themanyeyes
hypothesismakestwokeypredictions,bothofwhicharisefromtheassumptionthatvigilance
iscostlybecauseitimposesawithforagingiency:(a)individualpreyvigilance
willdeclineasagroupsizeincreases,and(b)becausepreycanmoreequitablydividethe
taskofwatchingforpredatorsinlargegroups,theywillexperienceabfrom
foragingmore.Therefore,therewillbeaselectiveadvantageforpreythatforageingroups
uptoacertaingroupsize.Inthe40yearssinceitsinception,thesepredictionshavebeen
examinedinnumerousspeciesacrosshundredsofindependentstudies[45,46,47,17,48].
Furthermore,severalgametheoreticalmodelshavebeenappliedtothepredictionsof
whencollectivevigilanceinforaginggroupsshouldevolve[49],andsubsequentlymatchedto
experimentaldata[50].
However,itstillremainsanopenquestionofwhether|andunderwhatconditions|
themanyeyeshypothesisprovidesantselectivepressuretofavortheevolutionof
collectivebehaviorinforagingspecies.Thisdissertationbuildsonpreviousworkonthe
manyeyeshypothesisbyexploringseveralconditionsunderwhichselectionfavorsgregarious
8
foragingbehavior.
2.2Digitalmodelsofevolutionforcollectiveanimal
behavior
Itisbynomeansanewideatousedigitalmodelstostudyanimalbehavior.Digitalmodels
havepreviouslybeenusedtoprovidekeyinsightsintocoreevolutionaryprocesses[51,52],
andseveralwell-knownstudieshaveadopteddigitalmodelsasamethodtostudycollective
behavior[53,54,55].Morerecently,digitalmodelshaveevenbeenusedtoelucidatethe
emergenceofpreycollectivebehaviorasaresponsetopredation[24].
Thesepreviousstudieshaveprovidedinsightintothefundamentaldynamicsofcollective
behavior.However,mosthavenotfocusedonisolatingtheevolutionarypressuresthatmight
favortheformationofgroups,andfewhaveexploredthecoevolutionofpredatorandprey
behavior.Infact,exceptforonlyahandfulofstudies,thecollectivebehaviorliterature
typicallyhasnotstudiedDarwinianevolutionasaprocessthepropertiesofgroups.
Itisthereforethegoalofthisdissertationtohighlightthestudiesthathaveexploredthe
evolutionofcollectiveanimalbehaviorandtosynthesizetheirworktobuildasolidtheoretical
foundationonwhichtheevolutionofcollectiveanimalbehaviorcanbestudied.
Whenconsideringtheevolutionofcollectivebehavior,itisvitaltotakeintoaccount
boththeb
and
costsimposedbythebehavior[56].Tosatisfythisrequirement,
severalresearchershaverecentlyturnedtodigitalmodelsofevolutiontostudytheevolution
ofanimalbehavior[32,13,57].Theseresearchersuseadigitalmodelofevolutiontoevolve
thebehaviorofapopulationoflocally-interactinganimats,enablingthemtoexplorethe
evolutionofbehaviorincomplexenvironmentsthatarebeyondthemeansofmathematical
9
models[58,59].
Withthesemodels,severalstudieshaveexploredtheevolutionofherdbehavior
inresponsetopredation[40,39].Otherstudieshaveinvestigatedtheevolutionofpredator
behaviorinresponsetopreydensity[60],theevolutionofpreybehaviorinthepresence
ofthepredatorconfusiont[61,62],theroleofrelativepredatorandpreyspeedson
theevolutionofgroupingbehavior[63],andhaveelaboratedupontheinteractionbetween
ecologyandtheevolutionofgroupingbehavior[64,65].
Inthisdissertation,Ibuildupontheideasfromthesestudiesandestablishageneral
frameworkforstudyingtheevolutionofcollectivebehavior.Ineachchapterofthisdisser-
tation,Iconstructadigitalmodelofevolutiontofocusonasinglehypothesizedbeof
collectivebehavior,andcontrolforthepossiblebenintroducedbyothermechanisms.To
performthesedigitalevolutionexperiments,Ievolvepreyagentswitha
geneticalgorithm
(GA),whichisadigitalmodelofevolutionbynaturalselection[66].InaGA,poolsof
genomesareevolvedovertimebyevaluatingtheofeachgenomeateachgeneration
andpreferentiallyselectingthosewithhigher(e.g.,fromconsumingmorefoodorsur-
vivinglonger)topopulatethenextgeneration.Thegenomesherearevariable-lengthstrings
ofintegersthataretranslatedintoMarkovNetworks(MNs)duringevaluation.More
informationonMNs|includingdetailsontheirgeneticencoding,mutationaloperators,and
functionality|isavailableinthefollowingsection.
2.3MarkovNetworks
Ineverydigitalmodelinthisdissertation,eachagentiscontrolledbyitsownMarkovNetwork
(MN),whichisaprobabilisticcontrollerthatmakesdecisionsabouthowtheagentinteracts
10
withtheenvironmentandotheragentswithinthatenvironment.SinceaMNisresponsible
forthecontroldecisionsofitsagent,itcanbethoughtofasan
brain
fortheagent
itcontrols.Everytimestepinthesimulation,theMNsreceiveinputviasensors(e.g.,a
visualsystem),performacomputationoninputsandanyhiddenstates(i.e.,memory),then
placetheresultofthecomputationintohiddenoroutputstates(e.g.,actuators).Inote
thatMNstatesarebinaryandonlyassumeavalueof0or1.WhenIevolveMNswitha
GA,mutations(1)whichstatestheMNpaysattentiontoasinput,(2)whichstates
theMNoutputstheresultofitscomputationto,and(3)theinternallogicthatconvertsthe
inputintothecorrespondingoutput.
2.3.1HowMarkovNetworksFunction
WhenIembedanagentintothesimulationenvironment,Iprovidesensoryinputsfromits
visualsystemintoitsMNeverysimulationstep(labeled\retina"and\MarkovNetwork",
respectively).OnceIprovideaMNwithitsinputs,Iactivateitandallowittostorethe
resultofthecomputationintoitshiddenandoutputstatesforthenexttimestep.MNsare
networksofMarkovGates(MGs),whichperformthecomputationfortheMN.InFigure2.2,
weseetwoexampleMGs,labeled\Gate1"and\Gate2."Attime
t
,Gate1receivessensory
inputfromstates0and2andretrievesstateinformation(i.e.,memory)fromstate4.At
time
t
+1,Gate1thenstoresitsoutputinhiddenstate4andoutputstate6.Similarly,
attime
t
Gate2receivessensoryinputfromstate2andretrievesstateinformationinstate
6,thenplacesitsoutputintostates6and7attimestep
t
+1.WhenMGsplacetheir
outputintothesamestate,theoutputsarecombinedintoasingleoutputusingtheOR
logicfunction.Thus,theMNusesinformationfromtheenvironmentanditsmemoryto
decidewheretomoveinthenexttimestep
t
+1.
11
Arbitraryencodingscanbeused,butsimplerencodingsaremoreconducivetotheevo-
lutionofebehavior.Inorderforagenttobeabletoreacttotheenvironment,the
outputstatesmustsomehowmeaningfullyconnecttotheinputstates.Additionally,ifmem-
oryaboutstateinformationfromtheprevioustimestepisrequiredformorecomplextasks,
MNscanstorestateinformationinmemorybyconnectinginputstatestohiddenstates,then
connectingthosehiddenstatestooutputstates.Finally,stateinformationcanbestoredin
memoryforlongerthanonetimestepbyconnectinghiddenstatestoyetmorehiddenstates.
InaMN,statesareupdatedbyMGs,whichfunctionsimilarlytodigitallogicgates,e.g.,
AND&OR.Adigitallogicgate,suchasXOR,readstwobinarystatesasinputandoutputs
asinglebinaryvalueaccordingtotheXORlogic.Similarly,MGsoutputbinaryvaluesbased
ontheirinput,butdosowithaprobabilisticlogictable.Table2.1showsanexampleMG
thatcouldbeusedtocontrolapreyagentthatavoidsnearbypredatoragents.Forexample,
ifapredatoristotherightoftheprey'sheading(i.e.,PL=0andPR=1,correspondingto
thesecondrowofthistable),thentheoutputsaremoveforward(MF)witha20%chance,
turnright(TR)witha5%chance,turnleft(TL)witha65%chance,andstaystill(SS)
witha10%chance.Thus,duetothisprobabilisticinput-outputmapping,theagentMNs
arecapableofproducingstochasticagentbehavior.
Table2.1AnexampleMGthatcouldbeusedtocontrolapreyagentwhichavoidsnearby
predatoragents.\PL"and\PR"correspondtothepredatorsensorsjusttotheleftand
rightoftheagent'sheading,respectively,asshowninFigure3.2.ThecolumnslabeledP(
X
)
indicatetheprobabilityoftheMGdecidingonaction
X
giventhecorrespondinginputpair.
MF=MoveForward;TR=TurnRight;TL=TurnLeft;SS=StayStill.
PLPR
P(MF)P(TR)P(TL)P(SS)
00
0.70.050.050.2
01
0.20.050.650.1
10
0.20.650.050.1
11
0.050.80.10.05
12
Figure2.2AnexampleMarkovNetwork(MN)withfourinputstates(whitecircleslabeled
0-3),twohiddenstates(lightgreycircleslabeled4and5),twooutputstates(darkgrey
circleslabeled6and7),andtwoMarkovGates(MGs,whitesquareslabeled\Gate1"and
\Gate2").TheMNreceivesinputintotheinputstatesattimestep
t
,thenperformsa
computationwithitsMGsuponactivation.Together,theseMGsuseinformationaboutthe
environment,informationfrommemory,andinformationabouttheMN'spreviousactionto
decidewheretomovenext.
Whiledigitallogicgatesaredeterministic,MGscanbecomposedofanysetofprobabil-
itiesintheirprobabilitytable.Therefore,whiletheoutputstatesstilldependontheinput
states,theycanalsohaveadegreestochasticitytotheiroutput.Figure2.3illustratesan
exampleMGwiththreebinaryinputsenteringtheMG:0and2comingfromsensoryinput
states,whileinput4comesfromahiddenstate.ThisexampleMGiscomposedofa2
3

2
2
statetransitiontable(becauseithasthreeinputsandtwooutputs)thatencodesthelogic
fortheMG.Onceprovidedwithinputs,theMGactivatesandupdatesoutputstate6and
hiddenstate4.BecausetheMGoutputstothesamehiddenstatethatitreceivesinput
from,itisforminga
recurrentconnection
,i.e.,memory.
TheMGsinthismodelcanreceiveinputfromamaximumoffourstates,andwriteinto
amaximumof4states,withaminimumofoneinputandoneoutputstateforeachMG.
Anystate(input,output,orhidden)intheMNcanbeusedasaninputoroutputforaMG.
MNscanbecomposedofanynumberofMGs,andtheMGsarewhattheinternal
13
Figure2.3AzoomedinviewoftheMarkovGate(MG)labeled\Gate1"inFigure2.2.
Gate1hasthreebinaryinputsandtwobinaryoutputs,andisthuscomposedofa2
3

2
2
probabilisticstatetransitiontablewhichencodesitslogic.Forexample,
p
52
inthe
probabilisticstatetransitiontableistheprobabilityoftheinputset101(state0is1,state
2is0,state4is1)mappingtotheoutputset10(state6is1,state4is0).Theprobabilities
acrosseachrowmustsumto1.0.
logicoftheMN.Thus,toevolveaMN,mutationschangetheconnectionsbetweenstates
andMGs,andmodifytheprobabilisticlogictablesthatdescribeeachMG.Mutationsact
directlyonthegeneticencodingoftheMN,whichisdescribednext.
2.3.2GeneticEncodingofMarkovNetworks
Weuseacircularstringofbytesasagenome,whichcontainsalltheinformationnecessary
todescribeaMN.Thegenomeiscomposedof
genes
,andeachgeneencodesasingleMG.
Therefore,agenecontainstheinformationaboutwhichstatestheMGreadsinputfrom,
whichstatestheMGwritesitsoutputto,andtheprobabilitytablethelogicofthe
MG.Thestartofageneisindicatedbya
startcodon
,whichisrepresentedbythesequence
(42,213)inthegenome.
Figure2.4depictsanexamplegenome.Afterthestartcodon,thenexttwobytesdescribe
thenumberofinputs(
N
in
)andoutputs(
N
out
)usedinthisMG,whereeach
N
=1+(byte
mod
N
max
).Here,
N
max
=4.Thefollowing
N
max
bytesspecifywhichstatestheMG
readsfrombymappingtoastateIDnumberwiththeequation:(bytemod
N
states
),
14
Figure2.4ExamplecircularbytestringsencodingthetwoMarkovGates(MGs)inFig-
ure2.2,denotedGene1andGene2.Thesequence(42,213)representsthebeginningofa
newMG(whiteblocks).Thenexttwobytesencodethenumberofinputandoutputstates
usedbytheMG(lightgreyblocks),andthefollowingeightbytesencodewhichstatesare
usedasinput(mediumgreyblocks)andoutput(darkergreyblocks).Theremainingbytes
inthestringencodetheprobabilitiesoftheMG'slogictable(darkestgreyblocks).
Table2.2TypicalmutationratesforexperimentsevolvingMarkovNetworks.
ParameterValue
Per-genemutationrate1%
Geneduplicationrate5%
Genedeletionrate2%
CrossoverNone
where
N
states
isthetotalnumberofinput,output,andhiddenstates.Similarly,thenext
N
max
bytesencodewhichstatestheMGwritestowiththesameequationas
N
in
.Iftoo
manyinputsoroutputsaresptheremainingsitesinthatsectionofthegeneare
ignored,designatedbythe#signs.Theremaining2
N
in
+
N
out
bytesofthegenethe
probabilitiesinthelogictable.
Wesequentiallythelogictablerow-by-rowwithbytesfromthegenome.Oncethe
logictableisIconvertthebytesintothecorrespondingprobabilities(
p
ij
)withthe
followingequation:
p
ij
=
1+byte
ij
P
2
N
out
j
=1
(1+byte
ij
)
(2.1)
wherebyte
ij
isthebyteinthegenomecorrespondingtotheprobabilityinthetableatrow
i
andcolumn
j
,and
N
out
isthenumberofoutputsusedbytheMG.BecauseIusebytesto
15
specifythevaluesinthetable,Inormalizethevaluesforeachrowintheprobabilitytable
sothesumofeachrowis1.0.Iapplythemodulooperatoronthenumberofinputs,the
numberofoutputs,andtheIDsofthestatesusedasinputsandoutputsinordertokeep
themwithintheallowedranges.
Themaximumnumberofstatesallowedandwhichstatesareusedasinputsandoutputs
arespasconstantsbytheuser.Combinedwiththeseconstants,thegenomedescribed
aboveunambiguouslynesaMN.Allevolutionarychangessuchaspointmutations,dupli-
cations,deletions,orcrossoverareperformedonthebytestringgenome,withprobabilities
asshowninTable2.2.Duringapointmutation,arandombyteinthegenomeisreplaced
withanewbytedrawnfromauniformrandomdistribution.Ifaduplicationeventoccurs,
tworandompositionsarechoseninthegenomeandallbytesbetweenthosepointsaredupli-
catedintoanotherpartofthegenome.Similarly,whenadeletioneventoccurs,tworandom
positionsarechoseninthegenomeandallbytesbetweenthosepointsaredeleted.Crossover
forMNsisnotimplementedinthisexperiment.
2.3.3VisualizationofMarkovNetworks
MNscanbevisualizedinseveralways.BecausethevisualizationoftheMNinFigure2.2
showsmanystatesthatarenotevenused,andtheMGsarelessimportantthanhowstates
causallydependoneachother,IusuallyonlydisplayagraphsimilartoFigure2.5showing
thecausalrelationsbetweenthestates.
16
Figure2.5AcausalgraphofthenodeconnectionsfortheMarkovNetwork(MN)inFig-
ure2.2.Theonlystatesdisplayedarestatesthatprovideinputtoorreceiveoutputfromthe
MarkovGatesoftheMN.Arrowsbetweenthenodesindicatethewofbinaryinformation
betweenthestates.
2.4Particleswarmoptimizationandswarmrobotics
Inthepastdecade,researchershavefocusedontheapplicationoflocally-interactingswarm-
ingagentstooptimizationproblems,calledParticleSwarmOptimization(PSO)[67].PSO
applicationsrangefromfeatureselectionfor[68],tovideoprocessing[69],toopen
vehiclerouting[70].ArelatedtechniquewithinPSOseekstocombinePSOwithcoevolv-
ing\predator"and\prey"solutionstoavoidlocalminima[71].Thus,elaborationsonthe
foundationsofcollectiveanimalbehaviorhasthepotentialtoimproveourabilitytosolve
engineeringproblems.
Further,researchershavesoughttoharnessthecollectiveproblemsolvingpowerof
swarmingagentstodesignrobustautonomousroboticswarms[72].Giventhatmostswarm
controlalgorithms|suchasthepopularBoidsalgorithm[73]|requiretcomput-
ingpowerandglobalinformationabouttheswarmthatistypicallyunavailableinthereal
world,itisvitaltodevelopswarmcontrolalgorithmsthatcanproducereliableswarming
behaviorwith
individual-based
controlmechanismsthatrequireonlylocalizedinformation.
17
Chapter3.4,inparticular,willfocusonhowsuchindividual-basedcontrolalgorithmscan
bediscoveredusingdigitalmodelsofevolution.
18
Chapter3
HerdHypothesis
Inthischapter,Iuseadigitalmodelofpredator-preycoevolutiontoexploreHamilton's
herdhypothesis[27].Bri,theherdhypothesisstatesthatpreyingroups
underattackfromapredatorwillseektoplaceotherpreyinbetweenthemselvesandthe
predator,thusmaximizingtheirchanceofsurvival.Asaconsequenceofthisbehavior,
individualscontinuallymovetowardacentralpointinthegroup,whichgivesrisetothe
appearanceofacohesiveswarm.Thischapterexpandsonmyearlierwork[74]bystudying
thelong-termevolutionaryofattackmodes,exploringanewattackmode
thatdirectlyselectsagainstswarmingbehavior,andprovidingananalysisofthecontrol
algorithmsthatevolvedintheswarmingprey.
ThischapterbeginswiththedetailsofthedigitalmodelthatIusedtoexplorethe
evolutionofherdbehavioringroupsofprey.Next,Idescribetheresultsfromthe
modelandhowpredatorattackmodetheevolutionofherdbehavior.Finally,
Iconcludethechapterbydiscussingsomeofthebroaderimplicationsoftheinthis
chapter.
3.1Modelofpredator-preyinteractions
Tostudytheevolutionoftheselherd,Idevelopedanagent-basedmodelinwhichagents
interactinacontinuous,toroidalvirtualenvironment(736

736virtualmeters),shownin
19
Figure3.1Adepictionofthesimulationenvironmentinwhichtheagentsinteract.Black
dotsarepreyagents,theblacktriangleisapredatoragent,andthelinesaroundthepredator
agentindicateitsofview.Agentswraparoundtheedgesofthetoroidalsimulation
environment.
Figure3.1.Atthebeginningofeachsimulation,Iplace250agentsintheenvironmentat
uniformlyrandomlocations.Theseagentsaretreatedas\virtualprey."Eachagentiscon-
trolledbya
MarkovNetwork
(MN),whichisaprobabilisticcontrollerthatmakesmovement
decisionsbasedonacombinationofsensoryinput(i.e.,vision)andinternalstates(i.e.,mem-
ory).IevolvetheagentMNswithageneticalgorithm(GA)[75,66]undervaryingselection
regimes,whichwillbedescribedinmoredetailbelow.MoreinformationonMNs|including
detailsontheirgeneticencoding,mutationaloperators,andfunctionality|isavailablein
Chapter2.3.
Duringeachsimulationtimestep,allagentsreadinformationfromtheirsensorsand
takeaction(i.e.,move)basedontheirs.Inmysetoftreatments,Isimulate
20
Figure3.2Anillustrationoftheagentsinthemodel.Lightgreytrianglesarepreyagents
andthedarkgreytrianglesarepredatoragents.Theagentshavea360

limited-distance
visualsystem(200virtualmeters)toobservetheirsurroundingsanddetectthepresenceof
otheragents.Thecurrentheadingoftheagentisindicatedbyaboldarrow.Eachagenthas
itsownMarkovNetwork,whichdecideswheretomovenextbasedofacombinationof
sensoryinputandmemory.Theleftandrightactuators(labeled\L"and\R")enablethe
agentstomoveforward,left,andrightindiscretesteps.
anideal,disembodiedpredatorbyperiodicallyremovingpreyagentsfromtheenvironment
andmarkingthemasconsumed,e.g.,whentheyareontheoutermostedgesofthegroup.
Subsequenttreatmentsintroduceanembodied,coevolvingpredatoragentwhichiscontrolled
byitsownMN.Thedata
1
andsourcecode
2
fromtheseexperimentsareavailableonlinefor
furtheranalysis.
Figure3.2depictsthesensory-motorarchitectureoftheagentsusedforthisstudy.A
preyagentcansensepredatorsandconspwithalimited-distance(200virtualmeters),
1
Data:http://d
2
Code:https://github.com/adamilab/eos
21
Table3.1Possibleactionsencodedbytheagent'soutput.Eachoutputpairencodesa
discreteactiontakenbytheagent.Theagent'sMNchangesthevaluesstoredinoutput
statesLandRtoindicatetheactionithasdecidedtotakeinthenextsimulationtimestep.
OutputLOutputREncodedAction
00Moveforward
01Turnright
10Turnleft
11Staystill
pixelatedvisualsystemcoveringitsentire360

visualItsvisualsystemissplitinto24
evenslices,eachcoveringanarcof15

,whichisanabstractionofthebroad,coarsevisual
systemsoftenobservedingroupingprey[76].Regardlessofthenumberofagentspresent
inasingleretinaslice,thepreyagentonlyknowswhetheraconsporpredatorresides
withinthatslice,butnothowmany.Forexample,inFigure3.2,thefourthretinaslicetothe
rightoftheagent'sheading(labeled\A")hasboththepredatorandpreysensorsactivated
becausetherearetwopredatoragentsandapreyagentinsidethatslice.Onceprovided
withitssensoryinformation,thepreyagentchoosesoneoffourdiscreteactions,asshown
inTable3.1.Preyagentsturnin8

incrementsandmove1virtualmetereachtimestep.
Inmycoevolutionexperiments,thepredatoragentscandetectonlynearbypreyagents
usingalimited-distance(200virtualmeters),pixelatedvisualsystemcoveringitsfrontal180

thatworksjustlikethepreyagent'svisualsystem(Figure3.2).Similartothepreyagents,
predatorsmakedecisionsabouthowtomovenextusingtheirMN,asshowninTable3.1,
butmove3

fasterthanthepreyagentsandturncorrespondinglyslower(6

persimulation
timestep)duetotheirhigherspeed.Finally,ifapredatoragentmoveswithin5virtual
metersofapreyagentthatisanywherewithinitsvisualsystem,thepredatoragentmakes
anattackattemptonthepreyagent.Iftheattackattemptissuccessful,Iremovetheprey
agentfromthesimulationandmarkitasconsumed.
22
Table3.2Geneticalgorithmandexperimentsettings.
GAParameterValue
SelectionFitnessproportionate
Populationsize250
Per-genemutationrate1%
Geneduplicationrate5%
Genedeletionrate2%
CrossoverNone
Generations40,000
Replicates100
3.2Predation
Inmysetofexperiments,Iobservetheevolutionofpreybehaviorinresponsetovarious
formsofpredation.Thisexperimentalsetupenablesmetocontrolthespmodes
ofpredationandobservetheirontheevolutionoftheherd.Ievolvetheprey
genomeswithaGAwiththesettingsdescribedinTable3.2.Ibegintheevolutionaryprocess
byseedingthepreygenomepoolwithasetofrandomly-generatedancestorgenomesoflength
5,000.Followingthis,Ievaluatetherelativeofeachpreygenomebytranslatingthe
genomeintoitscorrespondingMN,embodyingeachMNinapreyagent,andcompetingthe
preyagentsinasimulationenvironmentfor1,000simulationtimesteps.Thisevaluation
periodisakintotheagents'lifespan,henceeachagenthasapotentiallifespanof1,000time
steps.Iassigneachpreygenomeanindividualaccordingtohowlongitscorresponding
preyagentsurvived,followingtheequation:
W
prey
=
T
(3.1)
where
T
isthenumberoftimestepsthepreyagentsurvivedinthesimulationenvironment.
Thus,individualpreygenomesarerewardedfortheiragentsurvivinglongerthanotheragents
23
inthegroup.Onceallofthepreygenomesareassignedtnessvalues,Iperform
proportionateselectiononthepopulationofgenomesviaaMoranprocess[77],increment
thegenerationcounter,andrepeattheevaluationprocessonthenewpopulationofgenomes
untilthegeneration(40,000)isreached.
Inallcases,Igivethepreyaninitial250simulationtimestepswithoutpredationtomove
around,sothatpreystartingontheoutsideofthegrouphavethechancetomovetoward
thecenterofthegroupiftheywishto.Oncetheinitial250simulationtimestepselapse,I
applypredationevery4simulationtimestepsbysimulatinganidealpredatorthat
attacksthegroupaccordingtoaspattacktype.predatorssucceedwiththeir
attackseverytime.Ilimitthepredatorattackratetooneattackattemptevery
4simulationtimesteps,whichiscalledthe
handlingtime
.Thehandlingtimerepresents
thetimeittakesthesimulatedpredatortoconsumeanddigestapreyaftersuccessfulprey
capture,orthetimeittakestorefocusonanotherpreyinthecaseofanunsuccessfulattack
attempt.Iselectedahandlingtimeof4becauseitreducestheherdofpreydownto25%
ofitsoriginalsizebytheendofthesimulation,thereforeapplyingstrongselectionpressure
forsurvivorshipintheherd.
Foreachexperiment,Icharacterizethegroupingbehaviorbymeasuringthe
swarmden-
sity
oftheentirepreypopulationeverygeneration[78].Imeasuretheswarmdensityas
themeannumberofpreywithin30virtualmetersofeachotheroveralifespanof1,000
simulationtimesteps,whichIhaveexperimentallyshowntotiatebetweenswarming
andnon-swarmingbehaviorinpreviouspublishedexperiments[79].Qualitatively,aswarm
densityof

15indicatescohesiveswarmingbehavior,between15and5looselygrouping
behavior,and

5random,non-groupingbehavior.Thus,swarmdensitycaptureshow
cohesivelythepreyareswarming,orifthepreyareevengroupingatall.
24
Figure3.3Anillustrationofthefourpredatorattackmodes.A)Randomattacks,
B)Randomwalkattacks,C)Outsideattacks,andD)High-densityareaattacks.
Inthefollowingsections,Istudytheoffourtattackmodesontheevolution
ofswarmingbehavior:uncorrelatedrandomattacks(Figure3.3A),correlatedrandomattacks
(randomwalkattacks,Figure3.3B),peripheralattacks(Figure3.3C),andattacksthattarget
themostdenseareaoftheswarm(Figure3.3D).
3.2.1RandomAttacks
MyinitialstudysoughttoverifyHamilton'sherdhypothesisbymodelingevolving
preyunderattackbypredatorsthatambushpreyfromarandomlocationinthesimulation
environment.Iftheherdhypothesisholds,Iexpectpreytominimizetheir\domain
ofdanger"tothepredatorsbyplacingasmanyconspaspossiblearoundthem[27].
Similartopreviousmodelsstudyingtheherd[40],arandomattackproceedsby
selectingauniformlyrandomlocationinsidethesimulationspace,thenattackingtheprey
closesttothatlocation,asshowninFigure3.3A.
AsseeninFigure3.4,swarmingbehaviorisweaklyselectedforwhenthepredatorsmake
uniformlyrandomattacksontheprey
3
(lightgreytriangles).Particularly,Ifoundthatprey
tookupwardsof5,000generationstoevolvecohesiveswarmingbehaviorwhenexperiencing
3
EvolutionofpreybehaviorunderRandomAttacktreatment:h
25
randomattacks,comparedtofewerthan1,000generationswiththeotherattackmodes.
However,evenrandomattacksselectedformorecohesiveswarmingbehaviorthannoattacks
atall,whichresultedincompletelydispersivebehavior(Figure3.4,lightgreystars).
Thishasimportantimplications,namelythatoneoftheoriginalassumptions
oftheherdhypothesis|thatthepredatorattackmodehasnoimportantimpact
ontheevolutionofswarmingbehavior|isnotcorroboratedbythismodel.Followingthis
discovery,Ihypothesizedthatthe
directionality
ofthepredators'attacksplayacriticalrole
intheevolutionoftheshherd.Totestthishypothesis,Inextexploretwot
predatorattackmodes,eachwiththeirowndistinctdirectionalityofpredation.
3.2.2RandomWalkAttacks
Mynextexperimentaltersthemodeofpredationfromapredatorthatattacksrandomly
selectedlocationstoapredatorthatfollowsarandomwalkwithinthesimulationenviron-
ment.ShowninFigure3.3B,aftereachattackmadebythispredator,itisthenmovedto
arandomlocationwithin50virtualmetersofitspreviouslocation.Thismodelsapredator
thatpersistentlyfeedsonagroupofprey,ratherthanambushing.
Figure3.4showsthatswarmingevolvedquicklywhenthepreywereattackedbyapreda-
torfollowingarandomwalk
4
(darkgreycircles).Notably,evenbygeneration40,000,prey
experiencingrandomwalkattacksformedtlymorecohesiveswarmsthanpreyex-
periencingrandomattacks.Thus,therandomwalkpredatorattackmodeappearstocapture
animportantaspectofpredationthatselectsforswarmingbehavior.
4
EvolutionofpreybehaviorunderRandomWalktreatment:h
26
Figure3.4Meanswarmdensityoverallreplicatesoverevolutionarytime,measuredby
themeannumberofpreywithin30virtualmetersofeachotheroveralifespanof1,000
simulationtimesteps.Preyingroupsattackedrandomly(lightgreytriangles)tookmuch
longertoevolvecohesiveswarmingbehaviorthanpreyingroupsattackedbyapredator
thatfollowsarandomwalk(darkgreycircles)oralwaysfromtheoutsideofthegroup
(blacksquares).Whenpreyexperiencenoattacks,theydonotevolveswarmingbehaviorat
all(lightgreystars).Errorbarsindicatetwostandarderrorsover100replicates.
27
3.2.3OutsideAttacks
Inthelastofmyinitialartipredationexperiments,Isimulateapredatorthatalways
approachesfromtheoutsideofthegroupandattacksthepreynearesttoit,asin[80].
Thispredatorattackmodeelyhasthepredatorsconsistentlyattackingpreyonthe
outeredgesofthegroup.AsshowninshowninFigure3.3C,Isimulatethispredatorattack
modebychoosingarandomangleoutsideofthegroupforthepredatortoapproach
from.Onceanangleischosen,Iconverttheangleintoalocationontheedgeofthevisible
simulationspaceandattackthepreynearesttothatlocation.
AsshowninFigure3.4,thisformofpredationhasthemosttimpactonthe
evolutionoftheherdsofar.Whenattackedbypredatorsthatconsistentlytargetprey
ontheedgesofthegroup,preyquicklyevolvecohesiveswarmingbehavior
5
(blacksquares).
Takentogether,theresultsofthesepredationexperimentsdemonstrateanother
discoveryofthiswork:Themorepredatorsattackpreyontheoutsideofthegroup,the
fastertheherdwillevolve.
Onetranslationofthisdingisthatinorderfortheherdtoevolve,preymust
experienceahigherpredationrateontheoutsideofthegroupthaninthemiddleofthe
group.Whilethisphenomenoncanbeexplainedbyeachpreyhavinga\domainofdanger"
(DOD)edbyitsrelativepositioninthegroup[27,31,38],analternativehypothesis
isthatofdensity-dependentpredation.
28
Figure3.5Meanswarmdensityoverallreplicatesoverevolutionarytime,measuredby
themeannumberofpreywithin30virtualmetersofeachotheroveralifespanof1,000
simulationtimesteps.Evenwhenexperiencingdensity-dependentpredation,preyingroups
attackedrandomly(lightgreytriangles)tookmuchlongertoevolveswarmingbehaviorthan
preyingroupsattackedbyapersistentpredator(darkgreycircles)oralwaysfrom
theoutsideofthegroup(blacksquares).Errorbarsindicatetwostandarderrorsover100
replicates.
29
3.2.4Density-DependentPredation
Tostudytheimpactofdensity-dependentpredationontheevolutionoftheherd,I
imposeaconstraintonthepredatorwhichreducesitsattackwhenitattacksareas
ofthegroupwithhighpreydensity.Thisreducedattackismeanttorepresentthe
increasedpredationratethatpreyonedgesofthegroupareexpectedtoendure[27,31,38],
andsuchdensity-dependencecanalsobethoughtofasaproxyforgroupdefense.Icompute
thepredator'sprobabilityofcapturingapreyduringagivenattack(
P
capture
)withthe
followingequation:
P
capture
=
1
A
density
(3.2)
where
A
density
isthenumberofpreywithin30virtualmetersofthetargetprey,including
thetargetpreyitself.Forexample,ifthepredatorattacksapreywith4otherpreynearby
(
A
density
=5),ithasa20%chanceofsuccessfullycapturingtheprey.Abiologicalanalogue
ofthismechanismwouldbe,forexample,lionshavingmoresuccesscapturingonthe
edgeratherthaninthemiddleoftheherd.Asaconsequenceofthismechanism,theprey
experiencedensity-dependentpredation.
Figure3.5demonstratestheectofdensity-dependentpredationonthepreviousarti-
predationexperiments.Justasbefore,whenpredatorsdidnotpreferentiallyattack
preyontheoutsideofthegroup,asintherandomattackexperiment(lightgreytriangles),
swarmingbehaviortookmuchlongertoevolve.Incontrast,whenthepredatorsfollowed
arandomwalk(darkgreycircles)oralwaysattackedfromtheoutsideofthegroup(black
squares),thepreyexperiencingdensity-dependentpredationagainquicklyevolvedswarm-
5
EvolutionofpreybehaviorunderOutsideAttacktreatment:h
30
Table3.3High-densityareaattack(HDAA)experimenttreatments.Thevalueslistedfor
eachtreatmentarethehandlingtimesforthecorrespondingpredatorattackmode.
HDAA?OutsideAttackFrequencyHDAAFrequency
No10N/A
Infrequent10250
Frequent1025
ingbehavior.Themostnoticeableofdensity-dependentpredationisontherandom
attacktreatment,wheretheswarmdensitymeasurementatgeneration5,000increasedfrom
11.19

2.58(mean

twostandarderrors)to17.61

2.72,indicatingantlystronger
selectionforswarming.
3.2.5High-DensityAreaAttacks
Thusfar,Ihaveexploredattackmodesthatselectfortheevolutionofswarmingbehavior.It
isnotsurprisingthattherearealsoattackmodesexhibitedbynaturalpredatorsthatmust
selectagainstswarmingbehaviorintheirprey.Forexample,bluewhales(
Balaenoptera
musculus
)areknowntodiveintothedensestareasinswarmsofkrill,consuminghundreds
ofthousandsofkrillinthemiddleoftheswarminasingleattack[81].Icallthiskindofattack
modea
high-densityareaattack
.Suchanattackclearlyselectsagainstswarmingbehavior
becauseittargetsthepreythatswarmthemost.Ifkrillswarmsconsistentlyexperience
thesehigh-densityareaattacks,thenwhydotheystillevolveswarmingbehavior?
Itisimportanttonotethatkrillswarmsarealsofedonbysmallerspecies,suchas
crabeaterseals(
Lobodoncarcinophagus
),thatconsistentlyattackthekrillontheoutsideof
theswarm[82].Thus,krillswarmsareexperiencingtwoformsofattackmodessimulta-
neously:High-densityareaattacksfromwhalesandoutsideattacksfromcrabeaterseals.
Thus,itispossiblethattheselectionpressuretoswarmfromoutsideattacks(Figure3.4)
31
couldoutweightheselectionpressuretodispersefromhigh-densityareaattacks.
ShowninFigure3.3D,Imodelhigh-densityareaattacksasanattackthatalways
targetsthepreyatthemostdenseareaoftheswarm(i.e.,highest
A
density
).Inotethatthis
attackmodeistheoppositeofthedensity-dependentmechanismexploredintheprevious
section,whichfavorspredatorsthattargetpreyinthe
least
denseareaoftheswarm.Once
thetargetisselected,Iexecutetheattackbyremovingthetargetpreyandallotherprey
within30virtualmetersofthetargetprey.Outsideattacksaremodeledasdescribedabove.
Tostudytheofhigh-densityareaattacksontheevolutionofswarmingbehavior,Iallow
thepreytoevolvewhileexperiencingbothattackmodessimultaneously.Ivarytherelative
handlingtimesofbothattacks(Table3.3)toexplorewhetherrelativeattackfrequencycould
explainwhysomeswarminganimalsevolvedswarmingbehaviordespitethefactthatthey
experiencehigh-densityareaattacks.
AsshowninFigure3.6,preyexperiencingonlyoutsideattacksquicklyevolvecohesive
swarmingbehavior(lightgreytriangles).However,whenIintroduceinfrequenthigh-density
areaattacks(darkgreycircles),theselectionpressureforpreytoswarmisreduced.Finally,
whenIintroducefrequenthigh-densityareaattacks(blacksquares),thepreydonotevolve
swarmingbehavioratall.Thus,onepossibleexplanationforanimalsevolvingswarming
behaviordespiteexperiencinghigh-densityareaattacksisthatthehigh-densityareaattacks
aretooinfrequentrelativetootherattacktypestoexertastrongenoughselectionpressure
forpreytodisperse.
Insummary,thepredationexperimentsprovidedmewithtwoimportant
regardingtheevolutionoftheherd:(1)attacksonpreyontheperipheryoftheherd
exertastrongselectionpressureforpreytoswarmand(2)preyinlessdenseareas,suchas
thoseontheoutsideoftheherd,mustexperienceahigherpredationratethaninareasof
32
Figure3.6Meanswarmdensityoverallreplicatesoverevolutionarytime,measuredby
themeannumberofpreywithin30virtualmetersofeachotheroveralifespanof1,000
simulationtimesteps.Swarmdensitywasmeasuredfromevolvedpopulationsthatwere
notexperiencingpredationduringmeasurement,eliminatinganypossibleofattack
modesthatkillmorepreyfaster.Preyingroupsattackedonlybyoutsideattacks(lightgrey
triangles)evolvedcohesiveswarmingbehavior.Increasingtherelativefrequencyofhigh-
densityareaattacksfrominfrequent(darkgreycircles)tofrequent(blacksquares)caused
thepreytoevolveincreasinglydispersivebehavior.Errorbarsindicatetwostandarderrors
over100replicates.
33
denseprey,suchasthoseinthecenteroftheherd.
3.3Predator-PreyCoevolution
Buildinguponthelpredationexperiments,Iimplementeddensity-dependentpre-
dationinapredator-preycoevolutionexperiment.Addingpredatorsintothesimulation
environmentenablesmetoobservehowembodiedcoevolvingpredatorstheevolution
oftheherd.
Forthisexperiment,Icoevolveapopulationof100predatorgenomeswithapopulation
of100preygenomesusingaGAwithsettingsdescribedinTable3.2.Sp,Ievaluate
eachpredatorgenomeagainsttheentirepreygenomepopulationfor2,000simulationtime
stepseachgeneration.Duringevaluation,Iplace4clonalpredatoragentsinsidea512

512
virtualmeterssimulationenvironmentwithall100preyagentsandallowthepredatoragents
tomakeattackattemptsonthepreyagents.Thepreygenomepopulationsize,simulation
environmentarea,andtotalnumberofGAgenerationsweredecreasedinthisexperiment
duetocomputationallimitationsimposedbypredator-preycoevolution.Iassignedthe
preyindividualvaluesasinthepreviousexperiments,andevaluatedpredator
accordingtothefollowingequation:
W
predator
=
t
max
X
t
=1
(
S
0

A
t
)(3.3)
where
t
isthecurrentsimulationtimestep,
t
max
isthetotalnumberofsimulationtimesteps
(here,
t
max
=2,000),
S
0
isthestartinggroupsize(here,
S
0
=100),and
A
t
isthenumber
ofpreyaliveatupdate
t
.Thus,predatorsareselectedtoconsumemorepreyfaster,and
preyareselectedtosurvivelongerthanotherpreyinthegroup.Onceallofthepredator
34
Figure3.7Meanswarmdensityoverallreplicatesoverevolutionarytime,measuredbythe
meannumberofpreywithin30virtualmetersofeachotheroveralifespanof2,000simulation
timesteps.Preyingroupsexperiencingdensity-dependentpredation(blackcircles)evolved
cohesiveswarmingbehavior,whereaspreyingroupsnotexperiencingdensity-dependent
predation(lightgreytriangles)evolveddispersivebehavior.Errorbarsindicatetwostandard
errorsover100replicates.
andpreygenomesareassignedvalues,Iperformproportionateselectionon
thepopulationsviaaMoranprocess[77],incrementthegenerationcounter,andrepeatthe
evaluationprocessonthenewpopulationsuntilthegeneration(1,200)isreached.
Toevaluatethecoevolvedpredatorsandpreyquantitatively,Iobtainedthelineofdescent
(LOD)foreveryreplicatebytracingtheancestorsofthepreyMNinthe
populationuntilIreachedtherandomly-generatedancestralMNwithwhichthestarting
populationwasseeded(see[51]foranintroductiontotheconceptofaLODinthecontext
ofdigitalevolution).Iagaincharacterizedthepreygroupingbehaviorbymeasuringthe
swarmdensityoftheentirepreypopulationeverygeneration.
Figure3.7depictsthepreybehaviormeasurementsforthecoevolutionexperimentswith
35
density-dependentpredation
6
(blackcircles;meanswarmdensityatgeneration1,200

two
standarderrors:26.2

2.3)andwithoutdensity-dependentpredation(lightgreytriangles;
3.9

0.8).Withoutdensity-dependentpredation,thepreyevolvedpurelydispersivebehavior
asamechanismtoescapethepredators,evenafter10,000generationsofevolution([83],
FigureS1).Incontrast,withdensity-dependentpredation,thepreyquicklyevolvedcohesive
swarmingbehaviorinresponsetoattacksfromthepredatorswithin400generations.Asa
caveat,density-dependentpredationonlyselectsforcohesiveswarmingbehaviorwhenthe
predatorsarefasterthantheprey([83],FigureS2),whichcorroboratesearlier
exploringtheroleofrelativepredator-preyspeedsintheevolutionofswarmingbehavior[63].
HereIseethatdensity-dependentpredationprovidesatselectiveadvantagefor
preytoevolvetheherdinresponsetopredationbycoevolvingpredators,despitethe
factthatswarmingpreyexperienceanincreasedattackratefromthepredatorsduetothis
behavior([79],FiguresS3&S4).Accordingly,theseresultsupholdHamilton'shypothesis
thatgroupingbehaviorcouldevolveinanimalspurelyduetoreasons,withoutthe
needforanexplanationthatinvolvesthebtothewholegroup[27].Moreover,the
discoveriesinthisworktheherdhypothesisbyclarifyingthatthepredator's
attackmodehasatontheevolutionofherdbehavior:inparticular,
thatherdbehaviorismuchmorestronglyselectedforwhenthepredatorconsistently
attackstheedgesofthegroupratherthanattackingrandomly.
6
Preybehaviorfrompredator-preycoevolutiontreatment:http://dx.doi
36
3.4EvolvedPreyMarkovNetworkAnalysis
NowthatIhaveevolvedemergentswarmingbehaviorinanagent-basedmodelunderseveral
ttreatments,IcananalyzetheresultingMarkovNetworks(MNs)togainadeeper
understandingoftheindividual-basedmechanismsunderlyingswarmingbehavior.Forthis
analysis,Ichosethemost-abundantpreyMNfromeachoftheOutsideAttack
predationexperimentreplicates,resultingin100MNsthatexhibitswarmingbehavior.
First,Ianalyzethestructureofthe100MNsbylookingatthespretinasensors
thattheMNsevolvedtoconnectto.ShowninFigure3.8,thepreyMNsshowastrongbias
forconnectingtotheprey-spretinasensorsinfrontoftheprey,butnottothesides.
Additionally,someofthepreyMNsshowapreferenceforconnectingtotheprey-sp
retinasensorsbehindtheprey.Fromthisanalysisalone,Icandeducethattheretinasensors
thataremostconducivetoswarmingbehaviorareinfrontofthepreyagent.
Tounderstandhowpreymakemovementdecisionsbasedontheirsensoryinput,Imap
everypossibleinputcombinationintheprey'svisualsystemtothecorrespondingmovement
decisionthatthepreymade.DuetothestochasticnatureofMarkovNetworks,theprey
agentsdonotalwaysmakethesamemovementdecisionwhengiventhesameinput.Thus,
Itakethemost-likelyoutputoutof1,000trialsastherepresentativedecisionforagiven
sensoryinputcombination.ely,thisprocessproducesatruthtablethatmapsevery
possiblesensoryinputtoitscorrespondingmovementdecision.Iinputthistruthtableinto
thelogicminimizationsoftware
espresso
[84],whichoutputstheminimalrepresentativelogic
ofthetruthtable.Thisprocessresultsinatruthtablethatisreducedenoughtomakethe
evolvedpreybehaviorcomprehensiblebyhumans.
Surprisingly,theindividual-basedmechanismsunderlyingtheemergentswarmingbehav-
37
Figure3.8Numberofsensoryinputconnectionsfrom100evolvedpreyMarkovNetworks
mappedontoapreyagent.Onlycausalconnectionsfromthesensoryinputstotheactuators
areshown.Thearrowindicatesthefacingoftheagent.ThepreyMarkovNetworksevolved
astrongpreferenceforconnectingtopreysensorsinfrontandaslightpreferenceforsensors
behindthepreyagent,buttendedtonotconnecttothesensorsonthesides.
38
iorareremarkablysimple.MostofthepreyMNsevolvedtomaketheirmovementdecisions
basedofonlyonepreysensorinfrontofthepreyagent.Ifthepreysensordoesnotdetect
anotherpreyagent,theagentrepeatedlyturnsinonedirectionuntilitdetectsanotherprey
agentinthatsensor.Oncetheagentdetectsanotherpreyagentinthesensor,itmovesfor-
warduntiltheagentisnolongervisible.Thismechanismaloneprovedttoproduce
cohesiveswarmingbehaviorinthemajorityofmyexperiments.Interestingly,thisdiscovery
corroboratesthengsinearlierstudiessuggestingthatcomplexswarmingbehaviorcan
emergefromsimplemovementruleswhenappliedoverapopulationoflocally-interacting
agents[79,85,73].
InasmallsubsetoftheevolvedpreyMNs,IobserveMNsthatoccasionallyconnectto
oneofthepreysensorsbehindthem.TheseMNswatchforapreyagenttoappearina
singlepreysensorbehindtheagentandturnrepeatedlyinonedirectionuntilapreyagent
isnolongervisibleinthatsensor.Onceapreyagentisnolongervisibleinthebacksensor,
theMNmovesforwardorturnsdependingonthestateofthefrontalsensor.Inotethat
thismechanism
only
evolvedinpreyMNsthatalreadyexhibitedswarmingbehaviorusing
oneofthefrontalsensors,whichsuggeststhatthismechanismdoesnotplayamajorrolein
swarmingbehavior.Instead,thismechanismseemstocausethepreyagenttoturntoward
thecenteroftheswarminsteadofswarminginacirclewiththerestofthepreyagents.This
mechanismcanbethoughtofasaherd"mechanismthatattemptstomove
theagenttowardthecenteroftheswarmtoavoidpredation.
39
3.5Discussion
Inthischapter,IdemonstratedHamilton'sherdhypothesisinadigitalmodelof
evolutionandhighlightedthatitistheattackmodeofthepredatorthatcriticallydetermines
theevolvabilityofswarmingbehavior.Further,weshowedthatdensity-dependentpredation
isientfortheherdtoevolveaslongasthepredatorscannotconsistentlyattack
preyinthecenterofthegroup.Finally,Ishowedthatdensity-dependentpredationis
ttoevolvegroupingbehaviorinpreyasaresponsetopredationbycoevolving
predators.Consequently,futureworkexploringtheevolutionoftheherdinanimals
shouldnotonlyconsiderthebehaviorofthepreyinthegroup,buttheattackmodeofthe
predatorsaswell.Followingtheseexperiments,Ianalyzedtheevolvedcontrolalgorithms
oftheswarmingpreyandidensimple,biologically-plausibleagent-basedalgorithms
thatproduceemergentswarmingbehavior,includingamechanismthatproduces
behaviorthatdrivesthepreytowardthecenteroftheswarm.
Theinthischapterpointtotwogeneralconclusionsregardingtheevolutionof
collectiveanimalbehavior.Firstandforemost,thefactthatseeminglycooperativebehavior
evolvedforpurelyreasons(i.e.,tosurvivelongerthanotherconspinthegroup)
suggeststhattheadvantagesbygroupingdonotnecessarilyneedtobthe
entiregroup:Indeed,swarmingbehaviorevolvedinthesesimulationssimplybecausethe
preyfoundswarmingtobeaviabletactictosurvivelongerthanotherpreyinthegroup,
evenwhenswarmingdidn'tprovideanyinherentadvantagetotheentiregroup.Second,
therelativelysimplecontrolalgorithmsthatevolvedintheswarmingpreysuggeststhat
thecontrolalgorithmsusedintop-downswarmmodelingapproaches|suchasthepopular
Boidsmodel[73]|arelikelyoverlycomplicatedandrequiresensoryinformationthatisnot
40
realisticallyavailabletorealswarminganimals.Consequently,furtheranalysisoftheevolved
controlalgorithmsfromfutureagent-basedswarmingexperimentsshouldproveenlightening
foruncoveringthetruemechanismsthatrealanimalsusetoswarm.
41
Chapter4
PredatorConfusionHypothesis
Inthepredatorconfusionhypothesis,thepresenceofmultipleindividualsmovinginaswarm
confusesapproachingpredators,makingitforpredatorstosuccessfullyexecutean
attack[29,7,30,41].Despitetheinherentadvantagethatpredatorconfusionswarming
groupsofprey,itremainsunclearwhetherpredatorconfusioncanprovideatselective
advantageforswarmingbehaviortoevolveintheplace.
Inthischapter,Iusedigitalmodelsofevolutiontoexploretheevolutionaryconsequence
ofthepredatorconfusionhypothesisonpopulationsofcoevolvingpredatorsandprey.First,
IdescribethedetailsofthedigitalmodelthatIusedinthisproject.Next,Iexplainthe
resultsfromthemodelandhowpredatorconfusiontheevolutionofpreybehavior.
Followingthat,IdescribeanadditionalexperimentIperformedtoexplorehowpreda-
torconfusioncaninturntheevolutionofpredatorvisualsystems.Finally,Iconclude
thechapterbydiscussingsomeofthebroaderimplicationsoftheinthischapter.
4.1Modelofpredator-preyinteractions
Tostudytheofpredatorconfusionontheevolutionofswarming,Icreatedanagent-
basedsimulationinwhichpredatorandpreyagentsinteractinacontinuoustwo-dimensional
virtualenvironment.Eachagentiscontrolledbya
MarkovNetwork
(MN),whichisastochas-
ticstatemachinethatmakescontroldecisionsbasedonacombinationofsensoryinput(i.e.,
42
vision)andinternalstates(i.e.,memory)[86].Icoevolvethepredatorandpreywitha
geneticalgorithm
(GA),whichisadigitalmodelofevolutionbynaturalselection[66].In
aGA,poolsofgenomesareevolvedovertimebyevaluatingtheofeachgenomeat
eachgenerationandpreferentiallyselectingthosewithhighertopopulatethenext
generation.Thegenomesherearevariable-lengthstringsofintegersthataretranslatedinto
MNsduringevaluation.MoreinformationonMNs|includingdetailsontheirgenetic
encoding,mutationaloperators,andfunctionality|isavailableinChapter2.3.
Toperformthiscoevolution,Icreateseparategenomepoolsforthepredatorandprey
genomes.Next,Ievaluatethegenomes'essbyselectingpairsofpredatorandprey
genomesatrandomwithoutreplacement,thenplaceeachpairintoasimulationenvironment
andevaluatethemfor2,000simulationtimesteps.Withinthissimulationenvironment,I
generate50identicalpreyagentsfromthesinglepreygenomeandcompetethemwiththe
singlepredatoragenttoobtaintheirrespectiveThisevaluationperiodisakinto
theagents'lifespan,henceeachagenthasapotentiallifespanof2,000timesteps(enough
timeforthepreytotravelapproximately400bodylengths).Thevalues,calculated
usingthefunctiondescribedbelow,areusedtodeterminethenextgenerationofthe
respectivegenomepools.ParametersdescribingtheoperationofthisGAaresummarized
inTableS1.Attheendofthelifetimesimulation,Iassignthepredatorandpreygenomes
separatevaluesaccordingtothefunctions:
W
predator
=
2
;
000
X
t
=1
S

A
t
(4.1)
W
prey
=
2
;
000
X
t
=1
A
t
(4.2)
43
where
t
isthecurrentsimulationtimestep,
S
isthestartingswarmsize(here,
S
=50),
and
A
t
isthenumberofpreyagentsaliveatsimulationtimestep
t
.Itcanbeshownthat
thepredator(Eq.4.1)isproportionaltothemeankillrate
k
(meannumberofprey
consumedpertimestep),whiletheprey(Eq.4.2)isproportionalto(1

k
).Thus,
predatorsareawardedhighertnessforcapturingmorepreyfaster,andpreyarerewarded
forsurvivinglonger.Isimulateonlyaportionoftheprey'slifespanwheretheyareunder
predationbecauseIaminvestigatingswarmingasaresponsetopredation,ratherthana
feedingormatingbehavior.
OnceIevaluateallofthepredator-preygenomepairsinageneration,Iperform
proportionateselectiononthepopulationsviaaMoranprocess,allowtheselectedgenomes
toasexuallyreproduceintothenextgeneration'spopulations,incrementthegeneration
counter,andrepeattheevaluationprocessonthenewpopulationsuntilthegeneration
(1,200)isreached.
Iperform180replicatesofeachexperiment,whereforeachreplicateIseedtheprey
populationwithasetofrandomly-generatedMNsandthepredatorpopulationwithapre-
evolvedpredatorMNthatexhibitsrudimentaryprey-trackingbehavior.Seedingthepredator
populationinthismanneronlyservestospeedupthecoevolutionaryprocess,andhas
negligibleontheoutcomeoftheexperiment([79],FigureS1).
4.1.1Predatorandpreyagents
Figure4.1depictsthesensory-motorarchitectureofpredatorandpreyagentsinthissystem.
Thevisualsystemsensorsofbothpredatorandpreyagentsarelogicallyorganizedinto
\layers,"wherealayerincludes12sensors,witheachsensorhavingaofviewof15

andarangeof100virtualmeters(200virtualmetersforpredators).Moreover,eachlayeris
44
Figure4.1Anillustrationofthepredatorandpreyagentsinthemodel.Lightgreytriangles
arepreyagentsandthedarkgreytriangleisapredatoragent.Thepredatorandpreyagents
havea180

limited-distancevisualsystem(100virtualmetersforthepreyagents;200virtual
metersforthepredatoragent)toobservetheirsurroundingsanddetectthepresenceofthe
predatorandpreyagents.EachagenthasitsownMarkovNetwork,whichdecideswhere
tomovenextbasedofacombinationofsensoryinputandmemory.Theleftandright
actuators(labeled\L"and\R")enabletheagentstomoveforward,left,andrightindiscrete
steps.
45
attunedtosensingasptypeofagent.Sp,thepredatoragentshaveasingle-
layervisualsystemthatisonlycapableofsensingprey.Incontrast,thepreyagentshavea
dual-layervisualsystem,whereonelayerisabletosenseconspandtheothersenses
thepredator.(Inotethatthereisonlyasinglepredatoractiveduringeachsimulation,hence
thelackofapredator-sensingretinallayerforthepredatoragent.)
Regardlessofthenumberofagentspresentinasingleretinaslice,theagentsonlyknow
theagenttype(s)thatresidewithinthatslice,butnothowmany,representingthewide,
relativelycoarse-grainvisualsystemstypicalinswarmingbirdssuchasStarlings[76].For
exampleinFigure4.1,thefurthest-rightretinaslicehastwopreyinit(lightgreytriangles),
sothepreysensorforthatsliceactivates.Similarly,thesixthretinaslicefromthelefthas
bothapredator(darkgreytriangle)andaprey(lightgreytriangle)agentinit,soboththe
predatorandpreysensorsactivateandinformtheMNthatoneormorepredators
and
one
ormorepreyarecurrentlyinthatslice.Lastly,sincethepreynearthe4thretinaslicefrom
theleftisjustoutsidetherangeoftheretinaslice,thepreysensorforthatslicedoesnot
activate.Inotethatalthoughtheagent'ssensorsdonotreportthenumberofagentspresent
inasingleretinaslice,thisconstraintdoesnotprecludetheagent'sMNfromevolvingand
makinguseofacountingmechanismwhichreportsthenumberofagentspresentinaset
ofretinaslices.Onceprovidedwithitssensoryinformation,thepreyagentchoosesoneof
fourdiscreteactions:(1)staystill;(2)moveforward1unit;(3)turnleft8

whilemoving
forward1unit;or(4)turnright8

whilemovingforward1unit.
Likewise,thepredatoragentdetectsnearbypreyagentsusingalimited-distance(200
virtualmeters),pixelatedvisualsystemcoveringitsfrontal180

thatfunctionsjustlikethe
preyagent'svisualsystem.Similartothepreyagents,predatoragentsmakedecisionsabout
wheretomovenext,butthepredatoragentsmove3xfasterthanthepreyagentsandturn
46
Figure4.2Relationofpredatorattackcy(#successfulattacks/total#attacks)to
numberofprey.Thesolidlinewithtrianglesindicatessimulatedpredatorattack
asafunctionofthenumberofpreywithinthevisualofthepredator(
A
NV
).Similarly,
thedashedlinewitherrorbarsshowsthemeasuredsimulatedpredatorattack
giventhepredatorattacksagroupofswarmingpreyofagivensize,usingthe
A
NV
curve
todeterminetheper-attackpredatorattacksuccessrate.Errorbarsindicatetwostandard
errorsover100replicateexperiments.
47
correspondinglyslower(6

persimulationtimestep)duetotheirhigherspeed.
4.1.2Simulationenvironment
Iuseasimulationenvironmenttoevaluatetherelativeperformanceofthepredatorand
preyagents.Atthebeginningofeverysimulation,Iplaceasinglepredatoragentand50
preyagentsatrandomlocationsinsideaclosed512

512unittwo-dimensionalsimulation
environment.Eachofthe50preyagentsarecontrolledbyclonalMNsoftheparticularprey
MNbeingevaluated.IevaluatetheswarmwithclonalMNstoeliminateanypossible
ofselectionontheindividuallevel,e.g.,theherd"[40].
Duringeachsimulationtimestep,Iprovideallagentstheirsensoryinput,updatetheir
MN,thenallowtheMNtomakeadecisionaboutwheretomovenext.Whenthepredator
agentmoveswithin5virtualmetersofapreyagentitcansee,itautomaticallymakesan
attackattemptonthatpreyagent.Iftheattackattemptissuccessful,thetargetpreyagent
isremovedfromthesimulationandmarkedasconsumed.Predatoragentsarelimitedto
oneattackattemptevery10simulationtimesteps,whichiscalledthe
handlingtime
.The
handlingtimerepresentsthetimeittakestoconsumeanddigestapreyaftersuccessfulprey
capture,orthetimeittakestorefocusonanotherpreyinthecaseofanunsuccessfulattack
attempt.Shorterhandlingtimeshavenegligibleontheoutcomeoftheexperiment,
exceptforwhenthereisnohandlingtimeatall([79],FigureS2).
Toinvestigatepredatorconfusionasanindirectselectionpressuredrivingtheevolution
ofswarming,Iimplementaperceptualconstraintonthepredatoragent.Whenthepredator
confusionmechanismisactive,thepredatoragent'schanceofsuccessfullycapturingits
targetpreyagent(
P
capture
)isdiminishedwhenanypreyagentsnearthetargetpreyagent
arevisibleanywhereinthepredator'svisualThisperceptualconstraintissimilarto
48
previousmodelsofpredatorconfusionbasedonobservationsfromnaturalpredator-prey
systems[7,29,43],wherethepredator's
attack
(#successfulattacks/total#
attacks)isreducedwhenattackingswarmsofhigherdensity.
P
capture
isdeterminedbythe
equation:
P
capture
=
1
A
NV
(4.3)
where
A
NV
isthenumberofpreyagentsthatarevisibletothepredator,i.e.,anywherein
thepredatoragent'svisual
and
within30virtualmetersofthetargetprey.Byonly
countingpreynearthetargetprey,thismechanismlocalizesthepredatorconfusionto
thepredator'svisualsystem,andenablesmetoexperimentallycontrolthestrengthofthe
predatorconfusionAlthoughmypredatorconfusionmodelisbasedonthepredator's
visualsystem,itisqualitativelysimilartopreviousmodelsthatarebasedonthetotalswarm
size|e.g.,modelsofpredatorconfusionpresentedin[7,29,43,87]|inthatthereisagradual
(ratherthanimmediate)declineinpredatorattackencyasthepreygroupsizeincreases
(Figure4.2,dashedline).AsshowninFigure4.2(solidlinewithtriangles),thepredator
hasa50%chanceofcapturingapreywithonevisiblepreynearthetargetprey(
A
NV
=2),
a33%chanceofcapturingapreywithtwovisiblepreynearthetargetprey(
A
NV
=3),
etc.Asaconsequence,preyareinprincipleabletoexploitthecombinedofpredator
confusionandhandlingtimebyswarming.
4.2ofpredatorconfusion
Qualitatively,Iobservedtinpreybehavioroverthecourseofevolution
betweenswarmsexperiencingpredatorswithandwithoutpredatorconfusion.Figure4.3Ail-
49
Figure4.3Screencapturesof(A)dispersedpreyinaswarmhuntedbyapredatorwithout
predatorconfusion,(B)preyformingasingleelongatedswarmunderattackbyapredator
withpredatorconfusion,and(C)preyformingmultiplecohesiveswarmstodefendthemselves
fromapredatorwithpredatorconfusionafter1,200generationsofevolution.Blackdots
areprey,thetriangleisthepredator,thelinesprojectingfromthepredatorrepresentthe
predator'sfrontal180

visualandthestardenoteswhereapreywasjustcaptured.
50
lustratesthatpreyhuntedbyapredatorwithoutthepredatorconfusionmechanismdispersed
asmuchaspossibletoescapethepredator.Noreplicatescontainingapredatorwithout
predatorconfusionresultedinpreybehaviorthatresembledacohesiveswarm.Conversely,
whenevolutionoccurredwithpredatorconfusion,preyexhibitedcohesiveswarmbehaviorin
themajorityofthereplicates(70%ofmyreplicates).Figure4.3Bdepictsonesuchswarmin
whichpreyfollowtheconspdirectlyinfrontofthem,resultinginanelongatedswarm.
Similarly,Figure4.3Cshowsanotherswarmwherethepreycirclearoundtheirnearestcon-
spresultinginmultiplesmall,cohesiveswarmswiththepreyconstantlytryingto
circlearoundeachother.Bothoftheseswarmsevolvedasdefensivebehaviorstoexploitthe
predatorconfusion
Furthermore,predatorsexhibiteddivergenthuntingbehaviorswhenhuntingpreywith
andwithoutpredatorconfusion.AsseeninFigure4.3A,predatorsthatevolvedinthe
absenceofpredatorconfusion,andhencehadtocontendwithdispersedprey,simplytracked
thenearestvisiblepreyuntilitwascaptured,thenimmediatelypursuedthenextnearest
visibleprey.Ontheotherhand,predatorsthatevolvedinthepresenceofpredatorconfusion,
andhencewerechallengedwithcohesiveswarms,usedamechanismthatcausesthemto
attackpreyontheouteredgesoftheswarm.Thisstrategyissimilartoapredatorybehavior
observedinmanynaturalsystems[88,89],andelyminimizedthenumberofprey
inthepredator'svisualsystemandmaximizeditschanceofcapturingprey.Figure4.3B
demonstratesthisbehavior,wherethepredatorjustcapturedapreyonthetop-rightedge
oftheswarm(preycapturelocationdenotedbyablackstar).Videosoftheevolvedswarms
underpredationareavailableinthesupplementaryinformation([79],SIvideos1-5).
Toevaluatetheevolvedswarmsquantitatively,Iobtainedthelineofdescent(LOD)for
everyreplicatebytracingtheancestorsofthepreyMNinthepopulation
51
untilIreachedtherandomly-generatedancestralMNwithwhichthestartingpopulation
wasseeded(see[51]foranintroductiontotheconceptofaLODinthecontextofdigital
evolution).ForeachancestorintheLOD,Icharacterizedtheswarmbehaviorwithtwo
commonbehaviormeasurements:
swarmdensity
and
swarmdispersion
[78].Imeasuredthe
swarmdensityasthemeannumberofpreywithin30virtualmetersofeachotherovera
lifespanof2,000simulationtimesteps.Theswarm'sdispersionwascomputedbyaveraging
thedistancetothenearestpreyforeverylivingpreyoveralifespanof2,000simulationtime
steps.Together,thesemetricscapturedwhetherornotthepreywerecohesivelyswarming.
Figure4.4Ademonstratesthatthepreyhuntedbyapredatorwithonlyhandlingtime
(i.e.,withoutpredatorconfusion)movedclosetoeachotherbychancebutnevercoordinated
theirmovementatanypointintheirevolutionaryhistory(meanswarmdensity

1standard
erroracross180replicates:0
:
69

0
:
02).Incontrast,whenhuntedbyapredatorwith
predatorconfusion,thepreycoordinatedtheirmovementtoremainclosetoeachotherand
formaswarm(meanswarmdensity12
:
48

0
:
8atgeneration1,200).Likewise,Figure4.4B
showsthatintheabsenceofpredatorconfusion,preyevolvedtomaximizetheirdispersion
(meanshortestdistance46
:
69

0
:
44atgeneration1,200),whereaswithpredatorconfusion,
preyevolvedincreasinglycohesiveswarmbehavior(meanshortestdistance22
:
54

1
:
32at
generation1,200).Takentogether,theseresultsthatpredatorconfusionprovideda
tselectionpressuretoevolvecohesiveswarmingbehaviorinthismodel,eventhough
theswarmingpreyactuallyexperienceanincreasedattackratefromthepredatordueto
thisbehavior(see[79],FiguresS3&S4).
Figure4.4Cshowsthatasaresultoftheseevolutionarytrends,thecohesiveswarms
thatevolvedunderpredatorconfusionexperiencedtlyhighersurvivorshipthan
swarmsthatevolvedwithoutpredatorconfusion(34
:
7

0
:
6and25
:
54

0
:
49preysurviving
52
Figure4.4Meanswarmdensity(A),swarmdispersion(B),andsurvivorship(C)within
theswarmoverallreplicatesoverevolutionarytime.Theswarmdensitywasmeasuredby
themeannumberofpreywithin30virtualmetersofeachotheroveralifespanof2,000
simulationtimesteps.Swarmdispersionwasmeasuredbythemeandistancetothenearest
preyforeverylivingpreyoveralifespanof2,000simulationtimesteps.Survivorshipwithin
theswarmwasmeasuredasthemeannumberofsurvivingprey(outofaninitialtotalof
50)attheendofthesimulationatagivengeneration.Preyhuntedbyapredatorwith
predatorconfusion(blackcircleswithafullline)evolvedtomaintaintlyhigher
swarmdensityandtlylessdispersedswarmingbehaviorthanpreyintheswarms
huntedbyapredatorwithoutpredatorconfusion(greytriangleswithadashedline).Asa
result,tlymorepreysurvivedintheswarmshuntedbyapredatorwithpredator
confusionthantheswarmshuntedbyapredatorwithoutpredatorconfusion.Errorbars
indicatetwostandarderrorsacross180replicateexperiments.
53
thesimulations,respectively).Thisincreasedsurvivorshipthatswarmingbehavior
confusedthepredator,leadingtofewersuccessfulpreycaptures.Ifoundtheseresultsrobust
toavarietyofexperimentalparameters,includingweakerpredatorconfusion([79],
FigureS5&S6)andapplyingaminimumthresholdtopredatorattack([79],Figure
S7).
4.3Evolvedpredatorandpreybehavior
Todeducehowswarmsemergeinmymodelfromindividual-levelbehaviors,Inextdeter-
minedthefunctionalityoftheevolvedpredatorandpreyMNs.Iaccomplishedthisby
visualizingtheMNconnectivitytodiscernwhichslicesofthevisualsystemandmemory
nodesoftheMNwerecausallyconnected,thencreatedatruthtablefromtheMNmapping
everypossibleinputcombinationwithitscorrespondingmost-likelyoutputfromtheMN.
Withthisinput-outputmapping,IcomputedtheminimaldescriptivelogicoftheMNwith
LogicFriday,ahardwarelogicminimizationprogram.Iusedthemost-likelyoutputfor
everyinputcombinationduetothestochasticnatureofMNs,thereforethefunctionalityI
determinedwasthe
most-likely
behaviorofthepredatororprey.
Inallofmyexperiments,thepreyatgeneration1,200ignoredthepresenceofpredators
andinsteadonlyreactedtothepresenceofconspintheirvisualsysteminorderto
followtheotherpreyintheswarm.Thisresultwasparticularlystrikingbecauseitsuggested
thatpreycanevolveswarmingbehaviorinresponsetopredationwithouttheabilitytosense
thepredatorshuntingthem,whichwassuggestedinapreviousstudy[24].Iobservedthat
thepreyevolvedawidevarietyofsimplealgorithmsthatexhibitedadiversityofemergent
swarmingbehaviors,rangingfrommoderatelydispersed,elongatedswarmssimilartoStar-
54
lingmurmurations(Figure4.3B)totightly-packedcohesiveswarmsreminiscentofshbait
balls(Figure4.3C).
Asforthepredators,theevolvedbehaviorIobservedatgeneration1,200withpredator
confusionappearedtoberathercomplex:Thepredatorsavoideddenseswarmsandhunted
preyoutside,orontheedge,oftheswarm.However,thealgorithmunderlyingthisbehav-
iorwasrelativelysimple,whichallowedforthepredatorstoevolvethishuntingbehavior
fairlyearlyinthesimulations.Thepredatorswatchedonlythetwocenterretinaslicesand
constantlyturnedinonedirectionuntilapreyenteredoneofthoseslices.Onceaprey
becamevisibleinoneofthecenterretinaslices,thepredatormovedforwardandpursued
thatpreyuntilitmadeacaptureattempt.Thisprocesswasrepeatedregardlessofwhether
thepredatorsuccessfullycapturedtheprey.Thesimplicityofthepredatoralgorithmand
relativesimplicityofthepreyalgorithmssupportstheofearlierdigitalswarmstud-
iesthatcomplexswarmbehaviorscanbedescribedbysimplerulesappliedoveragroupof
locally-interactingagents[64,73].
4.4Eco-evolutionarydynamics
Predatorconfusionhasbeenhypothesizedtobenotonlyaselectivepressurefavoringswarm-
ing,butalsoasadeterminantofthe
functionalresponse
[43],i.e.,thenumberofpreycon-
sumedbythepredatorasafunctionofpreydensity[90].Figure4.5supportsakeyprediction
offunctionalresponsetheory:Bothwithandwithoutpredatorconfusion,thesystemdis-
playedaTypeIIfunctionalresponse(asaturatingofpreydensity),butwhenpredator
confusionwaspresentthefunctionalresponseshowedalowerplateau(24
:
01

0
:
49prey
consumedwithoutpredatorconfusion;15
:
18

0
:
57withpredatorconfusion).Thefactthat
55
Figure4.5Functionalresponsecurvesofcohesiveswarmshuntedbyapredatorwithpreda-
torconfusion(blackcircleswithafullline)anddispersedswarmshuntedbyapredatorwith-
outpredatorconfusion(greytriangleswithadashedline).Theevolved,cohesiveswarms
huntedbyapredatorwithpredatorconfusionresultinaTypeIIfunctionalresponsewitha
loweredplateau.Errorbarsindicatetwostandarderrorsacross180replicateexperiments.
therewasaTypeIIfunctionalresponseevenintheconditionwithoutpredatorconfusion
wastheresultofanadditionalconstraintpresentinbothconditions:Thehandlingtimethat
wasimposedonthepredatorafterpreycapturebeforeitcanattackagain.Additionally,
whenIvariedthehandlingtimeinmyexperiments,Ifoundthatincreasingthehandling
timealsolowerstheplateauoftheTypeIIfunctionalresponse([79],FigureS9).
Modelingfunctionalresponsehasbeenanimportantprobleminecology[91],andiscriti-
calforconstructingaccuratemodelsthatcapturethedynamicsofpredator-preyinteractions
overecologicalandevolutionarytime[92].Iprovidedevidenceherethatpredatorconfusion
hastonfunctionalresponsethatarenotcapturedintraditionalmodels[43].
Mostofthesetraditionalmodels,includingtheoriginalformulationofHolling[42],capture
theecologicalinteractionbetweenpredatorandprey.Evolutionisassumedtoshapethebe-
56
havioralstrategiesandconstraintsthatpredator-preydynamics,butonlyrecently
havebiologistsbeguntoexplicitlystudythedynamicsofpredator-preyinteractionsover
bothecologicalandevolutionarytime[44].IhaveshownthataTypeIIfunctionalresponse
evolvesevenwhenitisnotdirectlyselectedfor,andtheshapeofthefunctionalresponse
canbeattributedtospcconstraintssuchashandlingtimeandpredatorconfusion.
4.5Coevolutionbetweenpredatorvisualsystemsand
preybehavior
Intheprevioussections,Iimplementedpredatorconfusionbyimposingaperceptualcon-
straintthatreducestheprobabilityofsuccessfullycapturingpreyifoneormorepreynear
thetargetpreyarevisibletothepredator.Thisismeanttosimulatethey,arising
fromattentionalorcognitivelimitations,thatabiologicalpredatormighthaveinchoosing
amongmultipleavailablepreyatthemomentofattack.Toexaminetheofrelaxing
thisconstraint,Icoevolvedthepredatorandpreyagainandexperimentallyreducedthesize
ofthepredator'sofview.Thisprocedurereducesthepossibilitythatmultipleprey
canbedetectedatthemomentofattack,therebyreducingtheprobabilityofconfusion.For
example,experimentallydecreasingthepredator'sofviewfrom180

to60

decreases
bytwo-thirdstheareawithinwhichthepresenceofmultiplepreycanconfusethepredator.
Figure4.6demonstratesthatwhenthepredator'svisualsystemonlycoveredthefrontal
60

orless,swarmingtoconfusethepredatorwasnolongeraviableadaptation(asindicated
byameanswarmdensityof0
:
68

0
:
02atgeneration1,200).Inthiscase,thepredatorhad
suchanarrowviewanglethatfewswarmingpreywerevisibleduringanattack,which
minimizestheconfusionandcorrespondinglyincreasesitscapturerate([79],Figure
57
Figure4.6Meanswarmdensityatgeneration1,200asafunctionofpredatorviewan-
gle.Swarmingtoconfusethepredatorwasanebehaviorifthepredator'svisual
coveredonlythefrontal60

orless,duetothepredator'sfocusedvisualsystem.As
thepredator'svisualldwasincrementallyincreasedtocoverthefrontal90

andbeyond,
predatorconfusionviaswarmingagainbecameaneanti-predatorbehavior,asev-
idencedbytheswarmsexhibitingtlyhigherswarmdensityatgeneration1,200.
Errorbarsindicatetwostandarderrorsacross180replicateexperiments.
58
Figure4.7SwarmdensityandpredatorviewanglefromtheLODofasinglecoevolution
experiment.Thepredatorandpreypopulationsappeartocontinuallycyclebetweent
statesofviewanglesandbehaviors.
S8).Asthepredator'svisualsystemwasincrementallymodtocoverthefrontal120

andbeyond,swarmingagainbecameaneadaptationagainstthepredatorduetothe
confusion(indicatedbyameanswarmdensityof6
:
13

0
:
76atgeneration1,200).This
suggeststhatthepredatorconfusionmechanismmaynotonlyprovideaselectivepressurefor
thepreytoswarm,butitcouldalsoprovideaselectivepressureforthepredatortonarrow
itsviewangletobecomelesseasilyconfused.
Thisopensthepossibilityforcoevolutionbetweenthepredator'svisualsystem
andthepreyswarmingbehavior.Toexplorethispossibilityfurther,Iranthepredator-prey
coevolutionexperimentsagain,butthistimeallowingmutations(with5%probability)to
theviewangleofthepredator'sWhenamutationoccurstothepredator
viewangle,arandomnumberbetween[-50.0,50.0]isaddedtothe
viewangle.Thus,mutationscanwidenorshrinkthepredator'sviewangleinlargeorsmall
steps.
AtypicalcoevolutionaryexperimentisdepictedinFigure4.7.Surprisingly,thepredator
andpreypopulationsappeartocontinuallycyclebetweentstatesofviewangles
andbehaviors,respectively,suchthatthereisatnegativecorrelationbetweenthe
59
Figure4.8Pearson's
r
betweenswarmdensityandpredatorviewanglefromtheLODs
of30coevolutionexperiments.Allcoevolutionexperimentshaveanegativecorrelation
betweenswarmdensityandpredatorviewangle,indicatingthatwhenswarmdensitygoes
up,predatorviewanglegoesdownandviceversa.
P<
=0
:
001forallcorrelations.
predatorviewangleandswarmdensityacrossall30coevolutionexperiments(Figure4.8).
Thisissurprisingbecausethepredatorpopulationcanely\defeat"theswarm-
ingpreypopulationbyshrinkingtheirvisualsystemtothepointthatthepreywillnolonger
evolvetoswarm.Whythenwouldthepredatorpopulationevolvetowidentheirvisualsys-
temagain,allowingthepreypopulationtoagainevolveswarmingbehaviortoreducethe
predators'attack
Theanswertothisquestionliesinthepredators'attackwhenthepreyareno
longerswarming.ShowninFigure4.9,whenpredatorswithvaryingviewanglesare
competedagainstdispersiveprey,predatorswithwidervisualsystemsaremorelikelyto
apreyanywhereintheirvisualsystematanytime.Further,Figure4.10demonstrates
thatpredatorswithwidervisualsystemsarealsomorelikelytodispersivepreyina
60
Figure4.9Numberofsimulationtimestepsthatpreyarepresentanywhereinanevolved
predator'svisualsystemdependingonthepredator'sviewangle.Thepredatoriscompeted
againstdispersiveprey.Predatorswithhigherviewanglesaremorelikelytohaveprey
anywhereintheirvisualsystematagiventime.
P<
=0
:
001betweenallviewangles,
Kruskal-Wallismultiplecomparison.
Figure4.10Numberofsimulationtimestepsthatpreyarevisibleinaportionofanevolved
predator'svisualsystemthatitpaysattentionto,dependingonthepredator'sviewangle.
Thepredatoriscompetedagainstdispersiveprey.Predatorswithhigherviewanglesaremore
likelytospotpreyatagiventime,whichincreasestheirforaging.
P<
=0
:
001
betweenallviewanglesexcept180vs.210,Kruskal-Wallismultiplecomparison.
61
Figure4.11Fitnessofanevolvedpredatorwhencompetedagainstdispersiveprey,depend-
ingonthepredator'sviewangle.Predatorswithhigherviewanglesforageforpreymore
tly,thuscapturingmorepreyintheirlifetimeandimprovingtheir
P<
=0
:
001
betweenallviewanglesexcept150vs.180and180vs.210,Kruskal-Wallismultiplecom-
parison.
portionoftheirvisualsystemthattheypayattentionto,whichmeanstheyspendlesstime
searchingforprey.Thus,theincreasedforagingiencythatwidervisualsystems
predatorsagainstdispersivepreyresultsinhigherpredator(Figure4.11).These
pointtoathatnaturalpredatorslikelyexperiencewhenhuntingprey:
Wider,less-focusedvisualsystemsaremoreusefulforinitiallyspottingprey,butfocused
visualsystemsarebetteradaptedfortrackinganindividualpreydownandavoidingthe
ofpredatorconfusionwhenhuntingpreyingroups.
4.6Discussion
Idemonstratedthatswarmingevolvesasanemergentbehaviorinpreywhenasimpleper-
ceptualconstraint|predatorconfusion|isimposedonthepredator.Further,Ifoundthat
62
measuringswarmdensityandswarmdispersion,proposedin[78],servesasanesub-
stituteforqualitativelyassessingeveryswarmtodetermineifcohesiveswarmingbehavior
ispresent.Adiversecollectionofpreyswarmingbehaviorsevolvedinmymodel,suggesting
thatpredatorconfusioncouldallowforawiderangeofswarmingbehaviorstoevolve.Strik-
ingly,mostevolvedpreystrategiesusedalgorithmsthatrespondedtootherprey,butnot
totheattackingpredators.Thisraisestheinterestingquestionofwhatselectionpressures
wouldfavortheevolutionofpreythatdetectandrespondtothepredatorsthemselves.
Incontrasttothediversityofevolutionaryoutcomesforprey,acommonbehavioral
strategyemergedamongthepredatorswhenevolvedintheconfusioncondition.Namely,
theevolvedpredatorsfocusedonattackingpreyonthevulnerableedgesoftheswarms,which
isaphenomenoncommonlyobservedinnature[88,89].
Modelingfunctionalresponsehasbeenanimportantprobleminecology[91],andiscriti-
calforconstructingaccuratemodelsthatcapturethedynamicsofpredator-preyinteractions
overecologicalandevolutionarytime[92].Iprovidedevidencethatpredatorconfusionhas
tonfunctionalresponsethatarenotcapturedintraditionalmodels[43].
Mostofthesetraditionalmodels,includingtheoriginalformulationofHolling[42],capture
theecologicalinteractionbetweenpredatorandprey.Evolutionisassumedtoshapethebe-
havioralstrategiesandconstraintsthatpredator-preydynamics,butonlyrecently
havebiologistsbeguntoexplicitlystudythedynamicsofpredator-preyinteractionsover
bothecologicalandevolutionarytime[44].IhaveshownthataTypeIIfunctionalresponse
evolvesevenwhenitisnotdirectlyselectedfor,andtheshapeofthefunctionalresponse
canbeattributedtospcconstraintssuchashandlingtimeandpredatorconfusion.
IalsofoundthatIcouldreducetheadvantageofswarmingbydiminishingthepredator's
ofview,hencedecreasingthelevelofconfusionthepredator.Thissuggests
63
Figure4.12Diagramdepictingtheobservedcoevolutionarycyclebetweenthepredatorand
preyinthepresenceofthepredatorconfusion
thatpredatorconfusioncouldimposeaselectivepressureontheshapeofthepredator's
visualsystem:Onceswarminghasevolvedintheprey,selectionwillfavorpredatorsthat
arenolongerconfusedbyswarms.FollowingthetrendinFigure4.6,Iexpectedselection
tofavorpredatorswithanarrower,morefrontallyfocusedvisualsystem,asobservedinthe
visualsystemsofmanynaturalpredators[93].
Inthesectionofthischapter,Idirectlyexploredtheabovehypothesisandfound
mypredictiontobepartlytrue:AsdemonstratedinFigure4.7,selectiondoesindeedfavor
predatorswithamorefocusedvisualsystemonceswarminghasinvolvedinprey.However,
oncethepredatorsevolveafocusedvisualsystem,thepreyevolvedispersivebehaviorin
responseandacoevolutionarycyclecommencesbetweenthepredatorvisualsystemand
preybehaviorinmymodel.Generally,researchersassumethattheevolutionofcollective
behaviorisaone-waystreet,i.e.,collectivebehaviorissoevolutionarilyadvantageousthata
specieswouldonlyevolveincreasinglycollectivebehavior[94].Thesedemonstrate
acoevolutionarycyclethatcouldoccurbetweennaturalpredatorsandpreyduetothecon-
64
fusionshowninFigure4.12.Asapartofthiscoevolutionarycycle,Idiscovereda
conditionunderwhichthepreypopulationsconsistentlyevolvedawayfromcollectivebehav-
ior.Thisexperimentthereforehighlightsonepossiblemechanismthroughwhichcollective
behaviorcouldbelostevolutionarily.
65
Chapter5
ManyEyesHypothesis
Inthischapter,Ifocusonanti-predatorvigilance(i.e.,themanyeyeshypothesis)asapos-
sibleselectivemechanismfortheevolutionofgregariousforagingbehavior,andcontrolfor
theoftheotherbedescribedinChapter2.1.Iassumethatvigilancehas
b(e.g.,communicatingthepresenceofapredatorviaalarmsignals)butalsocosts
(e.g.,reducedforagingratesbywatchingforthepredator).Underthemanyeyeshypothesis,
groupingisbbecauseitreducesthecostofvigilancebysharingthecostofvigilance
amongthegroup,butitmayhaveadditionalcoststhatmustbeconsidered,e.g.,increased
predationratesonlargergroups[95].Furthermore,thisbwouldbedilutedifsomein-
dividualscanfreeloadonthevigilanceofothers(asinheterogeneousgroups),but
ifthegroupmembersarehighlyrelated.Thebandcostswouldalsobebythe
lifehistoryoftheprey,inparticularwhethertheirreproductionisiteroparous(i.e.,repeated)
orsemelparous(i.e.,allatonce):Vigilancemaybemorebinsemelparouspreybe-
causeapredationeventcancompletelypreventthemfromreproducing,whereasiteroparous
preyaremorelikelytohavereproducedatleastoncepriortoexperiencingapredationevent.
Toexploretheseissues,Imanipulatethegeneticrelatednessandreproductivestrategyof
groupsofpreythatareunderpredationandobservetheresultingbehaviorafterthousands
ofgenerationsofdigitalevolutionhavetakenplace.Apreliminaryinvestigationofthiswork
waspublishedintheALIFE14conference[96],andhasbeentlyextendedinthis
chapter.
66
Figure5.1
Depictionofthedisembodiedsimulation.
Preyseektoforageasmuchas
possiblewhileavoidingbeingcapturedbythepredator.Ifnoneofthepreyinthegroupare
vigilant,thetargetpreyiscaptured100%ofthetime.
Thischapterproceedsasfollows.First,IdescribethedetailsofthedigitalmodelthatI
usedinthisproject.Next,Idescribetheresultsfromthemodelandexplainwhatconditions
selectfortheevolutionofgregariousforagingbehavior.Finally,Iconcludethechapterby
discussingsomeofthebroaderimplicationsoftheinthischapter.
5.1Modelofpredator-preyinteractions
Figure5.1depictsmymodelofpredator-preyinteractionsinadisembodiedmodel,wherein
preymustbalancethebetweenforagingandvigilance[13].Inanembodiedmodel,
everyanimatissituatedintheworld,perceivestheworldviaitssensors,andcanacton
theworldviabehavioralorotherresponses[97].Whileembodiedmodelsmoredetail
andcancapturepotentiallyimportantaspectsoftherealworld,theyarealsosensitiveto
implementation-spdetailsofthesensorsandactuators,whichcanskewtheresults.I
thereforefocusonadisembodiedmodel
1
fortheremainderofthisstudy,whichenablesme
toexploreseveralfactorstheevolutionofgroupvigilanceinisolation.
1
Modelcode:https://github.com/phaley/eos/tree/non-embodied
67
Inthismodel,preyisdirectlyrelatedtotheamountoftimeitspendsforaging,
whereasingleroundofforagingincreasespreyby1.0.However,preyvigilance
determineswhetherapredator'sattackonthepreyissuccessful.Thesetwooptions|
foragingandvigilance|areassumedtobemutuallyexclusive.Thus,preymustevolveto
maximizetheirfoodintakewhileremainingvigilantenoughtosurvivetheentiresimulation,
whichisakintothemaximumpossiblelifespanoftheprey.
5.1.1Simulationofpredatorsandprey
Idesignedthismodeltocapturecertainfeaturesofnaturalpredatorsandtocontrolfor
potentiallycomplicatingfactors.First,toensurethatpredatorattacksarenottrivially
predictableIsimulatepredatorsthatattackatintervalsthatarenormallydistributedaround
aspattackrate.Thus,predatorattacksarerandomlydistributedthroughoutthe
2,000-time-stepdurationofthesimulation.Tomodeltheobservationthatlargergroupsof
preyoftenattractmoreattacksfrompredators|arealisticcostofgrouplivingknownas
the
attractionct
[95]|Iscalethisattackratewiththegroupsize,suchthatthegroup
experiences5predatorattacksforeverypreyinitiallyinthegroupoverthecourseofthe
simulation.Thisscalingfactoralsoallowsmetocontrolforthe
dilutionct
,whichhas
beensuggestedtoallowpreytosurvivewithlowervigilancelevelsinlargergroupsonly
becausetheyarelesslikelytobethetargetofapredator'sattack[17,98,99].
Eachtimeapredatorappears,Irandomlyselectatargetpreyfromthesurvivingprey
ofpreviousattacks.Thisisfollowedbya10timestepdelaybetweentheappearanceofthe
predatorinthesimulationandtheactualattack,representingthetimeittakesforapredator
toclosethedistancetotheprey.Itisduringthistimethatpreyvigilancebecomesimportant.
Ifthetargetpreyisvigilantatanytimeduringthisinterval,thenitspotsthepredatorand
68
theattackhasonlya10%chanceofsuccess.Ifthetargetpreyisnotvigilantbutoneor
moreotherpreyinthegrouparevigilant,thentheotherpreycommunicatethepresenceof
thepredatorviaanalarmsignalorotherbehavioralindicatorandthepredatorwillcapture
thetargetprey30%ofthetime.Theseprobabilitiesarechosenbasedonanalyticalmodels
ofgroupvigilance[13]suchthatgroupvigilanceisnotaseasindividualvigilance,
andmodelstheimperfectcommunicationbetweenmembersofthegroup[100].Finally,if
nomembersofthegrouparevigilantwhilethepredatorisclosingthedistancetoitstarget,
thentheentiregroupisunawareofthepredatorandtheattackwillsucceed100%ofthe
time.Inallcasesofasuccessfulattack,thetargetpreyisremovedfromthesimulationand
cannolongerforagetoincreaseits
Eachindividualpreymakesthedecisiontoforageorbevigilanteverysimulationtime
step.Thisdecision-makingprocessismodeledwitha
MarkovNetwork
(MN),whichisan
brain"thatcanstochasticallymakedecisionsbasedonsensoryinput,memory,
andpreviousactions[79,86,101].EverypreyMNisencodedbyalistofnumbersknown
asitsgenotype,suchthatchangestothegenotypecanresultinchangesinthefunctionof
theMN.BecauseIdonotprovideanysensoryinputtothepreyinthissimulation,Iam
elymodelingtheprobabilityofapreytakinganaction(e.g.,bevigilantorforage?)
everysimulationtimestep.MoreinformationonMNs|includingdetailsontheirgenetic
encoding,mutationaloperators,andfunctionality|isavailableinChapter2.3.
5.1.2Evolutionaryprocess
Atthebeginningofeveryexperiment,Icreateapopulationof100individualswithrandom
MarkovNetworks.Irepeattheevaluationproceduredescribedaboveuntilall100individu-
alsintheGeneticAlgorithm(GA)populationhavebeenassigneda(see,e.g.,[75]for
69
afulldescriptionofGAs).OnceallindividualshavebeenassignedaIuse
proportionalselectionaccordingtoaMoranprocess[77]toproducethenextgeneration's
populationofprey.Fitness-proportionalselectionensuresthatpreywithhigherval-
uesgenerallyproducemoreTheselectedpreyreproduceasexually,withasmall
probabilityofmutations(0.5%persite)theirgenotype.Irepeatthis
evaluation-selection-reproductionprocessfor2,500generationstoensurethattheGAhas
reachedanevolutionarilystablestrategy[102]andreplicatetheexperiments100timesfor
eachtreatment|eachwithadistinctrandomnumbergeneratorseed|toverifythatIam
capturingevolutionarytrendsratherthanoutlierscenarios.
5.1.3Groupsize
Sincethemanyeyeshypothesispredictsaninverserelationshipbetweenindividualvigilance
andgroupsize[22,15],Istudypreypopulationsacrossarangeofgroupsizes:5,10,25,and
50.Inmyearlyexperiments,Iobservetheequilibriumvigilancelevelswhenpreyareforced
togroup.Inmylaterexperiments,Irelaxthisassumptionandallowthepreytochooseto
group(ornot)everytimestep.Inthelattercase,Ireportthegroupsizeasthemaximum
initialgroupsize.Toprovideabaselinefortheoptionalgroupingexperiment,Icompare
itsequilibriumvigilancelevelstothatofexperimentswherepreyareforcedtogroupand
experimentswherepreyareforcedtoforageindividually.
5.1.4Geneticrelatedness
Foralloftheaboveexperiments,Istudytheofgeneticrelatednessongroupvigilance
behavior.Giventhatgeneticallyrelatedorganismsaremorelikelytocooperatewitheach
70
otherthangeneticallyunrelatedorganisms[103],Iexpectthatgeneticrelatednesswithin
thegroupwillplayacriticalroleintheevolutionofgroupvigilancebehavior.Toexplore
thetwoextremesofgeneticrelatedness,Iformgroupsintworentways.
In
homogeneousgroups
,eachindividualintheGApopulationisevaluatedseparately.
Duringanindividual'sevaluation,Ilthegroupinthesimulationwithexactcopies
oftheindividual,andtheforthatindividualistheaverageofallofitscopies
attheendofthesimulation.Thus,foraGAwithapopulationsizeof100individuals,Irun
100simulationseverygenerationtoacquirethetnessforeachindividual.
In
heterogeneousgroups
,IuseasubsetoftheGApopulation(whichcontainsmany
preywithtgenetics)tostudyhowthepreyfareindirectcompetition(orcooperation)
witheachother.Whenformingaheterogeneousgroup,Irandomlysampleindividualsfrom
theGApopulationwithoutreplacementuntilIreachthedesiredgroupsizeforthecurrent
treatment.Thisgroupisthenevaluatedinthesimulation,whereeachindividualhasonlyone
copythatisassignedaOncethesimulationItheevaluatedindividuals
sotheyarenotevaluatedagaininthatgeneration.Sincethedesiredgroupsizes(5,10,25,
and50)arealwayssmallerthantheGApopulationsize(100),thisprocedureisrepeated
untilallindividualshavebeenevaluated.Forexample,ifthedesiredgroupsizeis25and
theGApopulationiscomposedof100individuals,thentherandomly-group-and-evaluate
procedureisrepeated4times.Thus,byfollowingthisprocedure,allindividualsintheGA
populationareevaluatedonlyoncepergenerationinarandomly-assignedgroup.
Sincevigilanceindirectlybthevigilantindividualinhomogeneousgroupsbyaiding
itskin,Iexpectthatgroupvigilancewillbehighlybeninhomogeneousgroups.In
contrast,becausethevigilanceofonepreycanpotentiallyaidarivalpreyinheterogeneous
groups,Iexpecttoobservelowerlevelsofvigilanceinheterogeneousgroups.
71
5.1.5Reproductivestrategy
Thebofmakingtherightdecisioninthissimulatedenvironmentarestraightforward:
Thepreymustmaximizefoodintakebysurvivingthelongestwhileminimizingthetime
spentbeingvigilant.Butthecostofmakingthewrongdecisioncanalsodependonthe
lifehistoryoftheprey.Forexample,twotreproductivestrategies|semelparity
anditeroparity|shouldincurtcosts.Semelparousorganismssitononeendofthe
reproductivespectrumandarecharacterizedbyasinglereproductiveeventpriortodeath.
Ontheotherendofthereproductivespectrum,iteroparousorganismscontinuallyreproduce
throughouttheirlifetime.Iexplorethesetwoextremesbysimulatingsemelparousand
iteroparouspreyinseparatetreatments.
Whensimulating
semelparous
preyinmymodel,Iassumethattheirreproductiveevent
occursattheendofthesimulation.Therefore,ifasemelparouspreyisconsumedbythe
predatorbeforetheendofthesimulation,allofitsgatheredfoodcountsfornothing:itwill
leaveno
Whensimulating
iteroparous
preyinmymodel,Iassumethatthepreyareconstantly
reproducingthroughouttheirlifetime.Thereforewhenapredatorconsumesaniteroparous
prey,thepreycannolongerincreaseitsssviaforaging,butanyfooditgatheredprior
toitsdeathcountstowarditsforthesimulation.
Inotethatthesearehighlyedimplementationsofreproductivestrategiesand
aremeanttocaptureonekeyvariable:theprobabilityofreproductionoccurringbefore
apredationevent.Ihypothesizethattheincreasedriskofgeneticdeathintroducedby
thesemelparoustreatmentwillprovideanevolutionaryincentiveforpreytoinvestinvig-
ilance,whereaspreyintheiteroparoustreatmentwillbemorelikelytoengageinrisky,
72
non-cooperativebehaviorbecausetheirdemisedoesnotnecessarilydoomtheirgeneticlin-
eage[104].
5.1.6Explicitcostofgrouping
Themodeldescribedsofarincludesacostofvigilance(insofaraspreycannotforageatthe
sametimethattheyarevigilant),butthereisnoexplicitcosttochoosingtogroupaside
fromthepossibilityofaidingacompetingindividual.Inatreatment,Iimplementsuch
agroupingpenaltyinordertomodeltherealisticconstraintsoflimitedresourcesandthe
resultingscramblecompetitionforfood[105,50,98,106].Thisgroupingpenaltyisonly
assessedonpreywhochoosetoforageinthegroup,anddecreasestheamountoffoodthey
receiveinthatsimulationtimestepproportionaltothenumberofpreyinthegroup.The
groupforagingpenaltyisimposedaccordingtotheequation:
Food=
1
:
0
M

G
(5.1)
where
G
isthenumberofpreyinthegroupand
M
isthepenaltymultiplierthatallowsme
toexperimentallycontroltheseverityofthepenalty.Giventhispenalty,preyforagingin
largergroupsreceivelessfoodeverytimetheyforage,butpotentiallyenjoythebof
groupvigilance.
5.2Forcedgrouping
Ievolvedthevigilancebehaviorofpreybysubjectingthemtopredationunderavarietyof
treatmentsthatvaryreproductivestrategyandgroupcomposition.Vigilanceismeasuredas
73
Figure5.2
Treatmentcomparisonwhenpreyareforcedtoforageingroups.
Both
grouphomogeneityandasemelparousreproductivestrategyselectforhighlevelsofvigilance.
However,onlyhomogeneousgroupsexperienceanincreaseintnessasgroupsizeincreases.
Incontrast,vigilancebehaviorbreaksdowninlarger,heterogeneousgroupsofsemelparous
prey.Errorbarsindicatebootstrapped95%intervalsover100replicates;some
errorbarsaretoosmalltobevisible.
thepercentchancethatapreywillbevigilantatagivenmomentintime,averagedacrossall
ofthepreyinthepopulation.Thesetreatmentsarerepeatedacrossawiderangeofgroup
sizes,allowingmetostudynotonlywhethertheselectionforvigilancecanbegeneralized
togroupsofvaryingsizes,butalsowhetherIcanobservetheinverserelationshipbetween
groupsizeandvigilancepredictedbythemanyeyeshypothesis.
Inmyexperiment,allpreyinthesimulationareforcedtoforageinthesamegroup,
andtheonlytraitthatisevolvingisthepreydecisiontobevigilantornotateverytimestep.
Undertheseconditions,Ithatpreylivinginhomogeneousgroupsconsistentlyevolve
higherlevelsofvigilancethantheircounterpartslivinginheterogeneousgroups(Figure5.2).
Thissuggeststhatorganismslivingingroupswithhighgeneticrelatednessaremore
likelytoevolvecooperativestrategies.Thus,inmymodelasinmanynaturalsystems,
gregariousforagingismostfavorablewhengeneticinterestsarealigned.
Figure5.2alsoshowsthatsemelparouspreyaremorelikelytoevolvevigilantstrategies
thaniteroparousprey.Thisisbecausesemelparityselectsmorestronglythaniteroparityfor
successfulevasionofpredatorattacks,sincepreydeathnegatesallpreviousforaging
74
insemelparousprey.Thiseisseenacrossbothhomogeneousandheterogeneousgroups,
indicatingthatsemelparityisastrongenoughselectivepressuretoactindependentlyof
groupgeneticcomposition.Importantly,preyvigilancedoesnotevolveatallintheabsence
ofpredation(FigureS1),andgraduallyreducingthepredationrateleadstoacorrespondingly
gradualdecreaseinpreyvigilancelevels(FigureS2).Therefore,Iknowthattheselection
pressureimposedbypredationistheprimarydrivingforcebehindthisevolvedvigilance
behavior.
Allthreetreatmentsthatevolveanylevelofvigilancealsoseetheprevalenceofvigilance
decreaseasgroupsizeincreases.Thispatternisimportantbecauseitmatchesthepattern
predictedbythemanyeyeshypothesis:Asgroupsizeincreases,individualsareabletorely
moreoncollectiveratherthanindividualvigilanceandcaninturndevotemoreoftheir
owntimetoforaging.SinceIusearelativeattackratethatscalesthepredator'sattack
frequencywithgroupsize,thisphenomenonmustbecausedbygroupvigilanceandnot
thedilution(i.e.,fewerattacksperindividualinlargergroups)citedinotherstudies.
Inotethatvigilanceintheheterogeneous/semelparoustreatmentappearstoevolveaway
almostentirelyinagroupsizeof50.Toexplainwhythistrendmightbeduetosomething
otherthancollectivevigilance,Icaninsteadlookattrendsintheofthepopulations.
IobserveseveralinterestingtrendswhenIlookattheofgroupsizeonaverage
groupInbothhomogeneoustreatments,thereisasteadyincreaseinwithin-
creasinggroupsize,suggestingthatgregariousforagingbehaviorisunderpositiveselection.
Iseenosigtincreasewithgroupsizeintheheterogeneous/iteroparouspopula-
tions,wherethepopulationsdonotevolvevigilancebehavior(Wilcoxonrank-sum
p
=0
:
79
betweengroupsize5and50).Unliketheothertreatments,theheterogeneous/semelparous
populationsactuallyexperienceat
decrease
inwithincreasinggroupsize
75
Figure5.3
Treatmentcomparisonwhenpreycanchoosetoforageingroups.
Allowingpreytodecidewhethertheywishtobeinthegroupproducessimilarresults
comparedtowhentheyareforcedtogroup.Inhomogeneousgroups,preychoosetospend
mostoftheirtimeinthegroup.However,groupingbreaksdown(alongsidevigilance)in
heterogeneousgroupsofsemelparousprey.Thisoccursdespitetherebeingnodirectpenalty
assessedforchoosingtogroup.Errorbarsindicatebootstrapped95%intervals
over100replicates;someerrorbarsaretoosmalltobevisible.
76
(Wilcoxonrank-sum
p
=2
:
77

10

6
betweengroupsize5and50),whichsuggeststhat
cooperativebehaviorisnotevolutionarilystableinlargerheterogeneousgroups.Accord-
ingly,thesesuggestthatheterogeneouspopulationsaremuchmoresusceptibleto
non-vigilant,\cheating"preystrategiesthatsweepthepopulationandreducetheoverall
population
5.3Optionalgrouping
SofarIhaveshownthatpreyappeartotakeadvantageofcollectivevigilancetoincrease
theirwhentheyareforcedtogroup.Wemightexpectfromthisresult(andthe
manyeyeshypothesispredicts)thatgroupingprovidesaselectiveadvantage.Totestthis
expectationexplicitly,Irelaxtheconstraintsofthepreviousexperimentbyallowingtheprey
toevolvewhethertogroupornotateverysimulationtimestep.Sincethereisnodirect
forgroupinginthismodelyet(astherewasforforagingandvigilance),this
allowsmetostudywhethertheevolutionaryadvantagesofgroupingarefavorableenough
forvigilanceandgroupingtoco-evolve.
Figure5.3showsthatwhenIallowpreytochoosetogroup,Inearlythesameresults
asbefore.Thissuggeststhatcollectivevigilanceprovidesenoughofaselectiveadvantage
tofavortheevolutionofgrouping.Itisnotsurprisingthatthehomogeneoustreatments
evolvetogroupnearly100%ofthetime,giventhatthepopulationisgeneticallyidentical
andany\altruistic"actionindirectlybthealtruistaswell.Asintheforcedgrouping
experiment,Iobserveadeclineinintheheterogeneous/semelparouspopulations
asgroupsizeincreases,tothepointthatthepopulationisnearlydrivenextinct.The
inabilityoftheheterogeneous/semelparouspopulationstoevolveconsistentlyhighlevelsof
77
vigilancefurthersupportsthehypothesisthatevolutionisfavoringshort-termcompetitive
advantagesoverlong-termsurvival.Thisphenomenoniscommonlyknownasthetragedyof
thecommons[107,108],whereactionsthatprovideanindividualshort-termb
leadtoadecreaseinoverallgroup
5.4Tragedyofthecommonsinheterogeneousgroups
Toexplorethisapparenttragedyofthecommonsscenariofurther,Idirectlycomparevigi-
lanceandvaluesfromtheforcedandoptionalgroupingexperimentsalongsideathird
experimentwhereIforcethepopulationtoforageandsurviveasindividuals.Figure5.4
showsthatwhengiventhechoicetogroupinthehomogeneoustreatments,preybehavior
closelymirrorsthebehaviorobservedwhenforcedtoforageinagroup.Thisobservation
theprevioussuggestionthatcollectivevigilanceinhomogeneousgroupsprovidesa
bethatpositivelyselectsforgregariousforagingbehaviors.
Incontrasttothehomogeneouspopulations,heterogeneouspopulationsaremuchless
likelytoevolvegregariousforagingbehaviors.Heterogeneous/iteroparouspopulationsnever
evolvevigilancebehaviorregardlessofwhetherthepreyareforcedtogroupornot(Fig-
ure5.4).Similarly,heterogeneous/semelparouspopulationsonlyevolvevigilancebehavior
insmallergroups,whereastheadvantageofcollectivevigilanceislostinlargergroups.At
largergroupsizes,preywiththeabilitytochoosewhetherornottoforageinheteroge-
neous/semelparousgroupsinsteadevolvelowerlevelsofvigilancethanrequiredtoprotect
thegroup(Figure5.4),whichresultsinadecreaseinoverallgrouprelativetoprey
thatalwaysforageingroups(Figure5.5).
78
Figure5.4
Vigilanceinpreywithandwithouttheoptiontoforageingroups.
Inhomogeneousgroups,preywithforcedandoptionalgroupingevolvesimilarvigilance
behaviors.Incontrast,individualistic(non-grouping)preyevolvevigilancebehaviorsthat
maximizeindividualMeanwhile,individualsinheterogeneous/semelparouspopu-
lationswiththeoptiontogroupevolvetobelessvigilantthaneitheroftheothertwo
treatments.Errorbarsindicatebootstrapped95%conintervalsover100replicates;
someerrorbarsaretoosmalltobevisible.
Figure5.5
Fitnessforpreywithandwithouttheoptiontoforageingroups.
In
heterogeneous/semelparousgroups,preywiththeoptiontogrouphavelowerthan
preythatareforcedtogroup.Errorbarsindicatebootstrapped95%intervals
over100replicates;someerrorbarsaretoosmalltobevisible.
79
Figure5.6
Groupingbehaviorsinpreyexperiencinggroupingpenalties.
Even
withasmallgroupingpenalty(
M
=1
:
0),alltreatmentsexcepthomogeneous/semelparous
nolongerevolvegroupingbehavior.Preyinthehomogeneous/semelparoustreatmentevolve
onlyslightlylowerlevelsofgroupingbehavior,evenwithextremepenaltiestoforagingin
agroup(
M
=1
;
000).Errorbarsindicatebootstrapped95%intervalsover100
replicates;someerrorbarsaretoosmalltobevisible.
5.5Explicitcostofgrouping
Inmytreatment,Iinvestigatetheimpactofassessingadirectcostofforaginginagroup
(e.g.,competitionforfood).Figure5.6showsthatexceptinthehomogeneous/semelparous
treatment,anexplicitgroupingcostselectsagainstgregariousforagingbehaviorevenwhen
thegroupingpenaltyissmall(
M
=1
:
0).Conversely,preyinthehomogeneous/semelparous
treatmentmaintainsomelevelofgregariousforagingbehaviorevenwhenthepenaltyfor
foragingingroupsisextreme(
M
=1
;
000).Therefore,Iconcludethatinthepresence
ofevenasmallpenaltyforforaginginagroupandtheabsenceofadditionalselection
pressuresthatfavorgregariousforaging(e.g.,improvedsocialstatusforsentinels),onlythe
combinationofhighgeneticrelatednesswithinthegroupandasemelparousreproductive
strategyselectstronglyenoughforgregariousforagingbehaviortoevolveinmymodel.
80
5.6Discussion
Ifoundthatgregariousforagingbehaviorcanemergeunderavarietyofconditionswhen
thereisabofvigilanceandthespreadingofinformationaboutpredators.Preythat
forageinhomogeneousgroupsaremorelikelytoevolvegregariousforagingbehaviorscom-
paredtothethoseinheterogeneousgroups.Thesameistrueforsemelparousorganisms
(whoreproduceonlyoncebeforedeath)comparedtotheiriteroparouscounterparts(who
reproducecontinually),butgrouphomogeneityselectsmuchmorestronglyforgregarious
foragingbehavior.
Clearly,therearenumerouschallengestoevolvinganyformofcooperativebehaviorina
populationwithunconstrainedgeneticrelatedness.However,Ihaveshownherethatwhen
thereisstrongselectionforsurvival(asintheheterogeneous/semelparoustreatment),the
bofinformationsharingviabeingvigilantandmakingalarmsignalsistto
selectforcooperativebehaviorinheterogeneousgroups.Thisndingdemonstratesthat
kinshipisnotnecessaryforcooperativebehaviortoevolveaslongasthereissomeb
toinformationsharingwithinthegroup,e.g.,reducingpredatorattack.
Further,myresultspointtoaheretoforeunsuspectedcostofgregariousforagingthatis
uniquetoheterogeneousgroups.Icallthisthe\two-foldcostofvigilance."Inmymodel,
vigilancebehaviorinheterogeneousgroupsismorethanawithforagingonthe
individuallevel.Bychoosingtobevigilant,preyalsoriskaidinginthesurvivalofrivalprey,
whichthenputsthevigilantpreyatadisadvantagebecauseitaroundof
foragingtoaidtherivalprey.Together,thesecostscouldexplainwhypreyinheterogeneous
groupsevolvetobelessvigilantthanthoseinhomogeneousgroups.
Atthesametime,itisalsopossiblethattherearesomeevolutionaryadvantagesunique
81
toheterogeneousgroupsthatIhavenotyetaddressed.Forexample,mymodeldoesnot
currentlyallowforanykindofspecializationinrolesbetweenindividuals,whichcouldex-
plainthepresenceofmulti-speciesgroupsinnature[109,110].Ifthepreycouldevolveto
preferentiallypayattentiontocertain\sentinel"membersofthepopulation(who,inturn,
choosetobevigilantnearlyalwaysinordertoreceivesomeformofrewards,e.g.,foodor
increasedsocialstatus)thenperhapsanevolutionarilystableformofgregariousforaging
couldbefoundinheterogeneousgroupsofallsizes.Itisevenpossiblethatsuchacomplex
socialstructurecouldout-performtherelativelyprimitivecooperationinmyhomogeneous
groups.
Alongsidegeneticrelatedness,anotherpositiveselectivepressurefortheevolutionofvig-
ilanceisasemelparousreproductivestrategy.Whenpreymustsurviveanyandallpredator
attacksinordertoreproduce,theimpetustobevigilantismuchgreater.Semelparousor-
ganismsareknowntobemorerisk-aversethansimilar,iteroparousorganisms[111],andthe
decisiontoforageinsteadofbeingvigilantisanexampleofonesuchriskybehavior.Thus,
ratherthanspendingmostoftheirtimeforaging(asiteroparouspreyevolvetodoinmy
model),semelparouspreyinmymodeltendtodevotemostoftheirtimetowatchingfor
predators.Whengiventheopportunitytogroupwithotherpreyandtakeadvantageofcol-
lectivevigilance,semelparouspreyareactuallyabletospendlesstimebeingvigilant.Thus,
whensemelparouspreyevolvelowerlevelsofvigilanceinlargergroups,weareobservingthe
ofcollectivevigilance.
Giventhatmanyanimalswhorelyonvigilanceforsurvivalareiteroparous,myresult
thatvigilanceislesslikelytoevolveiniteroparouspopulationsmayseemtobecontra-
dictedbyevidence.Inmyexperiments,Iexplorethetwoextremesofreproductivebehavior:
Semelparousstrategieswherethepreyreproduceonlyonceattheendoftheirlifetime,
82
anditeroparousstrategieswherethepreyconstantlyreproducethroughouttheirlifetime.
Itisplausiblethatanintermediatestrategy|wherepreyreproducewithinafewbreeding
episodesthroughouttheirlifetime|couldselectforvigilancebehaviorwhileatthesametime
thebofamorereliableiteroparousreproductivestrategy.Eventhoughsuch
anintermediatestrategyisnotexploredinthiswork,itwouldmakeaninterestingfocusfor
futureworktoexplorethecontinuumbetweenthetworeproductivestrategies.
Althoughmyresultssuggestthattherisk-aversenessofsemelparityinducessemelparous
preytoevolvetotakeadvantageofcollectivevigilance,thisselectivepressuredoesnot
appeartobeasstrongasthepressureIobservedinhomogeneousgroups.Proofofthis
observationcanbefoundintheheterogeneous/semelparoustreatment,wheremostgroup
membersattempttocheattheirwayintocollectivevigilancebyevolvinglowerlevelsof
vigilancebehaviorthanisobservedinpopulationswherepreyareeitherforcedtoforage
ontheirownorinthegroup(Figure5.4).Ultimately,thisbehaviorresultsinlower
thantheofpreythatareforcedtoforageingroups(Figure5.5),butthe
constantly-present,short-termbofappeartobetooenticingtoallowa
moreadvantageous,cooperativebehaviortoemerge.
Thebreakdownofcooperationintheheterogeneous/semelparouspopulationssuggests
thatthepopulationsaresuccumbingtoatragedyofthecommons[107,108].Inmyexperi-
ments,allpreyarecompetingagainsteachothertoforageasmuchfoodaspossiblewithout
beingcapturedbythepredator.However,becausethereisanunlimitedamountoffood,the
onlydepletablegroupresourceisvigilance,whichprotectstheentiregroupfromthepreda-
tor.Astheresultingnon-cooperativebehaviorintheheterogeneous/iteroparouspopulations
demonstrate,absentanymajorselectivepressuresforcollectivevigilance,preywillevolveto
forage100%ofthetime.Therefore,grouphomogeneityandsemelparitycorrespond
83
totwopreviously-establishedmechanismsforpreventingatragedyofthecommons,namely
kinselectionandpunishmentfornon-cooperativebehaviors,respectively[107].Therelative
ofthesemechanismstopreventcheatingmeritsfurtherinvestigation,forexample,
doesgrouphomogeneityplayalargerrolethanreproductivestrategyintheevolutionof
collectivevigilance?
Inthepresenceofevenasmallpenaltyforforagingingroups,Iobservethatonlyprey
inhomogeneousgroupswithasemelparousreproductivestrategyarecapableofevolving
gregariousforagingbehavior(Figure5.6).Thissuggeststhat,intheabsenceof
unlimitedfoodresourcesorextremepredationrates,collectivevigilance(i.e.,themany
eyeshypothesis)isttoselectforgregariousforaging.However,theremaybe
importantaspectsofnaturalsystemsthatselectforgregariousforagingthatIdidnotmodel
here.Forexample,predatorshavebeenobservedtopreferentiallyattacknon-vigilantpreyin
groups[112],whichwouldrequirepreytobevigilantevenwithoutthebofcollective
vigilance.Thus,itwouldbeinformativeinfutureworktomodelsuchapreferencefor
non-vigilantpreyandobservetheevolutionofgregariousforagingunderthoseconditions.
84
Chapter6
Conclusion
Intotal,thisdissertationthoroughlyexploredthreeofthemanyhypothesesexplainingthe
evolutionofcollectiveanimalbehavior.Sofar,theseprojectshaveexpandedthetheory
surroundingtheevolutionaryoriginsofcollectivebehaviorbyproducingseveraltestable
hypotheses.ForexampleinChapter3.4,Idiscoveredasimplevision-basedmovementalgo-
rithmthatpreycouldusemaintaincohesiveswarmingbehavior,whichcontrastswiththe
complexalgorithmsthatarecommonlyusedtosimulateswarmingbehaviorinsilico[85,73].
Thisprovidesamuchsimplermovementalgorithmtoexplainthecomplexswarming
behaviorfoundinnature,whichcanbevalidatedinobservationalstudiessuchas[113].
SimilarlyinChapter4.5,Ihypothesizedthattheinteractionenabledbypredatorconfusion
betweenthepredator'sviewangleandpreyswarmingbehaviorshouldselectforpredators
withafocusedvisualsystem.Ifthisisthecase,wewouldexpecttoobservepotentially
uniquetraitsandmechanismsthatfocusthepredator'svisualsysteminnaturalpredators
thathuntswarmingprey.FinallyinChapter5,Ifoundthatreproductivestrategyplays
asigtroleintheevolutionofcooperativegroupforaging,namelybyshowingthat
semelparousspecieswillbestronglyselectedtoforageingroups.Thisrepresents
analtogethernewdiscoveryexplainingtheevolutionofcooperativegroupforagingthat
couldbecorroboratedbyameta-analysisofexistingspecieslinkingthespecies'proclivity
tocooperativelyforageingroupstoitslifehistory.
Duringthecourseofthisresearch,Icameuponseveralsurprisingresultsthatmy
85
expectations.Perhapsthemostnotableunexpectedwasthesimplicityoftheevolved
preyswarmingmechanismsacrosseveryembodiedswarmingexperimentthatIperformed.
Sincethemajorityofresearchersstudyingswarmcontrolmechanismssuggestthatnatural
preymustbefollowingsomeformofcomplexBoidsrules(separation,alignment,cohesion),
IexpectedmysimulatedpreytoevolvesomeformoftheBoidsrules.Instead,mysimulated
preyevolvedasimple\followthepreyinfrontofyou"rulethatresultsinemergentswarming
behaviorwhenappliedoveragroupoflocally-interactingpreywithouttheneedforglobal
informationabouttheswarm|andonlyminimallocalinformationaboutwhatisinfront
oftheprey.Althoughpartofthesimplicityofthemovementalgorithmmayresultfrom
thefactthatthepreycannotcollidewithoneanother,thisunexpectediscausefor
collectivebehaviorresearcherstoreevaluateandperhapssimplifythestandardmodelsthat
explainswarmingbehaviorinnature.
Anothersurprisingfromthisresearchwasthesigntimpactofpredatorattack
mode(i.e.,howpredatorschoosetoattackprey)ontheevolutionofswarmingbehavior.Most
researchpriortotheworkinthisdissertationhadassumedthatpredatorattackmodedid
notplayanimportantrole,andoftensimplyassumedthatthepredatorattackspreyat
random.Inthisdissertation,Ireevaluatedthisassumptionanddiscoveredthatpredators
thatconsistentlyattackpreyontheoutsideoftheswarmexhibitamuchstrongerselection
pressuretoswarmthanpredatorsthatattackrandomly.Thissuggeststhatitisnot
safetoassumethatthepredatorattackmodeplaysanunimportantroleintheevolutionof
collectivebehavior,andhighlightstheimportanceofexploringtheroleofcomplexpredator
attackmodesinmodelsexploringtheevolutionofcollectivebehavior[74,114].
Furthermore,thisworkhasprovidedinsightintopossibleapplicationsinComputer
Scienceandbiomimeticsolutionstoproblemsinparticleswarmoptimizationandswarm
86
robotics.ForexampleinChapter3.4,thesamesimplevision-basedcontrolalgorithmcanbe
usedasacontrolalgorithminswarmroboticsexperiments.Providedthatswarmrobotics
experimentsareoftenlimitedtosimple,inexpensiverobotswithminimalsensorsduetoman-
ufacturingcostandbatterylife,simplecontrolalgorithmsthatproduceemergentswarming
behaviorwillbenecessarytoadvancethe[72].InChapters3.2.4and4.5,Ielaborated
upontheroleofpredatorattackmodeandpredatorconfusioninthecoevolutionarydynamics
betweenpredatorandpreypopulations.Providedthatagrowingofparticleswarmop-
timizationseekstoharnesspredator-preycoevolutionduringtheoptimizationprocess[71],it
willbecriticaltounderstandthecorepredator-preycoevolutionarytheoryunderlyingthese
optimizationalgorithms.Finally,itisimportanttonotethatthecoreofthisresearchaims
atunderstandinghowitispossibletogetaheterogeneousgroupofindependentagentsto
cooperatetowardacommongoal,evenifcooperationentailstheperformanceof
someoftheindividualsinthegroup.TherearemanyparallelstothisprobleminComputer
Science,forexample,itiscommontoseeimprovedperformanceinMachineLearningclas-
problemsbycreatinganensembleofto\worktogether"towardbetter
performance[115].Althoughitisnotyetcommontoautomaticallycreatehet-
erogeneousensemblesoftheworkpresentedinthisdissertationwillbeinformative
forthispotentiallyfruitfullineofMachineLearningresearch.
Ofcourse,thisdissertationopensmanynewavenuesofresearchdirectlyfollowingthe
workpresentedhere.InChapter3.4,theevolvedpreyswarmingmechanismassumedthat
thepreydonotcollidewithoneanother.Itwouldbeinstructivetofollowuponthisworkby
implementingcollisionsforthepreyandobservingtheresultantbehavior:Dothepreyevolve
amoreBoids-likecontrolalgorithm,orisasimplefollow-the-prey-in-front-of-youmechanism
stillt?InChapter4.5,Ifoundthatthepredatorsandpreyenteraseemingly-endless
87
coevolutionarycyclewhenbothpreybehaviorandthepredatorvisualsystemareallowedto
coevolve.Anotherfascinatingvenueofresearchwouldbetoexplorepossiblemechanismsfor
visualpredatorstosecuretheir\evolutionaryvictory"byevolvingtoelyhuntboth
swarminganddispersiveprey|forexample,byevolvingacomplexvisualsystemthatwe
oftenseeinvisualpredatorsinnaturethatprovidesbothcoarse,broadvisionforsearching
aswellasnarrow,focusedvisionfortrackingprey.InChapter5,Idiscoveredthattheprey's
reproductivestrategyplaysanimportantroleinwhetheritwillevolvetocooperativelyforage
ingroups.However,Ionlyexploredthetwoextremesofreproductivestrategy|reproducing
continuouslyandreproducingonlyonceneartheendoftheirlifetime|andthereisanentire
continuumofreproductivestrategiesinbetweenlefttoexplore.
Finally,therearemanymorehypothesizedbofcollectivebehaviorthatremainto
beexploredinfuturework,suchasimprovedlocomotion[18]andthefeasibility
ofcollectivecognition[1].Onceallofthesehypothesizedbenehavebeenexploredin
isolation,itwillthenbepossibletocombinethesehypothesizedbintohybridexper-
imentswherewecananswerquestionssuchas,\Inthepresenceofthepredatorconfusion
doescollectivevigilanceplayanimportantroleintheevolutionofcollectivebehav-
ior?"Thesehybridexperimentswillbringusclosertosimulatingrealbiologicalsystems
andunderstandinghowandwhypreyevolvetoliveingroups.Bybringinguscloserto
understandingnature,thislineofresearchwillestablishasolidbasisofevolutionarytheory
surroundingcollectivebehaviorforresearcherstodrawupon,bothwhenstudyingcollective
behaviorinnatureandwhenharnessingcollectivebehaviorinroboticsandoptimization
problems.
88
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