BehaviouralProcessesxxx (2012) xxx–xxx
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Behavioural
Processes
j o u r n al ho m e p age :w w w . e l s e v i e r . c o m / l o c a t e / b e h a v p r o c
Computational
mate
choice:
Theory
and
empirical
evidence
Sergio
Castellano
a,∗, Giorgia
Cadeddu
a, Paolo
Cermelli
baDipartimentodiBiologiaAnimaleedell’Uomo,ViaAccademiaAlbertina,13,UniversitàdiTorino,Torino10123,Italy bDipartimentodiMatematica,ViaCarloAlberto,10,UniversitàdiTorino,Torino,Italy
a
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received25August2011
Receivedinrevisedform17February2012 Accepted26February2012 Keywords: Sexualselection Preferencefunction Matecopying Decisionmaking Bayes’theorem
Sequentialsamplingmodels Matesearchingtactics
a
b
s
t
r
a
c
t
Thepresentreviewisbasedonthethesisthatmatechoiceresultsfrominformation-processing mech-anismsgovernedbycomputationalrulesandthat,tounderstandhowfemaleschoosetheirmates,we shouldidentifywhicharethesourcesofinformationandhowtheyareusedtomakedecisions.We describematechoiceasathree-stepcomputationalprocessandforeachstepwepresenttheoriesand reviewempiricalevidence.Thefirststepisaperceptualprocess.Itdescribestheacquisitionofevidence, thatis,howfemalesusemultiplecuesandsignalstoassignanattractivenessvaluetoprospectivemates (thepreferencefunctionhypothesis).Thesecondstepisadecisionalprocess.Itdescribesthe construc-tionofthedecisionvariable(DV),whichintegratesevidence(privateinformationbydirectassessment), priors(publicinformation),andvalue(perceivedutility)ofprospectivematesintoaquantitythatisused byadecisionrule(DR)toproduceachoice.WemaketheassumptionthatfemalesareoptimalBayesian decisionmakersandwederiveaformalmodelofDVthatcanexplaintheeffectsofpreference func-tions,matecopying,socialcontext,andfemales’stateandconditiononthepatternsofmatechoice.The thirdstepofmatingdecisionisadeliberativeprocessthatdependsontheDRs.Weidentifytwomain categoriesofDRs(absoluteandcomparativerules),andreviewthenormativemodelsofmatesampling tacticsassociatedtothem.Wehighlightthelimitsofthenormativeapproachandpresentaclassof com-putationalmodels(sequential-samplingmodels)thatarebasedontheassumptionthatDVsaccumulate noisyevidenceovertimeuntiladecisionthresholdisreached.Thesemodelsforceustorethinkthe dichotomybetweencomparativeandabsolutedecisionrules,betweendiscriminationandrecognition, andevenbetweenrationalandirrationalchoice.Sincetheyhavearobustbiologicalbasis,wethinkthey mayrepresentausefultheoreticaltoolforbehaviouralecologistinterestedinintegratingproximateand ultimatecausesofmatechoice.
© 2012 Published by Elsevier B.V.
1. Introduction
Anadultfemalethatislookingforamate,havingsurvivedto thisstage,provestohavebeenagooddecisionmaker.Asayoung, shemadeappropriatedecisionsaboutwhentomoveandwhento rest,wheretogoandwheretoavoid,andwhatandhowtoeat.But thepositivefitnesseffectsofthesepreviousdecisionscouldbe sud-denlynullified,ifshenowchoosesthewrongmate.Indeed,mate choiceisoneofthemostimportantdecisionsthatfemalesmake intheirlife.Forthisreason,femalesareexpectedtohaveevolved acognitivemachinerythatmakethemabletochoosetheirmates effectively,byavoidingheterospecificsandbyfavouring discrim-inationbetweenconspecifics of differentqualities(Ryan, 1997;
RyanandRand,1993).Femalesusuallybasetheirmatingdecisions
∗ Correspondingauthor.Tel.:+39116704547.
E-mailaddress:sergio.castellano@unito.it(S.Castellano).
onseveralmales’signalsorcues,whichtheyperceiveineitherthe sameordifferentsensorymodalities(Candolin,2003;Partanand
Marler,1999).Sincetheinformationtheyacquirefromthesetraits
isalwaysnoisyandoftenconflicting,matingdecisionsare intrinsi-callyuncertainandpronetoerrors(JohnstoneandGrafen,1992). Tounderstandhowmatechoiceevolved,weshouldthus under-standhowtheuncertaintyprobleminmatingdecisionhasbeen solved.
Uncertaintyinmatingdecisionsdependsontwofactors.First,it dependsontheamountoftheinformation acquired.Normative modelsofmate choicetypicallyfocusonthis aspectand tryto findoptimaleconomicalrulesofinformationgathering(Luttbeg,
1996,2002;Real,1990;Sullivan,1994).Butuncertaintydepends
alsoonthecognitivemechanismsofinformationprocessing,that is,onhowseveralsourcesofinformationareintegratedandused toreachadecision.Untilrecently,thecognitiveaspectsofmating decision have receivedscarceattentionin sexualselection the-ory,becauseitwassimplisticallyassumedthat,ifmatechoiceis 0376-6357/$–seefrontmatter © 2012 Published by Elsevier B.V.
thewayforchoosingmatesaccurately.BatesonandHealy(2005),
Castellano(2009a),Ryanetal.(2007,2009)contendedthisview
emphasizingtheroleofcognitivemechanismsforunderstanding theevolutionofmatechoice.Followingthetheoreticalapproach proposedbyMarr(1982),Castellano(2009a)arguedthatsexual selectiontheoryneedsacomputationaltheoryofmatechoice,a theorythat couldexplainmatingdecisionsatboth theabstract levelofthecomputationalpropertiesandattheproximatelevelof algorithmimplementation.Inthepresentpaper,wemovefurther alongthispathofinquiry,bypresentingacomputationalmodelof matechoiceandbyreviewingempiricalevidenceinthelightofthis model.
Marr(1982) arguedthat themostgeneraland abstract
the-oryof an information-processingsystem(i.e. itscomputational theory) responds tothe questionof “what is being computed” and“whythecomputationiscarriedout”.Inmatechoice, com-putationinvolves theperceived qualities (i.e.attractiveness) of prospectivematesand itis carriedout toselectan appropriate male,giventheamountofavailableuncertainevidence. Statisti-caltheorypredictsthat anoptimaldecisionprocess thatwants toestimatetheprobabilityof anuncertainevent mustadopt a Bayesianapproach.Wethusmaketheadaptationistassumption thatselectionshouldhavepromotedtheevolutionofaBayesian modelofmatingdecision,thatis,weassumethatthe computa-tionaltheoryofmatechoiceisbasedontheBayesiancomputation oftheposterior probability thata male is anappropriate mate (seeSection2).
Bayes’theoremhasbeenoftenusedbytheoreticiansin mod-elinganimal behaviour (reviewin McNamaraetal., 2006)and, inparticular,matechoice(Collinsetal.,2006;LangeandDukas,
2009;Ueharaetal.,2005)andthereisempiricalevidencethat
ani-malsbehaveinawayconsistentwiththepredictionsofBayesian updatingmodels(Biernaskieetal.,2009;MabryandStamps,2008;
Valone,2006).ABayesiancognitivemachineryofmatingdecision
impliesthatfemalenervoussystemrepresentsinformationabout prospectivematesintermsofconditionalprobabilitydensity func-tions.Recentstudiesinneuroscienceprovideevidenceconsistent withthehypothesisthatperceptualcomputationsinhumansor
(Knilland Pouget,2004)and thatdecisionsarise byintegrating
informationovertimeaccordingtoaBayesianupdatingmechanism
(Körding,2007;YangandShadlen,2007).Itisnotclear,however,
towhatextentthesefindingsmaybegeneralizedtootheranimals withmuchsimplenervoussystems.Inthesespecies,femalesmay relyonrulesthataresimplerandlesscomputationaldemanding thanBayesiancomputations,butthatresultindecisionssimilarto thosepredictedbyBayesianupdatingstrategies(LangeandDukas,
2009).
In this paper we review patternsof mate choiceand tryto explainthemintermsoftheirunderlyingmechanismsof infor-mationprocessing.Weknowalotaboutmatechoice.Weknow thatmatingdecisionsdependonmatingpreferences(Section3) and that females make decisions on the basis of both private andpublicinformation(Section4).Weknowthatexperiencecan affect matingdecisions and that mate choice is often a highly plastic behaviour, which may beinfluenced by both the inter-nal stateand theexternal conditions in which choice is made (Section4).Weknow thatfemalesmayusedifferenttacticsfor samplingandevaluatingprospectivematesandthatchoosingis oftentimeconsumingandaccuratedecisionsrequirelong evalua-tionsessions(Sections5and6).Wereviewallthesephenomena withintheunitarytheoreticalframeworkoftheBayesianmodelof matingdecision.Althoughtheentiretheoreticalbuildingisbased ontheadaptationistassumptionofoptimalmatechoice,wewill notdealwithoptimalitynorwewillreviewtheoriesand empir-ical evidence on theadaptive significance of mate choice. Our focuswillbeontheinformation-processingmechanismsofmate choice.
2. ThemodelofBayesiandecisionmaking
ABayesianmodelofdecisionmakingisbasedona compari-sonofposteriorprobabilitiesthatcertaineventsoccur.Imaginea femalethatis evaluatingaprospectivematetodecidewhether heis oris notanappropriate mate(Fig.1,and seeGlossaryin
Box1).
Fig.1. AschematicrepresentationofaBayesiandecisionvariable.Afemaletreefrogislisteningtotheadvertisementcallofaprospectivemate.Shemustdecidewhether themale,whosecallsheperceivesatanattractivenesslevelA,isanappropriatemate(P(H|A)).Sincethefemalehasonlypartialanduncertaininformation,optimaldecisions dependonwhatshealreadyknowsaboutthatmale(priorprobability,P(H))andonthelikelihoodsthatamaleofattractivenessAbelongstothesampleofeitherappropriate (P(A|H))orinappropriate(P(A|Hc)mates.WecallUtheratiobetweenthesetwolikelihoods,becauseitrepresentstheperceivedutility(value)ofamale,givenhisattractiveness
S.Castellanoetal./BehaviouralProcessesxxx (2012) xxx–xxx 3
Box1:Glossary
Appropriateness(ofaprospectivemate)isthevalueof the
decisionvariable.It isthe posteriorprobability of consider-ingamaleanappropriatemateanddependsonhisperceived
attractiveness,onhispriorprobabilityandontheinternaland
externalconditionsofthedecisionmaker,whichinfluencethe perceivedutilityoftheprospectivemate.
Attractiveness(ofaprospectivemate)isdefinedbythe
pref-erencefunctionanddependsonlyonperception.Itrepresents
asourceofprivate informationthatisusedbythedecision variableduringtheevaluationprocess.
Choosinessisacomponentofmatingpreference,whichdoes
notdependontheprivate(i.e.thepreferencefunction)or pub-licinformation(priors) ontheprospectivemate,butonthe perceivedutilityofthatmale.Variationinchoosinessisdue toavariationintheutilityfunction,whichmayresultfroma changeofeithertheinternalortheexternalconditionsofthe decisionmakers.
Decisionruledetermineshowandwhenthedecisionvariable
isinterpretedtoarrivetoacommitmenttoaparticularchoice.
Decisionvariableisthesynonymofappropriateness.Itisthe
objectresponsiblefortheintragrationofmultiplepieceof evi-denceovertime.
Preferencefunctiondefinestheperceivedattractivenessofa
prospectivemateonthebasisofthesignalsandcuesreceived bythedecisionmaker.
Sequentialsamplingdescribesthedynamicofthedecisional
process,thatis,theaccommodationofmultiplepiecesof evi-denceover time.It includestwo components: the decision
variable,whichintegrates evidenceovertime,and the
deci-sionrule,whichestablisheswhenitistimetostoptheprocess
andtocommit.
Utility function describesthe relationship between the
per-ceivedattractivenessandtheperceivedutilityofaprospective mate.
Utilityisthelevelofuncertaintyassociatedtotheperceived
attractivenessofaprospectivemateanditisdefinedasthe
ratiobetweentheconditionalprobability(likelihood)thatthe maleisattractivegivenheisandgivenheisnotan appro-priatemate(U=P(A|H)/P(A|Hc)).Theutilityisassumedtobea
monotonicfunctionoftheperceivedattractiveness.
Decisiondependsontheamountofevidence(A)supportingthe hypothesis(H)thattheprospectivemateisanappropriatemate. Supposethatevidencedependsonasetofmale’straits(x)sothat, afterevaluation,theamountofevidencethefemalehasacquiredis
A=a(x)+ε (1)
wherea(x)representsthedeterministiccomponentofperception describinghow thefemaleintegratesdifferentsourcesof infor-mationencodedin x,whereas εis thestochastic componentof perception,anormallydistributedrandomvariablewithzeromean andvariance2(Castellano,2010;Phelpsetal.,2006).Sincethe
stochasticvariableAisconsistentwiththedefinitionof“preference function”proposedbyJennionsandPetrie(1997,p.286“theorder inwhichanindividualranksprospectivematesceterisparibus”), wenamethemaleperceivedattractivenessAasthefemale’s pref-erencefunction(PF).
AccordingtotheBayestheorem,theprobabilitythatamaleis anappropriatemateisgivenbythefollowingformula:
P(H|A)= P(A|H)
P(A) ×P(H) (2)
Inwords,theprobabilitythatHistrue,givenaperceived attrac-tiveness A, equals the probability that an appropriate mate is perceivedatlevelA(P(A|H))(i.e.thelikelihoodofAinappropriate mates),timesthepriorprobabilitythatthatmaleisanappropriate mate(P(H)),dividedbytheprobabilitytoperceiveanadvertising
levelA,independentofwhetherthemaleisorisnotanappropriate mate(P(A)).Thislatterprobability,P(A),isthesumofthe probabil-itiesofperceivingAwhenHiseithertrue(P(A|H))orfalse(P(A|Hc))
(whereHccorrespondtoanonappropriatemale).
P (A) =P(A|H)×P(H)+P(A|Hc)×P(Hc) (3)
Imagineafemalethathasnopreviousinformationaboutthe qualityofaprospectivemate,whichsheperceivesofattractiveness A(i.e.herpriorprobabilitybeingP(H)=P(Hc)=0.5).Theprobability
thatshewillperceivethismaleasanappropriatemateincreases withtheincreaseoftheratiobetweentheperceivedprobabilityofa correctassignment(P(A|H))andtheperceivedprobabilityofafalse positive(P(A|H)c).Forexample,ifP(A|H)=0.9ismuchgreaterthan
P(A|H)c=0.3(theirratiobeing3),thenP(A)=0.6andP(H|A)=0.72.
In contrast,as theprobability of a false negativeincreases (i.e. P(A|H)c=0.6,theratiobeing1.5),P(A)increasesaswell(P(A)=0.75)
and,consequently,thechoiceprobabilitydecreases(P(H|A)=0.6). Thissimplenumericalexampleshouldmakeclearthatthe effec-tiveness of a perceived signal A(x) depends on the perceived probabilitythatxisemittedbybothanappropriateandan inap-propriatemate.Inthissense,theratioU=P(A|H)/P(A|Hc)mightbe
viewedastheperceivedutilityofthemaleanditisdirectlyrelated totheperceivedvalueoftheinformationacquired(seeBox2).
Box2:Utilityandinformation
Theutilityfunctionu(A)isameasureofhowthepreference valueAisactuallyrelatedtotheappropriatenessofthemate. Infact,whenu(A)=1andthelikelihoodofAinan appropri-ate mateisthe sameasitslikelihood inanon-appropriate mate,i.e.,P(A|H)=P(A|Hc),thenP(H|A)=P(H)andchoicedoes notinvolvepreference.Forinstance,whennothingisknown aboutthemale,P(H)=1/2andchoiceisrandom.Ontheother hand,whenu(A)=0,thenP(H|A)=0andthemateisrefused withprobability1.
Therefore,itisnotsurprisingthattheutilityfunctionisrelated totheinformationcontentI(H,A)ofthepreferencevalueA,that measureshowtheassignmentofapreferencevaluereduces theuncertaintyofchoice:
I(H,A)=E(H)−E(H|A),
whereE(H)andE(H|A)aretheentropyofHandtheconditional entropyofHgiventhepreferenceA.Entropyisameasureof theuncertaintyofarandomvariablethatvariesbetween0(no uncertainty) and1(maximumuncertainty):correspondingly, theinformationvariesbetween-1and1,andisnegativewhen thepreferenceincreasestheuncertaintyofchoice:forinstance,
I(H,A)=0whenu(A)=1,I(H,A)isminimal(andnonpositive)
whenu(A)=P(Hc)/P(H).
Thefirst conditionmeansthatwhenAisequallylikely and
P(A|H)=P(A|Hc), preference doesnotentail anyinformation
gain.Ontheotherhand,theconditionu(A)=P(Hc)/P(H)implies
thatchoiceisrandomwithP(H|A)=1/2:inthiscase,preference obviouslyincreasestheuncertaintyintheselectionprocess.
The perceived utility is the ratio between two conditional probabilities.Forspecieswithrelativelysimplenervoussystems, however,suchacalculationmaybetoocomputationally demand-ingtobecarriedouteffectively.Inthesespecies,thus,selectionmay havefavouredtheevolutionofmuchcheaperwaysofrepresenting theperceivedutilityofprospectivemates.We,thus,makea fur-therandimportantassumption.Weassumethatfemalesdirectly translatesensoryinformation(theperceivedattractiveness)into likelihood ratio(i.e.theperceived utility),bymeansofa utility
perceivedattractiveness.Eq.(2)maybere-writtenas: P(H|A)= u(A)
(u(A)−1)+ 1 P(H)
(4)
In the special case of no priors (i.e. P(H)=0.5), P(H|A)=u(A)/(u(A)+1). As we will appear clear in Section 4.2, the distinction between preference and utility function is important if we assume that the perceived utility (value) of a prospective mate may depend not only on his perceived attractiveness(thequality ofthesensoryinformation), butalso on the internal state and the external conditions of choosing females.
Eq.(4)definestheposteriorprobabilityP(H|A).Wenamethis elementtheDecisionVariable(DV). TheDV combinesboth evi-denceandpriorsintoaquantitythatisinterpretedbyaDecision Rule(DR)toproduceachoice(GoldandShadlen,2007). Accord-ingtothismodel,matechoicemightbeviewedasathree-step process:(1)theacquisitionofevidence;(2)theevaluationofthe prospectivemateaccordingtoacquiredevidenceandpriors;(3)the applicationofaDecisionRuletotheDecisionVariable.Foreachof thesethreesteps,wereviewthetheoriesthathavebeenproposed andtheempiricalevidencethatsupportsthem.
3. Acquisitionofevidence:Thecomputationalmechanisms ofperceivedmaleattractiveness
Thepreferencefunction(Eq.(1))describeshowfemalesconvert theinformationofaprospectivemateinaninternal representa-tionofhisattractiveness.Implicitly,ourmodelofmatingdecision assumestheperceivedattractiveness(A)tobeaone-dimension variable,thatis, itassumesfemales toorderprospectivemates alonganordinalscaleofvalues.However,theinternal representa-tionofmateattractivenessmightnotbeone-dimensional.Female mating decisions depend on several male traits, often involv-ingdifferentsensorymodalities(reviewsinBro-Jorgensen,2010;
Candolin,2003;HebetsandPapaj,2005;JennionsandPetrie,1997)
andfemalesmayintegratethesedifferentsourcesofinformation inatleastthreedifferentways:(i)theymayformaone-dimension representationofmaleattractiveness,asassumedbyEq.(1);(ii) theymayformamulti-dimensionrepresentationofmale attrac-tiveness,butuseasingledecisionvariable(KnillandPouget,2004); or(iii) theymayintegratedifferentsources ofinformation into differentDVs,hierarchicallyorderedaccordingtoapriorityrule
(Candolin, 2003). Now, we consider the simple case in which
femalespossessa one-dimensionpreference functionandusea singleDVinmatingdecision.InSection7,wewillreturntothis issueandwewillconsiderthecaseofmulti-dimensionpreference functionsandtheuseofmultipleDVsinmatechoice.
3.1. Thepreferencefunctionhypothesis
Theconceptof“preferencefunction” wasfirstintroducedby
Lande(1981)todescribesexualselectiononmaletraits.Hedefined
a“preferencefunction”, (y,z),astheprobabilitythatafemalewith phenotypeychoosesamaleofphenotypez.Thisdefinition, how-ever,ismoresimilartoourdefinitionofdecisionvariable(Eq.(2))
thantotheJennionsandPetrie’s(1997)definitionofpreference
function(seeEq.(1)).Indeed,insexualselectionstudies,the con-ceptsofchoiceandpreferencehavebeenoftenusedassynonyms
(Wagner, 1998), probablybecause the only way toempirically
describematingpreferencesisbyobservingmatingdecisions. Nev-ertheless,Wagner(1998)emphasizestheimportanceofkeeping thesetwoconceptsdistinct,becausechoicedependsnotonlyon matingpreferences,butalsoonfemalesamplingbehaviour(i.e.
mentalconditionsinwhichchoiceiscarriedout(Wagner,1998). The Bayesian model of mate choice makes a clear distinction betweenpreferences andchoice and it alsohelpsus to under-standwhicharetheassumptionsthatmakeitpossibletoderive patternsofpreferencesfromobservedpatternsofchoice.Infact, imagineatypicalmate-choiceexperiment(i.e.recognitiontest,see below),inwhichwe measuretheconditionalprobabilityC(H|x) thatastimulusHofqualityxelicitsapositivetaxisinareceptive female.Iffemaleshavenopriors(i.e.P(H)=0.5)andifthe probabil-ityofrespondingtoastimulusistheprobabilityofperceivingitas appropriate(i.e.C(H|x)=P(H|x)),then,fromEq.(4),theperceived utilityu(A(x))(butnotice,nottheperceivedattractivenessA(x)) isu(A(x))=C(H|x)/(1−C(H|x)).Ifthemonotonicfunctionbetween utilityandattractivenessdoesnotchangebothbetweenandwithin femalesduringtheexperiment,thentheranksofprospectivemates alongthepreferenceandutilityfunctionsarethesame.
Theempiricalstudyofmatingpreferencesusestwo experimen-talparadigms:therecognition testand thecomparativechoice (reviewinWagner,1998).Inarecognitiontest,femalesareexposed toonestimulusata time(no-choiceexperiment),whereasin a comparativetesttheyaresimultaneouslyexposedtotwoormore stimuli.Inbothtests,preferencesaremeasuredbyobservingthe frequency orlatencyof behaviouralresponses,suchas positive taxis(e.g.therelative numberoffemales thatapproacha stim-ulusinphonotaxisexperiments,Gerhardt,1995),thespeed and directionona walkingcompensator orof tethered movements (i.ephonotaxisininsects,Doherty,1985),associationtime(i.e.the proportionoftimespentinproximitytoavisualstimulusinfish,
CummingsandMollaghan,2006;Wallingetal.,2010,andbirdsHoi
andGriggio,2011;ortoachemicalstimulusinmammals,
Clutton-BrockandMcAuliffe,2009),orthenumberofsignalselicited(i.e.
contactcallsinbirds,Moravecetal.,2006).Bothrecognitionand comparativetestshaveseveralpracticallimitations,mainlydueto thelowaccuracyandprecisionwithwhichpreferencesare mea-sured.Whilethelowaccuracyconstrainstheability todescribe variation inmatingpreferences and maylimitour understand-ingoftheselectiveforcesactingonfemalematingdecisions,the lowprecisionofthesetestsisasomewhatmoreseriousproblem, becauseofthesystematicerrorsitmayintroduce.Sincethereis noreasonstoassumethatchoiceprobabilityinrecognitiontests isa linearfunctionofpreferences,thesetestsmaydescribethe ranks,butnotthequantitativedifferencesinpreferencestrength betweenitems.Furthermore,dichotomouschoicetestsdonot con-trolfordifferencesinfemalesamplingtacticsand,thus,theymay confoundrepeatedsamplingofprospectivematesasevidencefor weakpreferences(Bushetal.,2002).
In mostcases, recognitionand the comparativechoicetests havebeenusedtoinvestigatehowfemalesrespondtovariationin singlecomponentsofmalesignals.Theinteractionbetween mat-ingpreferencesand maletraitdistributiondeterminesthetype of biologicalinformation receivedby females (Gerhardt,1992): amonotonicfunction(oranunimodalfunctionwithpeakeither higherorlowerthanthemean)suggeststhatthetraitis impor-tantformate-qualityassessment,whereasanunimodalpreference functionwithpeakclosetothepopulationmeanisusuallyseenas evidencethatthetraitisimportantforspeciesrecognitionbecause traitsonbothdistributiontailsareperceivedaslessattractivethan thoseclosetothemean.Anunimodalpreferencefunction, how-ever,mayalsoariseastheeffectofhomotypicpreferences,which makefemalesmorelikelytomatewithmalesofsimilar pheno-types,asithasbeendescribedinmonogamousbirds(Ludwigand
Becker,2008).Inthiscase,theunimodaldistributionofpreferences
reflectsanunimodaldistributionofphenotypesinthetwosexes. Inmanyinsectsandanurans,femaleschoosetheirmatesonthe basisoftheiradvertisementcalls(reviewinGerhardtandHuber,
S.Castellanoetal./BehaviouralProcessesxxx (2012) xxx–xxx 5
2002).Forexample,Gerhardt(1991)showsthatingreytreefrogs (HylachrysoscelisandH.versicolor)femalepreferencesare stabiliz-ingonsomefine-scaletemporalacousticproperties(pulserate,call duration,risetime)anddirectionalonsomegross-scaletemporal properties(callduration,callrate),suggestingthatfemalesacquire fromtheformerinformationimportantforspeciesrecognitionand fromthelatterinformationimportantforintra-specific discrimina-tion(mate-qualityassessment).Thisstudyhasbeenreplicatedon manyotheranuranandinsectspecies,confirmingthatoneofthe majoradvantagesofacousticcommunicationisthepotentialfor encodingmultiplemessagesintoasinglesignal(reviewinGerhardt
andHuber,2002;Ryan,2001).
Multiplemessagesinmatingsignalsposethequestionofhow femalesprocessdifferentsourcesofinformation.Sincedifferent cuesorsignalsmayprovidefemaleswithconflictinginformation, it hasbecome clearthatthe problemof assigninga preference valuetoprospectivematescriticallydependsonhowthesecues interactwitheachother(Hebetsand Papaj,2005).From a the-oreticalpointofview,femalescanintegratedifferentsourcesof informationintoaone-dimensionpreferencefunctionby follow-ingtwocomputationalrules:anadditiveintegration(Burkeand
Murphy,2007;KunzlerandBakker,2001;SchulandBush,2002),
whentheymakeaweightedsumoftheperceivedattractivenessof eachcomponent,oramultiplicativeinteraction(Castellano,2010;
CastellanoandRosso,2007;SchulandBush,2002),when
compo-nentshaveasynergiceffectontheoverallperceivedattractiveness. AsobservedbySchnuppandKing(2001),whenfemalesweighthe componentsofasignal,theyperformanoperationanalogtothe logical“OR”,becausejustasinglehighlyattractivecomponentmay maketheentiresignalattractive.Incontrast,whenfemales multi-plytheperceivedattractivenessofeachcomponent,theyperform anoperationanalogtothelogical“AND”,becauseitsufficesa sin-glepoorlyattractivecomponenttomaketheentiresignalpoorly attractive.Becauseofthesecomputationaldifferences,additiveand multiplicativeintegrationmaysolvedifferentfunctionalrolesin matechoice.Ifcomponentsconveyhighlyredundantinformation, thensummationisexpectedtoperformbetterthanmultiplication. Incontrast,iftheyconveydifferentsourcesofinformation,then multiplicationisexpectedtodobetter.CastellanoandRosso(2007)
andCastellano(2010)investigatedfemalematingpreferencesfor
multiple-attributesignalsintheItaliantreefrog,Hylaintermedia. Thesestudiessupportedtheone-dimensionpreference-function hypothesisandprovidedevidencethatacousticproperties impor-tantforspeciesrecognitionandmatequalityassessmentinteract multiplicatively with each other in determining overall signal attractiveness.
Brooks et al. (2005) described the shape of the preference
functionformulti-attributematingsignalsinthecricket Teleogryl-luscommodususingmultiple-regressionstechniques.Theytested female preferences ona set of 300artificial calls, opportunely constructedtoshowsimultaneousanduncorrelatedvariationin fiveacousticaltraits.Then,theyusednon-linearregression mod-els(withlinear,quadratic and cross-productterms)todescribe thefemalepreferencefunctionoverthissetofcallsandshowed adominantcomponentofstabilizingmultivariatepreferences act-ingonthecricketcall(Bentsenetal.,2006).Asimilarapproach
was used by Wagner and Basolo (2007) and by Gerhardt and
Brooks(2009)tostudymultivariatepreferencefunctionsonmating
calls,respectively,inacricket(Grylluslineaticeps)andinatreefrog (Hylaversicolor).WagnerandBasolo(2007)consideredonlytwo acoustic traits that were known to convey different biological informationandfoundthatonlyoneofthemhadstatistically sig-nificanteffectsonthemultivariatepreferencefunction.Gerhardt
andBrooks(2009),incontrast,consideredfiveacoustictraitsand
showedthatthemultivariatefemalepreferencefunctionwas sig-nificantlyinfluencedbylinear,quadratic,andcross-productterms.
3.2. Variationinpreferencefunction
Preferencefunctionsplayacentralroleintheevolutionofmale secondarysexualtraits(Andersson,1994)andamong-population variationinpreferencefunctionmaypromotepre-zygoticisolation and, thus,speciation(reviewinKirkpatrickand Ravigne,2002). Forthesereasons,variationinpreferencefunctionshasreceived greatattentionfromevolutionarybiologists(BrooksandEndler,
2001;JennionsandPetrie,1997;Schielzethetal.,2010;Widemo
andSaether, 1999).Sinceourfocusisontheprocessesofmate
choice,wewillnotreviewthisabundantliterature,butwebriefly considertheroleofexperienceonpreferencefunctions.Widemo
andSaether(1999)identifiedtwocomponentsofpreference
func-tions:afixed‘innatepredisposition’torespondtocertainstimuli and a ‘flexible referencetemplate’. Whether theformer can be explainedastheheritable componentsofneuro-sensoryorgans andmight beimmune toexperience,thelatterexplains prefer-encesthatarisebycomparingprospectivematesagainstinternal standardsoftenacquiredbyexperience.Forexample,inmanybirds (reviewbyRiebel,2003,2009)andsomespiders(Hebets,2003), femalepreferencesare influencedbyearlyexperience,whereas inseveralrodentstheyareaffectedbymalefamiliarity:insome species familiarmalesarepreferred overunfamiliar males(e.g. Harvestmice,Mycromysminutes,Brandtand Macdonald,2011), inothersspeciestheoppositepatternisobserved(e.g.mandarin voles,Microtusmandarinus,Taietal.,2000).
Inalltheseexamples,experiencecausesvariationinpreference functionsand,thus,inmatingpreferences.Variationinmating pref-erences,however,mayarisealsobyachangeinutilityfunctions. Inthesecases,experiencehasnoeffectontheperceived attrac-tiveness,butonlyonitsperceivedutility.Asweshallseeinthe nextsection,utilityfunctionsareanimportantcomponentofthe decisionvariables,theymayaffectchoosinessand,thus,theymay play acentralrolein explainingshorttermplasticityin mating preferences(seeSection4.2).
4. Thedecisionvariable
Theperceivedattractivenessofprospectivematesisoneofthe sourcesof informationfor matingdecision. Ourmodel assumes thatfemalesusetheperceivedattractivenessofmalestoinfertheir value(utility),whichweexpressastheratiobetweenthetwo like-lihoodsP(A|H))andP(A|Hc).Bycombiningthispieceofinformation
withwhatshealreadyknowsaboutamale(i.e.P(H)),afemalecan computetheposteriorprobabilitythatthemaleisanappropriate mate.But,toestimatethisquantity,shouldsherelyonlyonher ownperceptionofmales’attractiveness(i.e.privateinformation), orshouldsherelyalsoonothersourcesofinformation,whichshe mayacquire,forexample,byobservinghowmalesinteractwith eachotherandwithotherfemalesinthepopulation(public infor-mation)?Recentstudieshaveprovidedevidencefortheroleofthe socialcontextininfluencingfemalematingdecision.Wereview thesestudiesinthelightofourmodelofBayesianmatechoice.
4.1. Theroleofpublicinformationandsocialeavesdroppingin matingdecisions:P(H)
Socialeavesdropping(McGregor,2005)istheactofobtaining public information from signaling interactions between con-specifics(Valone,1989;ValoneandTempleton,2002).Itisthought tooccurwhenanindividualchangeshisbehaviourtowardsa con-specific,afterobservingthelatterinasocialinteraction(Bonnie
and Earley, 2007). Social eavesdropping hasbeen mainly
stud-iedintwobehaviouralcontexts:agonisticterritorialinteractions
(Magnhagen, 2006; Naguib and Todt, 1997) and mate choice
mainly in fish and birds (review Galef, 2006; Valone, 2007;
Westneat et al., 2000) and it appears to be more common in
femalesthaninmales(butseePlathetal.,2009;SchluppandRyan,
1997;Widemo,2006,forexceptions).Femalescanacquire
pub-licinformationonaprospectivemateintwodistinctways.They mayobserveprospectivematesinintra-sexualaggressivecontests
(DoutrelantandMcGregor,2000;Otteretal.,1999).Forexample,in
femaleblack-cappedchickadees,Poecileatricapillus,the probabil-ityofextra-paircopulationsdependsontheoutcomeofmale–male vocalcontests. By experimentallymanipulating theoutcome of contestsbetweenthefemale’ssocialpartnerandeitheran aggres-siveorsubmissivesimulatedopponent,Mennilletal.(2002,2003)
showedthatfemalespairedwithhigh-rankingmalesweremore likely to accept extra-pair sires when their partner had been exposedtoaggressiveratherthantosubmissiveopponents. Inter-estingly,OphirandGalef(2004)showedthat,inJapanesequails, theuseofpublicinformationdependsonfemales’previoussexual experience:whenobservinganantagonisticinteractionbetween twomales, youngvirginfemales preferredthemostaggressive male,whereasthesexualexperiencedfemalespreferredtheleast aggressivemale.In thisspecies,experiencemayaltertheeffect ofpublicinformation,butnottheaptitudeforusingitinmating decision.
Asecondmechanismtoacquiresocialinformationon prospec-tive mates is by observing them in inter-sexual courtship interactions.Thismechanismofnon-independentmatechoicehas beendubbed‘mate-copying’,becauseitassumesthatfemales,first, acquireinformation on prospective mates by observing sexual interactionsbetweennearbymalesandfemalesand,then,usethis informationtochooseamong those males(reviewin Dugatkin,
1996;GalefandWhite,2000).Operatively,evidenceformate
copy-ingisgivenbyshowingthattheprobabilitythata‘focal’female choosesacertainmaleeitherincreasesordecreasesdependingon whethershehaspreviouslyobservedanother(‘model’)femaleto chooseortorejectthatmale(WitteandUeding,2003).Originally describedinlekkingbirdsandshoalingfish(reviewinDugatkin,
1996;Witte, 2006), matecopying hasbeenfurtherobserved in
othervertebrateandinvertebratetaxa(insects,Meryetal.,2009; mammals,Galefetal.,2008;humans,Littleetal.,2008),suggesting thattheroleitplaysinmatingdecisionmightdependmoreonthe ecologicalconstraintsthatlimittheaccesstothissourceof pub-licinformationratherthanoncognitiveconstraintsthatprevent femalestouseit.
Accordingtoourmodel,publicinformationinfluencestheprior probability(P(H)),butithasnoeffectsoneithertheattractiveness (A)ortheutility(U(A))ofprospectivemates.Asimilarhypothesis wasfirstpresentedinaverbalmodelbyNordellandValone(1998)
and,successively,formalizedinamathematicalmodelofoptimal BayesiandecisionmakingbyUeharaetal.(2005).Accordingtothis view,mate-choicecopyingand,moregenerally,theuseofpublic informationinmatingdecisiondoesnotrepresentanalternative, butratheracomplementarystrategytotheuseofprivate infor-mation(Sirot,2001).Twolinesofempiricalevidencesupportthis
view(Valone,2007).First,theinfluenceofpublicinformationon
matingdecisionsincreaseswiththedecreasingqualityofprivate information.Indeed,inatwo-choicetest,afemaleismorelikely toadoptamate-choicecopyingstrategywhenthemalesare simi-lartoeachother(Dugatkin,1996;DugatkinandGodin,1992)than whentheydiffermarkedly(Brooks,1996).Second,theroleofpublic informationdecreaseswithincreasingmatingexperience.In gup-pies,youngfemalesaremorelikelytocopyolderfemalesthanvice versa(Dugatkinand Godin,1993)andwhen youngfemales are allowedtoobservebothayoungandanoldermodelfemale,they aremorelikelytocopythelatterthantheformer(Amlacherand
Dugatkin,2005).AccordingtoValone(2007),oldandexperienced
females.
Although several studies show results consistent with the hypothesisthattheeffectsofpublicinformationareonthemale involvedintheobservedsocialinteraction,thereisalsoevidence for the alternative hypothesis that females can generalize the acquiredpublicinformationtomodifytheirmatingpreferences.
WhiteandGalef(2000)showthat,inJapanesequails,femalesthat
havepreviouslyobservedaconspecificmalemating,may succes-sivelyshowapreferencenotonlyforthatspecificmale,butalso formalesthatsharehischaracteristics.Similarresultshavebeen observedinzebrafinches(Swaddleetal.,2005)andguppies(Godin etal.,2005)andalsoinaninvertebrate,Drosophilamelanogaster (Mery et al., 2009).According to this hypothesis female mate-choicecopyingisaformofculturaltransmission(Kirkpatrickand
Dugatkin,1994),becausematepreferencesevolvethrough
mech-anismsofsociallearning.
Wehaveemphasizedtheroleofpublicinformationonthe pri-orsofaBayesiandecisionvariable.However,femalesmayconstruct priorsalsofrompreviouslyacquiredprivateinformation.For exam-ple,femalesatinbowerbirds,Ptilonorhynchusviolaceus,areknown tochoosematesusingmatingexperienceofpreviousyears (Uy etal.,2000)and,onamuchshortertimescale,femalefieldcrickets, Teleogryllusoceanicus,areknowntouseinformationacquiredby assessinglong-rangecallsofaprospectivematewhenthey eval-uatetheattractivenessofhisshort-rangecourtshipsongs(Rebar
etal.,2009).
4.2. Theperceivedutilityofprospectivemates:U=P(A|H)/P(A|Hc)
TocalculatetheposteriorprobabilityP(H|A),femalesmustknow howtousethemale’sperceivedattractivenesstoestimatethetwo conditionalprobabilitiesP(A|H)andP(A|Hc),thelikelihoodof
per-ceivingamaleatanattractivenesslevelA,respectively,whenhe isandwhenheisnotanappropriatemate.Ourmodel(seeEq.(4)) assumesthatfemaleshaveencoded intheirgenesandwiredin theirnervoussystemthissimplerule:theratioP(A|H)/P(A|Hc)is
amonotonicincreasingfunctionofthemaleperceived attractive-ness.Wecalledthisrelationshiputilityfunction(UF).InFig.2,we assumethattheUFislinear,thatis,weassumethattheperceived valueofaprospectivematedependsonA(thepreferencefunction, PF)andonthetwoparametersthatdefinetheline:itsslopeand intercept.
Iftheslopeandtheinterceptarefixed,thenAunivocally deter-minesUandthedecisionvariable,DV.Inthiscase,PFandUFare virtuallyindistinguishable.Incontrast,whenfemalescanadjust theUFparametersinrelationtotheirexperience,internalstate,or externalconditions,thentheeffectofthePFontheDVmaychange andPFandUFaretobedistinguished.Supposeafemaleis evaluat-ingtwoprospectivemates(e.g.M1andM2inFig.2).Anincreasein
theslopeoftheUFwouldincreasethedifferenceintheperceived valuesofthetwomalesand,thus,itwouldincreasethefemale’s dis-criminationability(seealsoBailey,2008).Incontrast,anincreasein theinterceptwouldincreasetheperceivedvaluesofthetwomales ofaconstantamount,causinganincreaseinpermissivenessanda decreasein“choosiness”(JennionsandPetrie,1997).Indeed,when theperceivedvaluesofmalesincrease,femalesaremorelikelyto acceptthemindependentoftheirperceivedattractiveness. Varia-tionin“choosiness”hasbeenusuallyseenastheeffectofachange ofthedecisionrule(e.g.variationinthesearchingtacticorinthe acceptancethreshold).Ourmodelsuggeststhatthisvariationmay arisealsobyachangeintheDV.
Plasticityinmatingdecisionsisa widespreadand well stud-iedphenomenon(reviewinJennionsand Petrie,1997;Widemo
and Saether, 1999).Mate choiceoccurs onlyduring the
S.Castellanoetal./BehaviouralProcessesxxx (2012) xxx–xxx 7
Fig.2. TheUtilityFunctions(UFs)definetherelationshipbetweentheperceivedattractivenessandtheperceivedutilityofprospectivemates.Inthisexample,weassume thatUFsarelinearfunctionsofattractiveness.Thebottompanelsof(A)and(B)showthefrequencydistributionofmaleattractivenessinthepopulation.In(A)wecompare twofemales(F1andF2),whoseUFsdifferinintercept.Theirabilitytodiscriminatebetweenthetwomales,M1andM2,issimilarbecausethedifferenceintheirperceived utilitiesisthesame.However,F1ismorepermissivethanF2,becausesheassignsahigherutilitytoallmales,independentoftheirattractiveness.In(B),thetwofemales differinboththeslopeandtheintercept.Theydonotdifferinpermissiveness,becausetheirmeanperceivedutilityofmalesinthepopulationisthesame.However,they dodifferintheabilitytodiscriminatebetweenmates.Infact,thedifferenceintheperceivedutilityofM1andM2islargerinF1thaninF3.
stage(Forsgren,1997;GaborandHalliday,1997;Lynchetal.,2005;
Qvarnstrometal.,2000).Forexample,astudyonplasticityin
mat-ingpreference in Túngarafrogfemales (Lynchet al.,2005)has shownthattheprobabilityofrecognizingbothaconspecificcall (receptivity)andacalllessattractivethanaconspecificcall (per-missiveness)changesduringthereproductivestagesoffemales, probablybecauseofdifferencesintheirhormonalstate(Lynchetal., 2006).Receptivityandpermissivenessarehigherintheamplexed thaninthepre-andpost-amplexedstages,buttheprobabilityof discriminatingbetweentwoconspecificcallsofdifferent attrac-tivenessdoesnot change. Theseresults suggestthat hormones affecttheintercept,butprobablynottheslopeoftheUF.
Plasticityinmatingdecisionshasbeenfoundtoberelatednot onlytofemalereproductivestage, butalsotofemale condition
(BurleyandFoster,2006;Eralyetal.,2009;FisherandRosenthal,
2006;Fawcett andJohnstone, 2003a;Moskalikand Uetz,2011;
Poulin,1994;Slagsvoldetal.,1988),toage(Batemanetal.,2001;
Kodric-BrownandNicoletto,2001;MooreandMoore,2001),and
toecological(Booksmytheet al.,2008; Chaineand Lyon,2008;
Forsgren,1992;GodinandBriggs,1996;GongandGibson,1996;
Milneretal.,2010)andsocialconditions(BaileyandZuk, 2008,
2009;Collins,1995;Hebets,2003;IzzoandGray,2011;Lehmann,
2007;Rebaretal.,2011;Wagneretal.,2001).Inparticular,strong
evidenceforaneffectofsocialexperienceonmatingpreferences hasbeenprovided bystudiesonthecricketTeleogryllus oceani-cus.Inthisspecies,pre-copulatorymatechoiceisinfluencedby experienceofmalecallingsong:femalesarelessresponsiveifthey havebeenpreviouslyexposedtomalecalling(BaileyandZuk,2008, 2009).Furthermore,femalesthathaveexperiencedapoorly attrac-tivemalearesubsequentlymorelikelytochooseamaleandto retainhisspermatophoreforlongerthanfemalesthathave expe-riencedahighlyattractivemale(Rebaretal.,2011).Thispattern mightbeexplainedbyassumingthatfemalesadjusttheintercept oftheUFtothelocaldistributionofmaleattractiveness(seeFig.3), increasingchoosinessastheperceivedmeanattractivenesslevel increases.
Fig.3.TheplasticUtility-Functionhypothesis.Wepresentanhypothesisofhowa femalecouldadjustherdecisionvariabletothelocaldistributionofperceivedmale attractiveness,bychangingtheinterceptofherutilityfunction.Thethreelinesin thetoppanelrepresenttheutilityfunctions(UF)ofthesamefemalewhenshehas beenexposedtothreedifferentdistributionsofmaleattractiveness(P1,P2,and P3–bottompanel).ThemodelassumesthatthefemaleadjustsherUFsothatthe sameutilityscoreisassociatedtotheperceivedmeanattractivenessofmales.Asa consequence,theperceivedutilityofafocalmaleisnotconstant,butitdependson thefemale’spreviousexperience.
maybedue toa variationin thedecision rule(DR)rather than inthedecisionvariable(DV).Indeed,thispatternhasbeen usu-allyexplainedasevidenceforaflexiblethresholdindecisionrules
(Wagneretal.,2001).Sincethetwohypothesesarenotnecessarily
alternativetoeachother,itmaynotbeeasytodeviseanempirical experimentabletocontrastthem.Inthenextsection,wedealwith decisionrules.
5. Thedecisionrules
Whethera DVis continuous,choiceis a discrete categorical variable(femalesmustchooseeitheroneofthealternatives).The decisionrule(DR)isthefunctionthatconvertsthecontinuousDV intothediscretechoice(Goldand Shadlen,2007).Twotypesof DRscanbeidentified:theabsoluteandthecomparativeDRs.An absoluteDRisobtainedbysettingathreshold,whenaDVisabove thethresholdthenthedecisionmakercommitstothehypothesis associatedwiththatDV.Incontrast,acomparativeDR,typically, examinesseveralalternativehypothesesandcommitstotheone supportedbythemostrobustevidence.Forexample,instatistics,a traditionalnull-hypothesistestadoptsanabsolutedecisionrule.In thiscase,thestatisticsrepresentstheDVsandthecriticalvalueof thestatisticsassociatedtothedesiredTypeIerrorrepresentsthe threshold.Incontrast,themodelselectionapproachinstatistics mightbeviewedasanexampleofcomparativedecisionrule.
5.1. Theoreticalbackground
Although mate choice arises by applying a decision rule to apattern ofpreferences,thesetwo componentsofmatechoice havebeenrarelyanalysedwithinaunitarytheoreticalframework
(GibsonandLangen,1996).Typically,studiesthatfocuson
mat-ingpreferences(i.e.onthedecisionvariable)aimatunderstanding therelationshipbetweensignalvariationandmatingsuccess,and adopta‘descriptive’approach.Incontrast,studiesthatfocuson matingdecisionrulesaimatunderstandinghowfemalesgather anduseinformationonprospectivematesforoptimalmating deci-sionand,thus,theyadopta‘normative’approach(Castellanoand
Cermelli,2011).
SincethepioneeringtheoreticalstudiesofJanetos(1980)and
Parker(1978,1983),normativemodelsofmatechoicehavebeen
developedinanoptimalityratherthaninagametheoretic frame-work,in that theyassume there is a singlechoosy sex, whose behaviourdoesnot affect the advertisingstrategy of theother
sex(butseeFawcettand Johnstone, 2003a;Guallaet al.,2008;
Johnstone, 1996).These models tryto explain matingdecision
rulesonthebasisofhowinformationiscollected,thatis,onthe basis of how females sample prospective mates.These models haveidentified threemain samplingtactics:(i)random choice; (ii)sequentialsearching(SSmodels)and(iii)fixed-sample-search tactics(FSmodels,alsoknownasbest-of-nmodels).
Therandomchoicemodelassumessimplythatfemalesmate withthefirstconspecificmaletheyencounterand,thus,it repre-sentsasortof‘null-model’againstwhichtocomparetheothers. InSSmodels,femalesareassumedtouseanabsoluteDR,inthat theydonotkeepmemoryofpreviouslyassessedmalesand sam-pleprospectivematesuntiltheyfinda malewithqualityequal toorgreaterthanacertainthreshold.IntheFSmodels,females areassumedtouseacomparativerule,theysampleafixnumber ofprospectivemates,keepmemoryofthem,andchoosethebest amongthem(Real,1990).AninterestingvariantoftheFSmodel hasbeenproposedbyLuttbeg(1996)andnamedthe“comparative Bayesian”model(CB).LikeintheFSmodel,femalesareassumed tochoosethebestamongasampleofmales,butthesamplesize
byrepeatedlyassessingprospectivematesaccordingtoaBayesian updatingprocedure(seebelow).
Undertheadaptationistassumptionthatnaturalselectionhas favouredtheevolutionofoptimalmatesamplingtactics, theoreti-cianshavecomparedtheperformanceofthesenormativemodels ofmatechoicetofindoutwhichisexpectedtofarebetter. Opti-maldecisionrules,however,largelydependsontheassumptions onwhichthesemodelsarebased.
A first critical assumption is about searching costs. Janetos
(1980)assignsnocostsonmatesearchingand, thus,concludes
thatFSmodelsperformbetterthanSSmodels.Real(1990)shows, however,thatifcostsareintroducedinthemodel,theFSdecision ruleisoutperformedbyaSSmodelinwhichfemalesadopta fix-thresholddecisionrule(Wiegmannetal.,2010b).Thisrule,infact, allowsfemalesthatencounterahigh-qualitymaleatthebeginning oftheirsearchtoavoidthecostsoffurthersearch.
Asecondcriticalassumptionisabouttheroleofuncertaintyin thedecisionprocess.Twotypesofuncertaintymaybeidentified: uncertaintyaboutthedistributionofmatequalityinthe popula-tionanduncertaintyaboutthequalityofaprospectivemate.The uncertaintyonthelocalqualitydistributionhasarelevanteffect onmate-search tactics.Real’s(1990)modelassumesfemalesto knowthelocaldistributionofmalequalities,whichisuniformor truncatednormal.However,whenthedistributionofmale qual-ityisallowedtovarybothspatiallyandtemporally,theSSmodel withfixed-thresholdisnolongertheoptimalmatesampling
tac-tic(Mazalovetal.,1996;Luttbeg,2002)anditisoutperformedby
adaptiveSSmodels,inwhichfemaleslearnfromprevious expe-rienceandupdatetheiracceptancethresholdaccordingly(Collins
etal.,2006;DombrovskyandPerrin,1994;Mazalovetal.,1996).
Collinsetal.(2006)presentaBayesianmodelforupdating
informa-tioninasocialenvironmentwherethemate-qualitydistribution isexpectedtovaryinboththemeanandthedispersionaround themean.Inthismodel,femalesassessmalequalitywithouterror. Undertheseconditions,theoptimalruleislearning:femaleschoose theirmatesonthebasisofanacceptancethresholddefinedbythe sumbetweenthecurrentestimateofthepopulationmeanandan additivecomponentthatdecreaseswiththeincreasingnumberof sampledmales.
The effectof thesecond type of uncertainty (uncertainty in mate-qualityassessment)hasbeeninvestigatedbyWiegmannand
Angeloni(2007).Intheirmodel,femalesareassumedtobeableto
assessonlyasubsetofamale’sfitness-relatedattributessothat theexpectedbenefitsforafemalearenolongerdeterministic,but stochastic.Theyfindthat stochasticitydoesnot affectthe qual-itative behaviourof boththeFS and theSSmodels.Given that theexpectedbenefitsofchoicecontinuetoincreasemonotonically withtheobservedmaleattributes,theSSmodelalwaysfarebetter thantheFSmodel(seealsoWiegmannetal.,2010a).
InWiegmannandAngeloni(2007),femalesareassumedtohave
nocontroloverthelevelofuncertaintyintheirevaluation.In con-trast,the comparativeBayesianmodel of matechoice(Luttbeg, 1996), givesfemales control over theirassessment accuracy. In Luttbeg’smodel,femaleshaveanuncertainpriorestimateofthe quality ofeach prospective mate,and, at any stepof the deci-sionprocess,theycoulddecideeithertousethisinformation(and choose)ortocontinue theevaluationbyimprovingassessment accuracy.Femalesstopevaluatingmalesandchoosethebest alter-nativewhenthecostofmoreinformationexceedstheexpected benefitsofthatinformation(Luttbeg,1996).
Othertwoassumptionsthataffecttherelativeperformanceof matedecisionrulesaretheconstraintsonboththenumberof avail-ablealternativesand themaximumspendable time formaking decision.Allmodelspresentedsofarassumeaninfinitenumber ofalternativesfromwhichtochooseandaninfinitetimehorizon.
S.Castellanoetal./BehaviouralProcessesxxx (2012) xxx–xxx 9
Luttbeg(2002)usedsimulationstoinvestigatetheeffectsofthese
assumptionsonFS,SSandCBmodelsofchoice.Simulationsshowed thatareductioninboththenumberofoptionsandthetimefor choosinghadstrongereffectsontheperformanceofSSmodel(with fixthreshold)thanonthatofboththeFSandCBmodels.He con-cludedthat,innaturalconditions,comparativedecisionrulescould beaseffectiveas,orevenmoreeffectivethanabsolutedecision rules.
5.2. Theempiricalevidencefordecisionrules
Theoretical studies of mate choice have strongly influenced the empirical research. Based onthe adaptationist assumption thatselectionwouldprovidedecisionmakerswithoptimal deci-sion rules, researchers have used simulations to compare the performance of differentmodelsand to predictwhich of them was most likely to occur in natural conditions (Janetos, 1980;
Luttbeg,2002;Real,1990).Aswehaveshownabove,however,the
relativeperformanceofdecisionmodelsstronglydependsontheir assumptions(Luttbeg,2002;LuttbegandLangen,2004).Itseems, thus,unlikelythattheoptimalityapproachontheoreticalmodels couldprovidedirectevidenceforoptimalmatesearchingtactics innaturalconditions.
Nevertheless,theoreticalmodelscouldplayaninvaluablerole inunderstandingmatechoiceinnaturalconditions,fortwo rea-sons.First, empiricists dealwithpatterns and,withoutmodels, itwouldbeimpossibletoexplainthemintermsoftheir under-lyingmechanisms.Second,empiricists wanttounderstandwhy suchmechanismsevolvedandmodelscouldshowwhichfactors aremorelikelytohavefavouredorconstrainedtheevolutionof thesemechanisms.
5.2.1. Randomchoice
Manyfieldstudieshaveshownpatternsapparentlyconsistent withtherandomchoicemodel.Inlekkinganurans,females usu-allysamplemalessimultaneouslyfromadistanceandseveralfield studieshaveshownfemalepreferencesfortheclosestmale(Arak,
1988;FriedlandKlump,2005;Grafe,1997),apatternwhichhas
beensuggestedtoariseastheeffectof“passiveattraction”tothe perceivedloudestcall(Arak,1988;Parker,1982;butseeCastellano
etal.,2004;Murphy,2008).FriedlandKlump(2005)observedthat
inlekkinganurans,thematingsuccessofmalesdependedmoreon theirlekattendancethanontheircourtshipperformanceand con-cludedthatfemalechoicewasrandomandplayedamarginalrole indeterminingmalematingsuccess.AccordingtoFriedlandKlump
(2005),afemalethatmatesrandomlysavesthecostsofsearching
and,atthesametime,isstilllikelytomatewithahigh-qualitymale, becausehigh-qualitymalescouldspendmoretimeinadvertising andthusaremorelikelytoberandomlyselectedbyfemales.
Ingeneral,however,itishardtoseehowrandomfemalechoice couldhavepromotedtheevolution ofa courtshipbehaviouras costlyasthecallingofchorusinganurans(Castellano,2009b).What weperceiveasevidenceofrandomfemalechoice(i.e.thelackof acorrelationbetweenmatingsuccessandcourtshipbehvaiourof males)maybetheeffectofastrongfemalepreferencefor high-advertising levels,which forces males either toattain to those levelsortoabandonthecompetition(Castellano,2009b;Johnstone, 1994).Forthisreason,wesuggestcautionfromtaking random-choicepatternsas evidencefor permissive matingdecisions,in particular,whenthecostsofmatesearchingarepresumablylow (suchasinleks).
5.2.2. Fixedsample
Evidence for comparison decision rules (FS model) in mate choicecomesmainlyfromlekkingspecies(reviewinJennionsand
Petrie,1997),inwhichthecostsofsearchingaregenerallylowand
femalesmayassessseveralmatessimultaneously.Inmany cho-rusingtreefrogs,forexample,femalesdonotmoveamongcalling males,butreachalocation,fromwheretheyassessseveralmales simultaneously(MurphyandGerhardt,2002).Fieldexperiments ongraytreefrogs haveshownthatthetimerequiredtoreacha decisionmayberathershort(about2min)(Schwartzetal.,2004). Itisnotclearwhetherthisshortassessmenttimeisdueto cog-nitiveconstraintsonworkingmemory(AkreandRyan,2010)or whetheritrepresentsanoptimaltradeoffbetweenthecostsand thebenefitsofmaleassessment.Amate-samplingpattern consis-tentwithaFSdecisionmodelhasbeenobservedalsoinnon-lekking speciesofbirds(HoviandRatti,1994)andmammals(Byersetal.,
2005;Ferrettietal.,2011).Forexample,Daleetal.(1992)provided
evidencethatfemalepiedflycatchersadoptedacomparison deci-sionrule:femalesvisitedseveralmales(three,onaverage)before committing,oftenreturnedtoapreviouslyassessedmale,andthe probabilityofchoosingamaledidnotdependonhispositionin thesamplingsequenceofprospectivemates(DaleandSlagsvold, 1996).Onaverage,femalesspentabout5hsearchingformates,and inonehourtheywereabletovisituptosevendifferent prospec-tivemates.In theSatinbowerbird(Ptilonorchynchusviolaceous), femaleswerefoundtosearchformatesforverylongperiods(15 days,Uyetal.,2000).Beforechoosingtheirmate,femalesvisited severalmalesforcourtshipandthentheyreturnedtoasubsample ofthemforfurtherevaluation.Femaleswerefoundtoremember theassessed malesnotonly within,but alsobetweenbreeding seasons.Since malesof thisspecies usethesamebowersitein successiveyears(Borgia,1993),thereisevidencethatfemalesuse previousmatingexperienceinmatingdecisions:femaleswho,in thepreviousyear,matedwithhighlyattractivemates,inthe suc-cessiveyearvisitedasmallernumberofmalesandweremorelikely tore-matewiththesamemalethanwerefemalespreviouslymated withunattractivemales(Uyetal.,2000).
5.2.3. Sequentialsearch
InSSmodels,femalescomparemalesagainstaninternal stan-dard,whichmaybeeitherfixedorvariable.Thedistinctionbetween thefixedandvariablethresholdmodelsisambiguousbecause,as we have pointed out above,it is not clearwhether experience affectsthedecision rule(i.e.thethreshold)orthedecision vari-able(asassumedbyourBayesianmodel)orboth.TheSSmodelsdo notrequirefemalestokeepmemoryofindividualmales(butonly oftheirdistribution)andthusthesetacticsarethoughttoimpose lessseverecognitiveconstraintsonfemaleperformancethanthose imposedbytheFSmodel(andcomparativeDR).
Inpractice,bothfieldstudiesandchoiceexperimentshavebeen difficulttoprovideclearevidenceforSSdecisionrules(Jennions
andPetrie,1997;Valoneetal.,1996;WidemoandSaether,1999).
TheSSmodelassumesnorecallofpreviouslysampledmalesand thus predicts that choice is for the last of a sequence of sam-pledprospectivemates.However,thisrulemayresultinapattern consistentwiththeFSruleifmales,bychance,canbesampled morethanonce,andiffemalesacceptmalesthatwerepreviously rejectedbecauseofeitheravariationinflexiblethresholdsor, sim-ply,anevaluationerrorincaseoffixedthresholds(Luttbeg,2002;
Luttbegand Langen,2004).StrongevidenceforSSdecision rule
wasreportedbyGibson(1996)inthesagegrouse, Centrocercus urophasianus,andbyReidandStamps(1997)inthepineengraver, Ipspini.Inthelatterstudy,theobservedpatternwasconsistent withtheSSmodelwithaflexiblethreshold:femalesoftenmated withthefirstmaleencountered,rarelyreturnedtoavisitedmale, andadjustedtheiracceptancethresholdinrelationtothequality ofthepatches.
As it concerns theexperimentalapproach, two linesof evi-dencehavebeenproposedtosupportthehypothesisofSSdecision rules. First, in two choicediscrimination tests, thepresence of
betweentwo low-qualityalternatives.Zuketal.(1990)showed thatredjunglefowlfemales(Gallusgallus),whengivenachoice between two males with large combs, preferred the one with thelargestattribute,butwhenbothprospectivemateshadsmall combs,femalesdidnotchooseorchoserandomly. Itshouldbe noticedthat,even ifan acceptance thresholddoesexist in this species,itdoesnotpreventfemalesfromchoosingthebestofthe twoalternativeswhenbothwereabovetheacceptancethreshold.A secondlineofevidencecomesfromstudiesthatcomparepatterns ofmatingpreferencesobtainedunderdifferentexperimental con-ditions.Moore&Moore(1988)studiedfemalematingdecisionin acockroach(Nauphoetacinerea)andfoundthatmatingbehaviour wasunaffectedbythenumberofavailablealternatives:thelatency toapproach,torespondtoortomatewithamaledidnotdepend onwhetherfemalesweretestedintwo-choicetest(between dom-inantandsubordinatemales)orinno-choicetest(eitherdominant orsubordinatemale).Theyconcludedthatfemalecockroachesdid notcomparealternativesagainsteachother,butagainstaninternal, fixedstandard.
AnotherstudysupportingtheSSmodelisthatbyBeckersand
Wagner(2011)onmatesamplingstrategiesinGrylluslineaticeps.
Femalesweretestedinthree-stimuluschoiceexperiments.They showedpreferencesforchirprateshigherthan3chirps/sover alter-nativeswithchirprateslowerthan3chirps/s,butfailedtoshow anypreferenceamongcallswithchirpratesallhigheroralllower than3chirps/s.Interestingly,previousexperimentsusinga two-choicetestingparadigmprovidedevidenceformuchfinerlevels ofdiscriminationamongchirprates(WagnerandBasolo,2007), thussuggestingthatdecisionrulesmaydependonthenumberof stimulitowhichfemalesaresimultaneouslyexposed.
5.3. Doesvariationinthepatternofchoicereflectvariationin decisionrules?
Despitethestrongtheoreticalandempiricaleffort,the ques-tionofhowfemaleschoosetheirmatesremainslargelyunresolved.
Jennions and Petrie(1997) suggested that this may be due to
variationinmate-decisionrules.Variationmayoccuratthe within-populationlevel.Forexample,mostfemalepiedflycatchersvisit severalmalesbeforemating(Daleetal.,1992;DaleandSlagsvold,
1996;HoviandRatti,1994),butothersmatewiththefirstorwith
thelastencounteredmale,showingpatternsconsistentwithboth theFSand theSS models(FiskeandKalas, 1995).Butvariation mayalsooccuratthewithin-individuallevel.Asreportedabove,
Beckers and Wagner (2011) showedthat G.lineaticeps females
useda thresholdrulewhen choosingamong threealternatives, butswitchedtoacomparativerulewhenchoosingbetweentwo alternatives.MacLarenandRowland(2006)comparedfemale pref-erencesformalebodysizeinsailfinmollies,Poecilialatipinna.They observedamuchstrongerpreferenceforlargesizewhen alterna-tiveswerepresentedinapairedfashionratherthansequentially, suggestingthatfemalesappliedcomparativedecisionrulesonly whensimultaneousevaluationwaspossible.Brandtetal.(2005)
showedthatlesserwaxmothfemales,Achroiagrisella,usedboth absoluteandrelativecriteriatochoosetheirmates:independent ofthenumberofavailableprospectivemates,theyrejectedmates thatcallataratelowerthanafixedthreshold,but,whenseveral malescalledabovetheacceptancethreshold,femaleschosetheone withthehighestrate.
Theseempiricalstudiesposeanimportanttheoreticalquestion: Isvariationinthepatternofchoicetheeffectofdifferentdecision rules,orisit theeffectofdifferentcontextsin whichthesame decisionruleisused?Wearguethattorespondtothisquestion, weshouldadoptacomputationalapproachthataimsatexplaining
mechanisms(Castellano,2009a).
Castellanoand Cermelli(2006)and Phelpset al.(2006)
pre-sentedtwomodelstostudytherelationshipbetweenrecognition anddiscriminationinmatingdecision.InCastellanoandCermelli’s
(2006)model,theprobabilityofchoosingamateAoveran
alter-nativeB,wasassumedtobethesumoftheprobabilitythatonlyA wasrecognizedasanappropriatemateandthecombined proba-bilitythatbothAandBwererecognized,butAwaspreferredto
B.Phelpset al.(2006)usedsignaldetectiontheorytolink
per-ceptiontodecision. Intheirmodel, theperceivedattractiveness ofaprospectivematewasastochasticnormalvariablewith vari-anceproportionaltothelevelofuncertainty(seeEq.(1)).Females wereassumedtochoosethemostattractivemalethatexceededa minimalrecognitionthreshold(Phelpsetal.,2006).Inthese mod-els,themating-decisionmechanismdependsonbothabsolute(the recognitionthreshold)andcomparativeDRsanditcouldbeused independentoffemales’mate-samplingtactics.
Accordingtothesemodels,recognitionanddiscriminationare theexpressionofthesamecognitivemachinery,whichusesthe same“currency”formakingdecision(thepreferencestrengthin
Phelpsetal.(2006),theamountofevidence,A,inourmodel– see
Eq.(1)).Anotherpossibility,however,isthatrecognitionand dis-criminationaredifferentprocessesthatevolvedtosolvedifferent tasks.Inthiscase,weshouldexpectatask-specificroleofsignal attributesinrelationtothetypeofinformation theyconvey.In recognitiontests,signalattributesthatconveyinformation impor-tantforspeciesrecognitionshouldaffectfemalematingdecision morestronglythanattributesimportantformatediscrimination. Indiscriminationtests,theoppositepatternshouldbeobserved.
Phelpsetal.(2006)measuredfemalepreferencestrengthoveraset
ofsignalsinbothrecognitionanddiscriminationexperimentsand foundastrongcorrespondencebetweenthetwopreferencescales.
Bushetal.(2002)usedrecognitiontests,butmeasuredfemale
pref-erencesastheratiobetweenthetimerequired torespondtoa certainstimulusandtoastandardsignal(thelatency-ratiotest). Theyfoundbroad similaritiesbetweenthepreference functions obtainedwiththelatency-ratiotestandthetwo-choice discrimi-nationtests.Overall,thesestudiesprovideempiricalevidencethat recognitionanddiscriminationaretheexpressionofthesame cog-nitivemachinery(Castellano,2009a).
6. Sequentialsamplingmodelsofmatechoice
In Phelps et al.’s model (2006), the strength of preference
betweenthetwoalternativesdependsonthelevelofuncertainty (accuracy)ofmaleassessment,butfemaleshavenocontrolover it.Asinmostofsignaldetectionmodels,inPhelpsetal.’s(2006)
model,uncertaintymaybeviewedastherandomsamplingerror that arises from the integration of independent pieces of evi-denceoverafixedevaluationtime(Castellano,2009a;Pleskacand
Busemeyer,2010).Infact,supposethat(i)afemale,duringafixed
timeintervalT,usesnpiecesofevidencetoassessthe attractive-nessofamate,(ii)eachpieceofevidencecanbeeitherapositive (+1=themaleisanappropriatemate)oranullevaluation(0=no evidencethatthemaleisanappropriatemate),and(iii)pisthe probabilityofapositiveevaluation.Ifnissufficientlylarge,then theamountofevidenceapproximatesanormaldistributionwith meannpandvariancenp(1−p).
Recently, Castellano and Cermelli (2011) presented a sequential-sampling model of mate choice that can be viewed as a logical extension of the signal detection model of Phelps
et al. (2006). Sequential-sampling models of decision making
are a dynamic variantof signaldetection models (Pleskac and
Busemeyer,2010),inthattheydroptheassumptionthatdecision
S.Castellanoetal./BehaviouralProcessesxxx (2012) xxx–xxx 11 decision is made as soon as the accumulating noisy evidence
reaches a fixed threshold (Castellano, 2009a; Castellano and
Cermelli,2011).
Unlike signal detection models, sequential-sampling models incorporatetimeinthedecisionprocessand,thus,theycouldbe usedforinvestigatingspeed-accuracytradeoffsindecisionmaking
(Chittkaetal.,2009;Sullivan,1994)andformakingtestable
pre-dictionsontherelationshipbetweenchoiceprobabilityandtime response(Kacelniketal.,2011;Shapiroetal.,2008).Althoughthese modelshavebeenonlyrecentlyintroducedinbehaviouralecology
(CastellanoandCermelli,2011;Kacelniketal.,2011;Shapiroetal.,
2008;Trimmeretal.,2008),theyhavealonghistoryincognitive
psychology(reviewinRatcliffandSmith,2004)andin neurobiol-ogy(reviewinBogacz,2007;GoldandShadlen,2007;Smithand
Ratcliff,2004)andtheycouldrepresentausefultheoreticaltoolfor
buildingbridgesbetweenneurobiologyandbehaviour(Busemeyer
etal.,2006).
Sequentialsamplingmodelshavebeendevelopedtoaccountfor simpletwo-choicedecisions,althoughtheyhavebeenalsoused formodeling multi-alternativedecisions(Roe etal.,2001).Two typesofsequentialsamplingmodelshavebeenproposed:race(or accumulator)andrandom-walk(ordiffusion)models.Inrace mod-els,evidencein favourofonealternativeisaccumulatedinone responsecounterandevidenceinfavouroftheotheralternative isaccumulatedonanothercounter.Decisionismadewhenoneof thetwocountersreachesafixedcriterionamountofevidence.This stoppingruleisdefinedas‘absolute’ becausecounters accumu-lateevidenceovertimeindependently,withoutinteraction.Inthe secondtypeofsequentialsamplingmodels(random-walkmodels sensustricto),evidenceforeitherthealternativesaccumulateas asingletotal,whichisthedifferenceintheamountofevidence betweenthealternatives(for thisreason,Kacelnik etal.(2011)
proposedfor them the picturesquename of ‘tug-of-war’ mod-els).Random-walkmodelsassumethatevidenceaccumulatesat discretetimeintervals.Whenevidenceaccumulatescontinuously withtime,sequentialsamplingmodelsarenameddiffusionmodels
(RatcliffandSmith,2004).
Castellanoand Cermelli’s(2011)model ofmate choiceisan
exampleofaccumulatormodelinthatitassumesfemalesto asso-ciatetoeachprospectivematea“counter”.Althoughfemalesmay evaluateseveralmalessimultaneously,assessmentisassumedto beaserialratherthanaparallelprocessingtask:females,infact, arethoughttoconductarepeatedsequentialscanningof prospec-tivematesandtoacquireinformationononemaleatatime.Inthis way,themodelmakestheplausibleassumptionthattherateof informationgatheringdependsmoreonfemaleintrinsiccognitive constraintsthanonextrinsicecologicalfactors(suchasthenumber ofmalesthatcouldbeevaluatedsimultaneously).
Two issues were investigated using this model (Castellano
andCermelli,2011).Thefirstwasoptimalityinmatingdecision.
Optimalchoicewasdescribedintermsofthetrade-offbetween theacceptance threshold and the number of males simultane-ouslyassessed.Resultsof simulationsshowedthat,unlesscosts wereveryclosetozero,theoptimalstrategywasalways assess-ingseveralmalesusinga cost-dependentacceptancethreshold. Thesecond issue wasthedescription offemale mating prefer-ences under three experimental choice paradigms: recognition (no-choice),discrimination(two-choice),andtime latencytests. Themodelshowedthatrecognitionanddiscriminationtests pro-videdan inaccuratedescription of matingpreferences,because theyintroducedsystematicerrorsthateitherattenuated (recogni-tiontests)orexaggerated(discriminationtest)thetruedifferences inmatingpreference.Incontrast,thelatency-ratiotest(Bushetal., 2002)performedmuchbetterthantherecognitionand discrim-inationtests,emphasizing theimportanceof time responsesin assessingfemalematingpreferences(Bushetal.,2002;Leonard
andHedrick,2010;Rebaretal.,2011;Shackletonetal.,2005),as
alreadyshown inothercontextsof choice(i.e.foodpreferences
BatesonandKacelnik,1995;ReboredaandKacelnik,1991).
Thesequentialsamplingmodelsmaybecomeanappropriate theoreticalframeworktounderstandmatechoicefromthejoint perspectiveoftheultimate(functional)andproximate (mechanis-tic)causes(Castellano, 2009a).CastellanoandCermelli’s(2011)
model, as well as all the accumulator models, assumes that evidence for each alternative accumulates separately without interaction.Fromthisassumptionitderivesthepredictionthat, in two-choicediscriminationtests,themore similarthe attrac-tivenessofthetwostimuli,theshorterthelatencytochoose.In contrast,ifthemodelassumesadirectcomparisonbetweenthetwo alternatives,sothatthereexistsonlyonedecisionvariable(either thedifferenceortheratiobetweenthestrengthofevidence sup-portingoneovertheotheralternative),thenthe(random-walk) modelpredictsthatthemoresimilartheattractivenessofthetwo stimulithelongerthelatencytochoose.Inhumans,weusually findsupportforthecomparativemodel:responsetimeincreases andaccuracydecreaseswithincreasingdifficultyofthe discrimi-nationtask(Luce,1986).Incontrast,verylittleisknownonhow otheranimalsuseinformationinsimultaneouschoice.
So far, behavioural ecologists have tackled this question in a context different from mate choice: prey selection (Kacelnik
etal.,2011;Shapiroetal.,2008;Vasconcelosetal.,2010).
Kacel-nikandcolleaguestestedthetwosequentialsamplingmodelsof makingdecision(withandwithoutcomparisonbetween alterna-tives)usingtheEuropeanStarling,Sturnusvulgaris,inlaboratory testsonpreyselection.Bymeasuringlatencytochoose,they pro-videdevidencethatstarlings,insimultaneousencounters,didnot adopt acomparativeevaluation, but processedeach alternative independently.Since,innaturalconditions,starlingsrarelyincur in two fooditems simultaneously, they suggested that natural selection had not favoured the evolution of cognitive mecha-nisms to efficiently compare and select the best of the two alternatives.
Asitconcernsmatechoice,wemayexpectnaturalselectionto havefavouredtheevolutionofcomparativemechanismsofchoice inspecies wheresimultaneousencountersofprospectivemates arecommon,asitisinlekkingspecies.Althoughnostudieshave yet tested this hypothesis, episodic evidence seemsto support it.InTungarafrogs,forexample,Phelpsetal.(2006)andBosch
etal.(2000)foundanegativecorrelationbetweenthedifficulty
ofdiscriminationandthelatencytochoose,aspredictedbythe comparativesequentialsamplingmodelsofchoice.
6.1. ABayesiansequential-samplingmodelofchoice
Inallsequential-samplingmodelsdescribedsofar,theDVisa scalarquantityandtheevaluationprocess(theintegrationof evi-denceovertime)isequivalenttothecomputationofthearithmetic mean.Inourmodel,however,theDVis theposterior probabil-ityofa Bayesiancomputationand integrationover timecanno longerbemodeledasanadditive,linearprocess.Bayes’ruleyields an alternativeframework tostudythe processby which males areevaluatediteratively(Deneve,2009).Assumingthatevaluation takesplaceatdiscretetimestepsti,theresultingaccumulationof
evidencecanbedescribedbyanupdateofthepriorestimateof themaleaccordingtotheactualestimateofthemale attractive-ness,i.e.,P(H,ti)=P(H|A,ti).ByBayes’rule,wemayincorporatethis
assumptionintherecursiverelation
P(H|A,ti+1)= u(A)
(u(A)−1)+ 1 P(A|H,ti)
