macroevolutionary patters pollination accuracy

8/10/2019 Macroevolutionary Patters Pollination Accuracy

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Macroevolutionary Patterns of Pollination Accuracy: A Comparison of Three GeneraAuthor(s): W. Scott Armbruster, Christophe Plabon, Thomas F. Hansen and Geir H. BolstadSource: New Phytologist, Vol. 183, No. 3, Plant Adaptation: Following in Darwin's Footsteps(Aug., 2009), pp. 600-617Published by: Wiley on behalf of the New Phytologist Trust

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New |T^2Research Phytologist ^

Macroevolutionarypatterns of pollinationaccuracy:a

comparisonof three

generaW. ScottArmbruster1'2'3,hristophePlabon4,Thomas F. Hansen5and GeirH. Bolstad4School ofBiologicalciences,UniversityfPortsmouth,ortsmouth O12DY,UK;departmentofBiology,NTNU, N-7491,Trondheim,orway;institute of ArcticBiology,UniversityfAlaska,Fairbanks,K99775, USA;4Centre or Conservationiology,Departmentf Biology,NTNU,N-7491,Trondheim,orway;CentreorEcologicalndEvolutionary ynthesis,Departmentf Biology,UniversityfOslo,PO Box1066,N-0316Oslo,Norway

Author forcorrespondence:W.Scott ArmbrusterTel:44 (0)2392842081

Email:[email protected]. ukReceived:1 February2009Accepted:18May2009

NewPhytologist(2009)183: 600-617doi:10.1111/j.1469-8137.2009.02930.x

Keywords: adaptiveaccuracy,adaptivesurface, Collinsia,Dalechampia,optimality,pollination,precision,Sty d urn

Summary We hypothesize that pollination efficiency selects for equal distances between the

pollinator reward and the anthers, and the stigmas, creating an adaptive ridge. We

predict that this fitness surfacegoverns the divergence of many plant species. Weuse the theory of adaptive accuracy, precision and mean optimality to assess howclose populations lie to the hypothesized adaptive ridge and which factors contributeto departure from the optimum. Patterns of accuracy of pollen placementand receipt were compared across speciesin three study systems, Dalechampia (Euphorbiaceae), Collinsieae (Plantaginaceae)and Stylidium (Stylidiaceae),inorder to assess theroles ofstamen/stigma imprecisionand populationmean departure from the optimum inthe generation of floralinaccuracy. We found that population mean departure from the optimum was the most

important factor inDalechampia, female imprecisionand departure from the optimumwere about equally importantfactors inCollinsieae,and stamen and stigma imprecisionwere equally important in Stylidium, with virtuallyno departure from the optimum. Possible reasons forimprecision and departure from the optimum were assessedusing phylogenetically informed methods, indicating important roles of limitedfloral

integration in the generation of imprecision, and conflicting selective pressures,associated withoutcrossing, in the generation of departure from the optimum.

IntroductionAlthoughmanyfundamentalquestionsn evolutionarybiologyremainunanswered,one of the mostcompellingis: what is therelativeimportanceof adaptation, geneticconstraintsandhistoricalcontingencyin the divergenceof populationsandspecies(Williams,1992; Schluter,2000; Gould,2002)?Thediversityof floraldesign among plant specieshasbeen invoked

repeatedlyas one of the mostdramatic examplesof thediversification ofspecies bynatural selection(for example,Darwin, 1877; Stebbins, 1951,1974), and constitutes agoodstudy systemto addresschallengingmacroevolutionaryquestions.Since Darwin'stime, it hasbeenlargelyassumedthatfloraldiversificationamongspeciesreflectsadaptiveevolu-tion andspeciationin responseto divergentselection exertedby pollinators(Grant, 1971; Stebbins,1974; Schluter, 2000;Gavrilets,2004).Somerecentstudieshavesuggested,however,thatpollinatorsmaybeonlyone of severalpossibleevolutionary

forcesgeneratingfloraldiversity(for example,Armbruster,1991,2002; Strauss & Irwin, 2004). Instead,the potentialimportanceofdevelopmentalconstraintsand geneticfactors,such aspleiotropy,as well as selectionby other interactors,forces us tos^sess loraldiversitymorecautiously,withadaptivediversificationbeingjust one of severalpossiblecontributors.In thepresentcontribution,weexplorethe roleofadaptationas aprobablefactor,but in the context ofbeingonlyone of

severaltestablehypothesesfor floraldivergence.The treatmentof adaptiveevolutionas the movementofpopulations on an adaptivelandscape(or surface)in alelefrequency(Wright,1931)or morphologicalspace(Simpson,1944)representsa usefulway to conceptualizeevolutioninresponseto natural selection.The adaptivesurfaceconcepthas beenapplied argelyo assesscomponentsofrelativeitnessof particular genefrequenciesor values ofselectedmorpho-logicaltraitsfor individualsn apopulation(Lande&Arnold,1983;Schluter,1988;Schluter& Nychka,1994;O'Connell

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&Johnston,1998).Thisconceptcan, however,also beappliedto the adaptivedivergenceof populationsand species,underthe assumptionthat theyall experiencethe samepre-existingadaptive landscapefor the componentsof fitness and traits

beingexamined(forexample,with multiplepeaksor bumpyridges;Armbruster,1990;Arnold etai>2001).Althoughthisis notalwaysthe case,it appearsto be true for relatedspecieswith similarecologies,andisthus a usefulconceptualapproachto study the roles ofadaptation, constraint, history andrandomness inmacroevolution.It is important to note thatadaptive optima(highpoints on the landscape)can pertainconceptuallyto the totalityof biologicalfunctionsand traits,but mustusuallyapplyoperationallyoonlysubsetsoffunctionsand traits (componentsof fitness).In the presentstudy,weconsider theshape of the adaptivesurfacegoverningonefunctionandtwotraits:pollinationperformanceacomponentof reproductiveitness)in responseto thepositionsof anthersand stigmasin flowers.

Arelated,complementary approachto theassessmentofanorganisms positionon itsadaptivesurface is toevaluate the'adaptiveaccuracy'of populations.This requiresthe identifi-cation ofadaptiveoptima(forfitnesscomponents),estimationof trait deviationfrom theseoptimaand theassessmentof thepossiblecausesofmaladaptation.Thelatter nvolves hedecom-positionof adaptive inaccuracyinto three components:thedistanceofthepopulationmean fromthephenotypic optimum;variation ofthe phenotypic optimum;and variance of thepopulationphenotypearound thepopulationmean('popula-tionimprecisionArmbruster tal., 2004,2009;Hansenetal.,2006; Plabon& Hansen,2008). The populationimpreci-sion itselfcomprisestwo components:genetic imprecision(varianceof the geneticvaluesaround thepopulationmean);anddevelopmental/environmentalvariancearound thegeno-typic target (phenotypicimprecisionor noise;Hansenetai,2006).Exceptin the brieftheoreticalintroductionbelow,wedo notseparateempiricallythese lasttwocomponents.

In the present study,we combineadaptive accuracyandadaptivesurfaceapproachesn an attempt to understand thecausesof floraldiversification,r lack ofdiversification,n threegeneraorwhich we haveassembleddataon floralmorphologyand pollination.We focus on apair of traits that areeasilymeasured andfor which'adaptiveoptima' (withreference toacomponentoffitness)can bereadilyhypothesized.Weexplorethe degreeto which traits track theirhypothesizedadaptive

optimathroughmacroevolutionarytime and

space.We first

beginwith afewcomments onpreviousworkand thengiveabrief introduction to thetheoryof adaptive accuracy,beforeintroducingthe threestudysystemsn Materialsand Methods.

Adaptive accuracy and fitness surfacesin flowerpollinator Jfitr

Previouswork on theadaptive accuracyof flowershaslargelyfocusedon the fitbetweenflowers andpollinatorswithrespect

to the location ofthe rewardand the length of pollinatorstructuresobtainingthe reward. Darwin(1877)speculatedon theevolutionarymatch offloralnectarspursand thepro-bscides ofpollinators,invokingcoevolution.Indeed,some

of thebest evidence forthe coevolution offloralspursor tubeandpollinatorappendagelengthhascome fromcomparisonsamong conspecificpopulationsandcongeneric species(Steiner& Whitehead,1990,1991;Johnson& Steiner,1997).Therearealso afewstudiesofrelativeitness andphenotypicselectionwithinpopulations,showing higherfitness nfloralphenotypeswithnectar pursortubes thatmatch thepollinators'robscides(Nilsson,1988;Maad &Alexandersson,2004).

The adaptivesurfacemodel ofnaturalselectionhas beenappliedto componentsoffitnessinfluencedbyfloralmorpho-logyin two ways.One is toestimate theshapeof the fitnesscomponentlandscapebyrelatingndividualcomponentfitnessestimatestowithin-populationvariation nfloralmorphology(O'Connell & Johnston, 1998;Maad, 2000). The secondapproach,and that usedhere,is toestimatethe fitness com-ponentlandscapetheoreticallyandtest itagainsttheobserveddistribution ofpopulationsandspeciesn morphologicalspace(Armbruster, 990).Previously,Armbruster 1990)found thattheblossom sizeofnumerouspopulationsandspeciesofDale-champiahad apparentlyadapted to fit the size ofthe mainpollinators.Largebeesgenerallydo notvisitblossomswithsmallamounts ofrewardfor energeticreasons(Heinrich& Raven,1972;Armbruster,1984),and small-rewardblossomsmustthereforehavefertilestructures, .e. anthersand stigma,suffi-cientlyclose tothe reward(nectar,oil, resin,etc.)in ordertocontact thepollinatorwhenthe lattercollectsthe reward.ThepopulationsandspeciesofDalechampiavaluatedn thisstudyappearedargelyo haveevolved mean floralvalues closeto thepredictedoptima(but seeHansenetal.y2000).

In the present study, we consider anadaptivelandscapenot consideredin previousstudies ofspeciesdivergence:thebivariateadaptivesurfacegoverningthe accuracyof pollenplacementon pollinatorsin relationto stigmacontact withpollinators(acomponentoffitness;seeGrant, 1971;Stebbins,1974;Faegri& van der Pijl, 1979).This fitnesscomponentfunctioncan beparaphrasedsimplyas:the expectationthatanthersand stigmascontactthe pollinatorsin the sameplace,which willbegenerallyreflectedasan isometric(45slope)relationshipbetween stamenlengthand stylelength(orequi-valentmeasurements;eeConner& Via, 1993;Conner,1997;Armbruster

etal, 2004,2009).It should beemphasizedthat adaptivesurfaceanalysiss aheuristic tool.We are not usuallyableto assesstotal lifetimefitness,but insteadonlycomponentsof fitness.Hende,oursurfacewillapplyto rates ofpollen dispersal,pollenarrivalorseedset,whilstignoringsurvival,herbivory,eedpredationandoftenoffspringquality.One canderivemorecompletesurfaces,but theyarestilllikelyto besimplifiedmodels. Thisis anespe-ciallyimportantadmissionwhenapplying adaptivesurfacesomore thanonespecies;differentspeciesarelikelyto experience


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a diversityof conflictingselectivepressuresand constraints,and hence the surface thatgovernsall thestudy specieswillnecessarilybe related to a restrictedsetof fitnesscomponents.

Logicof theadaptivesurfaceof thestamen-stigma'fit'A functionalanalysisof pollinationmechanicsin the contextof adaptiveaccuracy theoryleadsto the expectationthat thehighestmale function fi tness accrues to individualsthat placepollenon pollinatorswherestigmasare mostlikelyto contactthem. On the femaleside,highestfitness accrues o individualswhosestigmascontactpollinatorswhere thepollen is mostlikelyto be. In terms of floralmorphology,this translates ntotheexpectationthat the 'reward-antherdistance'[thedistancebetween theanther and the reward or the floral constriction('throat')that stopsthe pollinatorfromgettinganycloser tothe reward]will match the mean 'reward-stigmadistance'(the distance between thestigmaand the reward orthroat).This is the malecomponentofpollinationfitness.The reverse(stigmamatch to antherposition) correspondsto the femalecomponentofpollinationfitness.In termsofadaptiveaccuracytheory, the maximum maleaccuracy(for a genotype or apopulation; see Hansen etal.y2006) is achieved when themeanreward-antherdistanceequalsthe meanreward-stigmadistance(high 'mean optimality') and there is low varianceabout that mean(highfloral'precision').In turn, maximumfemaleaccuracy(fora genotypeor population)is achievedbythe meanreward-stigmadistanceequallingthe mean reward-antherdistance(highmeanoptimality)andhavingow varianceabout thatmean (highprecision; Fig.1).We first test thesesimple predictionsand then interpret deviationsfrom the

expected patternsin the light of constraints andconflictingselectivepressures.It should be noted that severalsimplifyingassumptionsare

embeddedin thisconceptualmodel of floralfitness,and thusour modelmay not applyto allsystemsand circumstances.We assume that fitness risesmonotonicallywith:(1)increasingamounts ofpollen arrivingon stigmas;and (2) increasingamounts ofpollenbeingplacedin the 'right place'on legiti-matepollinators(and then dispersedto conspecific stigmas).We thus ignorepossiblenegativeeffects of excessconspecificpollenon stigmas,but assume,instead,that fitness is enhancedby intensifiedpollen competitioneven after seedproductionhas been maximized. We alsoignorepossibleinteractions and

frequencydependence,such as selection for

longerstyles,when

pollen competitionis ofintermediateintensity(seeMulcahy,1983;Armbrusteretal., 1995,Armbruster, 1996;Lankinen& Skogsmyr,2001). We alsoignorecomplexitiesrelated tosaturation of thepollen-carrying capacityof thepollinator.Undercertaincircumstances,it maybeadvantageouso placepollen on the pollinator somewhere otherthan the placemostfrequentlyusedbyotherconspecificflowers,because thesite isalreadysaturated and new pollen falls off(althoughlayeringmaybe morecommon;see Harder &Wilson,1998).

Fig.1 The

postulatedaxis of the

adaptive ridge governingthe

accuracy of pollination is the isometric line(y = x) relating the locationof pollen placement to the expected location ofstigma contact withthe pollinator. It also relates the location ofstigma contact to theexpected location of pollen placement on pollinators. Populationmeans may lie closeto, or far from, the ridge (optimalityof the mean),and individuals in apopulation may be close to, or far from, the mean(population precision). Ellipsoidsmarked P1-P5 represent the spreadof individualvalues with fivepopulations. The broken lines indicateparallel contours of the slope.

We ignorefor the momentthe tendencyof someflowerstoplace pollenin severalplaceson pollinators(asa resultof eithervariationamong flowersin a populationor amongstamenswithin eachflower),creating 'horizontal heterogeneity'or

structure (Harder & Wilson, 1998), which may selectfor multiple stigmapositions and/or increased variance[Armbrustertal.,2009;see the extensiveiterature n accuracyin heterostylousflowers(for example,Sanchezetai, 2008,and the studies citedtherein)].These situationsmayrequiremodificationsof the modelspresentedhere,but becausethestudy systemswe examineddo not appearto showvariationof this sort,we do notexploretheseissues further.

At thepopulationand specieslevels,the aboveconsidera-tions lead to theexpectationof correlateddivergenceof reward-antherand reward-stigmadistances.This is becausethistypeof interaction betweentraitsgeneratescorrelationalselection:selection on reward-antherdistanceis influencedbythevalueof the

reward-stigmadistancein a

population,and vice versa.

Thus, selection oneach traitwill be influencedby the valueof the other, setting up trait covarianceacrosspopulations(and species)as each achievesits adaptivecombination ofmeans.However,becauseselectionis relatedto differentialreproduction,but not differentialsurvival,thiscorrelationalselectiongeneratescovarianceonlyamong,not within,popu-lations(seeWallace, 1975;Endler, 1986,1995;andArmbruster& Schwaegerle,1996for further discussions).This relation-shipshould be reflectedin populationsand species fallingout

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on an isometric(45) line passingnear the origin. In otherwords,we expect populationsand speciesto havedivergedalongan adaptiveridgerunningon a 45 diagonalacross thebivariatemorphologicalspacedefinedby the anther-reward

and stigma-rewarddistances(Fig.1).In considering adaptivecovariance asa source of traitcorrelation,we need to becognizantof the fact thatfactorsother thancorrelationalnaturalselectioncangeneratecovari-ancebetween traits(for example,Lande &Arnold, 1983;Armbruster,1991;Armbruster & Schwaegerle,1996).First,styleand stamenlengthmaybegeneticallycorrelatedbecauseofoverlappinggenetic-developmentalcontrolsystems(pleio-tropy; orexample,Conner,1997,2002).Second,selectionforlargeroverall lower sizebypollinatorscouldgenerateamong-populationandamong-speciesorrelations etween floralraits,even if they are geneticallyindependent (Armbruster &Schwaegerle,1996).We considerthesealternativehypothesesin the context of the data wepresentbelow.

Departures from the optimumThere have been extensive discussions asto why organismsmightexhibitgeneticload ormaladaptationand departfromtheir selectiveoptima(forexample,Bradshaw,1991;Williams,1992; Orzack & Sober, 1994a,b;Thompson etal, 2002;Hansen &Houle,2004;see alsoNesse,2005).Contributingfactorsncludegeneticactors,uchasdrift,geneflow,pleiotropyand lack ofgeneticvariation,as well as naturalselectivefactors,suchaslagin responseorapidlychangingspeciesnteractions,amongothers.In the contextof the measurement ofadaptiveaccuracy,we wish to evaluatethe rolesof twogeneticfactors:

floral ntegration(thetendencyoffloralstructures o be fusedand/or their variation becorrelated),or lackthereof,whereinindependentrandomvariation offloralpartsdecreasespreci-sion and/ormeanoptimality;and developmentalandgenetic'constraints' forexample, pleiotropy).

Lackof floralntegrationmaylimit apopulationsabilitytostayperchedon theadaptiveridge,andthismaydriveselectionfor increasedintegration and reductionsin the number offloralparts (Stebbins,1951, 1974;Armbrusteretal, 2004).Otherpossible geneticeffects includedevelopmentalrelation-ships and genetic correlationsthat preclude independentevolutionaryoptimizationof the reward-antherand reward-stigmadistances(Armbruster& Schwaegerle,1996; Schluter,

1996;Hansenetal, 2003a).Comparisonof thepopulationmeanwith speciesmean conformancewith thepostulatedadaptiveurfacemayrevealhe effectofgenetic/developmentalconstraints.This is becausegeneticconstraintswill usuallyhavestrongereffectson covariationwithinspeciesthanamongspecies(Endler,1986, 1995;Armbruster,1991;Armbruster& Schwaegerle,1996),because the Gmatrixis itselfa poten-tially evolving'trait' at the levelof populationsand species(Lande,1980;Turelli,1988;Jonesetal., 2003, 2004;Revell,2007;Polly,2008;Arnoldetal, 2008).

With respectto other componentsof fitness,we wishtoassess therole of possibleconflictingselectivepressuresindriving departurefrom the modelledadaptiveoptima.Mosttraits areinfluencedbyseveralselectivepressuresand, when

these involvetrade-offs,it is usuallyimpossibleto respondoptimallyto all(Schluteretal, 1991;Strauss& Irwin,2004),leadingto adaptive compromise(seeArmbruster,1996,2001for floralexamples).One littlestudied, but striking,floralexampleis the conflict betweenselectionfor increased out-crossingin self-compatible speciesthat arenot dichogamous(sexualfunctionsnot temporally separated)and selectionforplacing pollenin the sameplaceon pollinatorscontactedbystigmas.The formerfavoursherkogamy (spatialseparationofanthers and stigmas),but this may often reduce thecorre-spondencein the points of antherand stigmacontactwithpollinators,hencereducinghe meanoptimalityn ouranalysis.

Interestingly,hereare atleast threepossibleroutes ofescapefrom the trade-offbetween

accuracyand

herkogamy(out-

crossing)in monomorphicflowers(the situation differsforheterostylouslowers;eeDiscussion),andwewished toexploretheireffects on floralaccuracyanditscomponents.One 'escaperoute' is being a self-pollinatorthat 'tolerates' inbreeding(althoughthis is more likelyto precludethe conflictratherthan bean escapefromit).Asecond route isto escapein timebysegregatingmale and femalefunctionstemporally(dicho-gamy).The third route isto achieveherkogamywhilst main-tainingaccurate fit withpollinatorsby escapinginto higherdimensionalspace.This works in someflowersby havingreward-anthereparationn onedimension andreward-stigmaseparationn another. Inthissituation,theseparationbetweenanthersandstigmassgreaterhanthe difference etween he two

distances romthe rewardseebelow for a furtherexplanation).

Theoretical basis ofadaptive accuracyWe presenthereonlya briefprecisof the theoryof adaptiveaccuracy.Moredetailedaccounts aregivenin the treatmentsbyHansen etal.(2006)and Armbruster tal (2009).Althoughmaladaptationand inaccuracyarelogicallymeasured on indi-viduals,theyare alsopropertiesof populations,and it is thelatter applicationthat is used here to study populationandspeciesdivergence.

Considerirst hedispersalfpollento otherstigmas,as deter-minedbythedepositionofpollenon pollinators(i.e.the male

function).Let0 be a

randomvariablewith a

specifieddistri-

bution, representingthe optimal position ofstigmasin thepopulationrelative o the landmark.[Thelandmark susuallythe rewardor theperianthrestriction('throat') hat stopsthepollinator gettinganycloser to thereward.]We can think ofdeviation fromtheoptimumasdecreasingitness and thereforebeingsubjectto selection. Selectionoperatingn the context ofasinglepopulationthus hascomponentsrelatingo thevariouscauses ofphenotypicdeviationfrom theoptimum,and mal-adaptationtthepopulationevel s the sum of thesecomponents:


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s{E[z]- E[Q])2+ iVar[ZJ+ /var[G]+ sE[Vd] Eqn 1

[s,strengthof stabilizingselection; E,expectedvalueof thevariablen the followingbrackets; ,the observedphenotype;

0,optimalphenotype;Var[ZJ,variancen thegenotypic target(thetarget s theexpectedphenotypeproducedbyagenotype);Var[0],variancen theoptimum;Vd,variancen thephenotypearound the genotypic targetas a result of environmentalvariationand developmentalnoise].

Thereare thus fourcomponentsof inaccuracyto considerwhenassessingpopulation properties.These fourcomponentscanbeoperationalizedas:(1)the 'bias',E[z]- Eq[Q],which ismeasuredas thedifferencebetween thepopulationtraitmeanand the population optimum;(2) the variance ofthe fitnessoptimum,Var 9] which ismeasuredasthepopulationvariancein the optimum; (3) the variancein the genotypic target,Var[Zt],which is measuredasthepopulationvarianceofgeno-typemeans;and (4) the phenotypic

imprecision resultingfromdevelopmentalnoiseand environmental varianceVd,whichis measuredas the within-plantvariance for the focaltrait (for example,across flowers ona plant), and E[V\istreated as the meanwithin-plantvariance for thepopulation.However,for population studiesin the field, it is useful topoolterms(3)and (4)andestimatethemjointlyasthe within-population phenotypicvariance of thetrait. This leads to asimplifiedmeasure ofinaccuracy:

Inaccuracy= (E[z\- 6)2+ Var[8]+ Var[z] Eqn 2

In otherwords:

Inaccuracy= (PopulationTrait Mean- Optimum)2+Varianceof Optimum + PopulationImprecision

This measureof inaccuracyand its componentshaveunitsequalto thetrait unitssquared.Forcomparisonacrossspeciesand traits, they can bestandardizedby dividingby the traitmeansquared.When this isperformed,their numerical valuecan beinterpretedasthepercentagereductionin fitness,whenthemeanstandardizedelection coefficient s inEqn 1isequalto unity (i.e. sE[z]2 =1).

Materials and Methods

Study ystemsWecomparedpatternsof floraloptimalityandaccuracywithinandamongthreegenerafor which we have extensivemorpho-logicaldataseisand phylogeneticinformation(two of threetaxa).These threesystemsare drawn fromdistantlyrelatedfamilies,and hencerepresenta broadsampleof angiosperms.Theyalsorepresent broadrangeoftypesoffloralorganization.DalechampiaRosidae:Euphorbiaceae)aspseudanthial,unc-tionallybisexual blossomsaspollinationunits;thesecomprise

unisexual flowers and hence have low structuralintegration(blossompartsaredevelopmentallymoreindependentand/orshowless fusionthan partsof asingleflower)comparedwiththe other twogenera(Webster& Webster,1972;Armbruster,

1988, 1993;Armbrusteretal., 2004). Collinsiaand Tonella(Asteridae:Plantaginaceae:Collinsieae)have flowersaspollina-tion units,and these have an intermediatelevelof structuralintegrationbyfusion within(connation:synsepaly,ympetaly,syncarpely)and among (adnation: epipetalous stamens;Armbrusteretal., 2002,2004)whorls.Stylidium(Asteridae:Stylidiaceae)has flowers aspollinationunits,and thesehavean evengreater evelofstructural ntegrationbywi thin-whorlfusion(synsepaly,sympetaly,syncarpely)and among-whorlfusion(completeadnation ofstaminate andpistillatetissues;Armbrusteretal, 1994,2004).

Dalechampias a dade off. 120speciesofmostlyperennialvines,distributedhroughoutmost of the lowlandtropics.Thebilaterally ymmetrical,aterallyriented,blossominflorescence(pseudanthium)usuallycomprises10-15 staminateflowers,threepistillatelowersandaglandthat,in mostspecies,secretesresin(c.100species)or fragrance threespecies).Thesepartsare subtendedby two,usually showy,bracts.The rewardandall floralpartsarefullyexposedwhen the bractsareopen,butpollinators generallyorient themselvesconsistentlyon thebilaterallyarranged lowerswhilstcollectingresinor fragrance.Pollination ofmostspeciesisby resin-collecting,femalebees,which use resinin nestconstruction,or fragrance-collecting,male bees,which probablyuse fragranceso attract females(Armbruster, 1993).We measuredseveralfloral size andorientation raitson flowers romusually5-45 plantsper popu-lation,1-20 populationsper speciesand35specieswithdigitalor dialcalliperspreciseto 0.01mm.Collinsia andits closerelative, Tonella,orm a clade(tribeCollinsieae)of c.25 annual species, primarilyof temperatewestern NorthAmerica(Armbrustertal., 2002).The flowersarezygomorphic(bilateral),with alandingplatformformedby the lowerlip and a banner formedby the upper lip.Thefour stamensand styleareenclosedin a keel-likefoldof thelower lip, and exposedonly when anectar-seekingbee ofsufficient ize andson the flower.Pollination sbylong-tongued,nectar-feedingbees(whichmayalso collectpollen;Armbrusteretal., 2002).We measured flowers on5-20 plantsper popu-lation, one to eight populationsper speciesand 24 specieswith digitalor dialcalliperspreciseto 0.01mm.

Stylidiumontainsover250

speciesof

herb,perennialrosette

plants and small shrubs, most of which areendemic toAustralia. Theflowers arezygomorphicand characterizedbythe fusion of staminateand pistillatetissuesinto amotile,protandrouscolumn.Pollinationisby nectar-feedingbeeflies(Bombyliidae)and smallsolitarybeeswhich,on contactingthetrigger-pointwhilstforagingfornectar,causethe columntospringforwardto place pollenon, or pick it from,the back,sideor venterofthepollinatingnsect(Armbrustertal, 1994).The column 'reloads'o theoriginalpositionin c.30 min,and

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has theabilityto repeat his action numerous times(40+ times)in the c.3-5 d lifeofa flower.The flowersplace pollenon polli-natorsn the first1-2 d ofreceptivityand thenpick up pollenin the samewayin the final1-2 d. We measured flowerson

5-10 plants per population,1-12 populations per speciesand31 specieswith digitalor dialcalliperspreciseto 0.01 mm.

Measurements andanalysisIn this analysisof floralaccuracyand pollinationfitness,werestrict our attentionto the matchof stigmapositionto thesite ofexpectedpollen depositiononpollinators,andthematchof antherpositionto theexpectedsite ofstigmacontact withpollinators.We usedthreestudy systemsin whichpollinatorsarelargelyimmobileafterlandingon the flower. Thisallowsus to use floral measurements(thedistance between the florallandmark,e.g. resingland or throat of floraltube, and theanthers orstigmas)to predict quite closelythe sites of

pollenplacementand pick up, respectively,on the pollinator (seeArmbrusteretal, 2009). This isnot the caseif pollinatorscrawl around on the flowers.

FollowingEqn 2, we calculated the fitnessdecrementresultingfrom'floral naccuracy'as:

(MeanReward-AntherDistance- MeanReward-StigmaDistance)2+ Variancen Reward-StigmaDistance(varianceofoptimum')+ Variancen Reward-AntherDistance('population precision) Eqn 3

This is theabsolutenaccuracyf both maleand femaleunctionsin thisparticular ystem,because thevarianceof theoptimumformaleinaccuracys thevarianceof thefemaletrait,andviceversa(thisis not ageneral property,however).In otherwords,althoughEqn 3 is actuallymale inaccuracy,it is obviouslyequivalentto theequationfor femaleinaccuracy:

(MeanReward-StigmaDistance- MeanReward-AntherDistance)2+ Variancen Reward-Anther Distance(varianceofoptimum)+ Variance nReward-StigmaDistance(populationprecision) Eqn 4

As a resultof thisequivalencefor the traitsunderstudyhere,we treat the value as the'joint floralinaccuracy'ofboth maleand female functions.

Becausehevarianceofmorphological

measurementsusuallyscales with thetrait means,we scaledinaccuracycalculations

beforemakingcomparisonsbetweenspeciesand betweenstudysystemswith flowers of different sizes andshapes.We scaledthejointinaccuracywith theproductof the traitmeans,whichis, in fact,the squareof thegeometricmean ofthe two traits(seeSokal& Rohlf, 1981;Hansenetai, 2003b).Suchscalingisdesirablebecause it conserves theadditivepropertiesof thevariancecomponents,a propertythat coefficients of variation(CVs)do not have.

Because,in thissystem,thevarianceof the optimumisthesame as thevariance of thealternativetargettrait (hencetheequivalenceabove),we alsowished toassess theindependentcontributions ofmale(staminate)and female(pistillate)func-

tions to adaptive inaccuracy.We thereforecalculated'pure'maleinaccuracyat the populationlevel as:

(MeanReward-AntherDistance- MeanReward-StigmaDistance)2+ Variance n Reward-AntherDistance Eqn 5

The pure' femaleinaccuracyat the populationlevelwas thusdefined as:

(MeanReward-StigmaDistance- MeanReward-AntherDistance)2+ Variance n Reward-StigmaDistance Eqn 6

We calculated theabovecomponentsof inaccuracyand, for

purposesof

comparison,scaledthemto the

squareof themean

traitvalues andconverted themto percentages.Thisallows allcomponentsto becomparedamongstudysystemsand traits,whilstmaintainingtheiradditiveproperties.When scaled inthisway,the imprecisioncomponentreduces to/, the mean-squaredscaledphenotypicpopulationvariance. (=CV2)hastheoreticaladvantagesrelatedto additivityand interpretationas traitevolvabilityseeHansenetal, 2003b;Hansen &Houle,2008). Inaccuraciesand mean departure from optimalitywerealsoscaledto the squareof the traitmeanandconvertedto percentagesor comparisonsacrosstraits,populationsandstudysystems.

Our analysisof interpopulationand interspecificdata tookseveralapproaches.First,wewished to testthe ideathat there

isa fitness surfacegoverningthe interactionofreward-stigmaandreward-antherdistancesacrossmultiplespecies.Weexam-ined the relativepositionsof anthers and stigmas,treatingthem asbivariatemorphological space.We hypothesizedthatmaximum fitness is apositive,isometricadaptiveridgepassingthrough (or near) the origin.We tested thisproposition bymappingpopulationandspeciesmeansonto thehypothesizedadaptivesurface forthree distantlyrelatedgenera.We thenconsidered theadaptiveaccuracyof asampleofspeciesdrawnfrom thesegenera,assessingherelativeontributionsofimpre-cisionand meandeparturefromthe optimumto inaccuracy.We attemptedto discover reasons forlocaldeparturesfromtheadaptiveridge,consideringfloralntegrationandprecision,

geneticconstraintsand

conflictingselective

pressures.We alsotried to refine ourunderstandingof theshapeof theadaptivesurface,specificallywhether theridgewasbroad ornarrow.

We analysedpatterns of speciesdivergenceby relatingpopulationmeans andvariances othehypothesizedadaptivesurface,an adaptiveridgedepictingthe trajectoryof highestaccuracy.Asnotedabove,thissurface shypothesizedtogovernthepollinationcomponentoffitness,but not necessarilyotalfitness,exceptunder a ceterisaribusassumption('other hingsequal' is a simplifying assumptionin these analyses).The

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adaptive ypothesissbasedonempiricalbservationsmadeonthese hreetudysystemsArmbruster,988,1990;Arm-bruster tal.,1994,2002)and hesimple ogichat, orpollento reach astigma,it must beplacedin a locationon the

pollinatorhattouchestigmasn subsequentisitso otherflowers.imilarly,orastigmaoreceiveollen,t mustcontactthepollinatorn the locationn whichpollenhas beenpre-viouslyplacedbyotherflowersseeArmbrustertai, 2004,2009).

Numericalharacterizationnd comparisonswerebasedoncorrelationtatistics,multiple egression,athanalysisndcalculationf severalesswell-knownvolutionaryarameters,such asevolvabilitynd conditionalorrelationseeHansenetai, 2003a,b).Mostpopulation/speciesomparisonswerecalculatedromthe sumof allmeasurementsf thattrait orallpopulationsi.e.weightedmeansatherhanmeansfgeno-typemeans).Speciesmeans,however,were calculatedromthe

populationmeanswithout

weighting.Analysesfpopu-lation meansacrosspeciesmplicitlygnoredphylogenetic

structure ndpossibleheterogeneitynslopesofrelationshipsamongspeciesandat thepopulationandspeciesevels(seeArmbruster, 988,1991; Bell,1989).However,we felt thatthisproblemwasminorbecause,with afewexceptions,nlya fewpopulationsweresampledper species.

Inordero testwhetherhe correlationetween hegland-stigmadistanceGSD)andgland-antherdistanceGAD)iscausedbya spuriouselationshipithglandarea GA) (andselectionbybees orsmallorlargeGA),wecalculatedondi-tional correlationsollowingthe methodof Hansenet al.(2003a).We firstusedmaximumikelihoodstimatorsdivid-ingbyn notn- 1)tocomputehevariance-covarianceatrixforDalechampia opulationmeanswithcompletedata forGA,GSDand GAD.We thencomputedhe variancematrixofGADand GSD conditionalon GAusingthefollowingrelationshipseeHansenetal.,2003a):

Vy x=Vy VyxV-1 xy Eqn7

(V"1,nverse fVr,Vyx,covariancematrixbetween andx).Inthisanalysis, {GAD,GSD},= GAandVyx={Cov[GAD,GA], Cov[GSD,GA]}.

Hypothesisestingf statisticalnalysesfinterspecificrendsin Dalechampiand Collinsiawas basedon phylogeneticallyinformedndependentontrastsmplementedn 'Compara-

tiveAnalysisyIndependentContrasts'CAIC)Felsenstein,1985;Purvis& Rambaut, 995)usingpublishedr in-pressmolecularphylogeniesseeArmbruster& Baldwin, 1998;Armbruster tal., 2002).It was notpossibleto assess hephylogeneticontributiono thetrait orrelationsnStylidiumbecausef the absenceof anindependent hylogeneticsti-mate,althoughhiswasprobablyot aseriousroblemecauseof theapparentxtremevolutionaryabilityf columnengthandthetightrelationshipetweenmaleandfemale unctions(seeArmbrustertal, 1994).

Results

Testsof thehypothesizedadaptivesurfacegoverningthe stamen-stigmaJfitr

Asexpected,hepopulationnd peciesmeans fall hreetudygroupsell nearhe crestof thehypothesizeddaptiveidge(Fig.2).Thetightnessf thefitis indicatedytheR2values,whichrangedrom0.615in Collinsiand0.723nDalechampiato near10inStylidium.

Thefit ofpopulationsndspecieso anisometricineisonlyaweak estof theadaptive idgehypothesis,n so farasthereareotherpossiblereasonsor sucha relationship.nepossiblealternatives that argerpollinatorselector argerflowersand loral tructures)handosmallerollinators,ndthat hisrelationshipasgeneratedpuriousovarianceinthepathanalyticalense;Li,1975)betweenreward-anthernd

reward-stigmaistances.We wereableto testthis ideain

Dalechampiay assessingherole ofGA(adeterminantfpollinatorizeandhenceareasonableroxyor t;Armbruster,1988)vs GSDaspotentialdeterminants'f GAD.IfallthecovarianceetweenGSDand GADwereexplainedbytheeffectofphenotypicorrelationsithGA,selectionnglandsizeby pollinators,atherhan selectionoraccuracy,ouldexplainheobservedGAD-GSDcovariancecrossopulationsand pecies.We estedhisbycomputinghecovariancef GADand GSDconditionallyn GA(Hansenetal, 2003a)acrosspopulationmeans.Althoughheconditioningreducedhecovariancerom5.40to1 18mm2,underscoringhe mportanceofglandize,hetrait arianceserealsoreduced,ndastrongcorrelationf0.71remainedfter onditioningn GA.This s

lowerhan heunconditionalorrelationf0.89,butstill howsthatcovarianceetweennthers ndstigmascausedbymorethanoveralllossomize.Apathdiagramllustrateshisrelation-ship usingpartial egressiontatistics,howinghateventhepartialffect f GADon GSDsquite trongFig.3).(It houldbe notedhatwhetherGADor GSDis usedasthedependentvariablen thisexercisespurelyrbitrary;wappingroundhedependentariableseducedven urtherhe mportancefGA.)

We alsoevaluatedhe strengthsand trajectoriesf thehypothesizeddaptiveovarianceelationshipn comparisonwith otherntertraitelationshipsn ordero assessurtherhelikelihoodthat theexpectedamong-specieselationshipssimplyhe resultofgeneraleneticorphenotypicovariation

inthesizeof floralraits,atherhanafit to an

adaptiveand-

scape.ForDalechampiapeciesmeansmean caledo reflectproportionallopes),thehypothesizeddaptiveorrelationbetweenGSDandGADwasargerr= 0.86)thanallbutoneofthefiveother rait orrelationsmeanr - 0.72 0.058),asexpected.imilarly,he nterceptf theGSD-GADtrajectorywasmuchclosero zero hanforanyother raitcombination(0.0003vs meannterceptalueof0.47 0.043),asexpected.Theslopewas closero 1.0thananyother raitcombination(0.9997vs0.530.043).

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Fig. 2 Bivariateplots of population means relative to thehypothesized adaptive ridge for the three study systems. Broken linesindicate the isometric linehypothesized to be the adaptive ridgegoverning the fitness response to both intraspecific and interspecificvariation in anther-reward and stigma-reward distances. Each pointrepresents a population mean for the two traits,(a) Seventy-fourpopulation means from 28 species of Dalechampia (Euphorbiaceae)in relation to the hypothesized adaptive ridge governing the distancebetween the resingland and the anthers (GAD) and the stigmas(GSD); square points and regression represent populations of onespecies, D. scandens. (b) Thirty-one population means from 15species of the monophyletic tribe Collinsieae (Plantaginaceae) inrelation to the hypothesized adaptive ridge governing the distancebetween the floral throatand the anthers and the stigmas,(c) Twenty-one population means from 1 1 species of StyI d i urn(Stylidiaceae) in relation to the hypothesized adaptiveridge governingthe length of the column in the staminate and pistillate phases.

Fig. 3 A path diagram illustrating the large partial effect ofthegland-stigma distance (GSD) on gland-anther distance (GAD) aftercontrolling for the effects of gland area. The choice of GADas thedependent variable was arbitrary, but the same pattern is seen if GSDis used as the dependent variable. The data analysed were thepopulation means; the numbers are the standardized path coefficients(= standardized partial regression coefficients), which vary from -1 to+1, with values near zero indicating no effect.

For Collinsiaspeciesmeans,the hypothesizedadaptivecor-relationbetweenmean-scaledtyleand stamenengths(r= 0.89)waslargerthan the meanof thenine othertrait correlations(meanr = 0.81 0.03),asexpected.The expectationwas thatthe intercept {a)would be closerto zerothan for the othertraits,and thiswas indeedthe case:a = 0.10forstamen-stylelengthvs a meanof 0.24( 0.07)forothertrait combinations.The expectationfor the slopeof thestamen-stylelengthrela-tionshipwasthat it wouldbecloser to1 0 thanwere othertraitcombinations;thiswas indeedthecase:0.90vs0.76 ( 0.07).For the mean-scaledStylidiumspeciesmeans, the adaptivecorrelationwas estimatedas1 0,whichwas muchlargerhananyothertraitcorrelation(meanr = 0.42 0.084).The observedinterceptwasapproximatelyzero,asexpected,vsa meanforother traitcombinationsof0.63 0.061.The regressionlope

was closeto 1 0, asexpected,vs anaverageof0.37 0.061fortheother trait combinations.Together, hese dataindicatethatin none ofthe threestudysystemscan the fit of antherandstigmadistancesto the hypothesizedridgebe explainedas apureallometricresponseto variationin overallflower size.

Adaptive accuracy and precisionThe mean standarderror (SE),joint mean-product-scaled,blossominaccuracy(wherejoint floralinaccuraciesarescaledto theproductof themean GSDandmeanGAD)of74popu-lationsof 28speciesofDalechampiawas14.27 1.30%.Thecorrespondingmean,mean-product-scaled,floralinaccuracyof31populationsof 15speciesof the Collinsieaedade{Collinsiaand Tonella)was 16.56 1.17%.These valueswouldcauseasubstantialreductionn fitnessfstabilizingelectionwasstrong(sE[z]2~ 1wouldcauseasimilarpercentageeductionnfitness).Bycontrast,themean,mean-product-scaled,floral naccuracyof 21 populationsof 11 speciesof Stylidiumwas only 0.980.21% (Table1).

The three contributorsto joint floralinaccuracydifferedintheir importanceacrossthe three systems.Mean departurefrom the optimumwasby far the most importantfactorin

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Fig. 4 Path diagrams illustratingthe relative, unique contributions ofstamen (male) imprecision, stigma (female) imprecision andpopulation mean departure from the optimum to the joint floralinaccuracy in: (a) 74 populations in 28 species of Dalechampia(Euphorbiaceae); (b) 31 populations in 15 species of the tribeCollinsieae (Plantaginaceae); and (c) 21 populations in 11 species ofStylidium (Stylidiaceae). Joint floral inaccuracy was measured as thesum of the variancesin stigma position and stamen position plusthe square of the difference between stigma and stamen position.Numbers are standardized path coefficients (= standardized partialregression coefficients), which vary from -1 to +1, with values nearzero meaning no effect. All variables weremean-squared scaled andhence are unit-less percentages.

Fig. 5 The relationship between mean, mean-squared-scaled maleinaccuracy and mean female imprecision (/ = CV2) in 31 populationsin 15 species of the tribe Collinsieae (Plantaginaceae).

Dalechampia,althoughit wasmoderatelycorrelatedwith maleimprecision (Fig.4a). In Collinsieae,meandeparture fromthe optimum and femaleimprecisionwereroughlyequallyimportant.Meandeparture rom the optimum and femaleimprecisionwere strongly correlated (Fig.4b). The jointfloralaccuracyofStylidiumspp.wasthe result ofimprecisiononly(Fig.4c),becausemean deviationfrom theoptimumwasestimatedas zeroin allspecies.

Male andfemaleaccuracyandprecisioncomparedThe joint

floral inaccuracieso Dalechampiaand Collinsieaewerequitesimilar.However,when male and femalecomponentswereseparated,wedetectedamoreimportantcontributionof femaleimprecisionin Collinsiai.e.variancen stigmaposition)com-paredwith maleimprecision (Fig.4b). Bycontrast,thesetwofactorswere aboutequallymportantinDalechampia Fig.4a).

Male andfemale inaccuracieswere generallycorrelatedbecausetheyboth containthe same term:meanoptimality.However,male andfemaleprecisionsare ndependentand canbecompared meaningfully.Surprisingly,heywere notstronglycorrelatedin eitherDalechampia(r= 0.12) or Collinsia(r=-0.13). Stylidiumcould not be assessedbecausemale andfemaleprecisionswerenot measuredindependently.

Anotherexpectationwas that maleinaccuracynotincludingthe optimum varianceterm) would trackfemaleprecision(optimum variance)because,if stigmapositionsarehighlyvariable,herewould be relaxedelectionfor maleaccuracy.Asdiscussedbelow,stigmapositionsare sometimessubjecttoconflictingselectiveforcesandconstraints,whichmayleadtosignificantimprecision.Maleinaccuracydid not trackfemaleimprecisionin Dalechampia(r= 0.005),but didsocloselyinCollinsia(r= 0.826; independentcontrastP< 0.01; Fig.5).A similar trendis suggestedby comparingthe study systems:

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Stylidiumspecieshad lower mean femaleimprecision(6.952.25%) and lowermean male inaccuracies(0.98 0.58%),whereasDalechampiaand Collinsiahad higherfemaleimpre-cision(17.3 6.3%and29.9+ 13.7%,respectively)ndhigher

maleinaccuracies13.7 19.6%and 6.2 5.3%,respectively).Althoughwe wouldsimilarlyexpectfemaleinaccuracyto

be influencedby male imprecision,there was nodetectablerelationshipn eitherDalechampiaor Collinsia.We mightalsoexpectmaleprecisionto track femaleaccuracy(inaccuratelypositionedstigmas mightselect for lowerprecisionin stamenposition),althoughno such trend was detectable.Similarly,femaleprecisionmight track maleaccuracy,and this relation-shipwasdetectedin Collinsia,but it cannot bedistinguishedfrom therelationshipshown inFig.5 (withaxesinverted).Nosuchrelationshipwas detectedin Dalechampia.

Causes ofmeandeparturefrom theoptimumGenetic and meandevelopmentalconstraints Random varia-tions infloralparts that lackintegrationmay increase bothimprecisionnddeparturerom theoptimum.Thismayexplainthe lowaccuracyofDalechampia pp.and Collinsiapp.relativeto Stylidiumspp.Dalechampiahave male flowersfunctioningasstamensand female lowersunctioningaspistilsn apseudan-thialinflorescence(blossom),and hence the fertile structuresare not only unfused,theyare in differentflowers,and onlysecondarilycoordinated(thatis at the level of the inflorescencerather than the flower).In Collinsieae,both sexual functionsarein singleperfectflowers,which have fused(connate)petalsand staminalfilaments adnate(fused)to the base of the corolla(epipetalousstamens).Bothgroupshavecomparativelyhigh

inaccuracies,althoughit issurprisingthat Dalechampiais asaccurateasCollinsia,givenits low level of structuralntegration.Collinsiauffers from another mechanicalgenetic'constraint':its stamens areenclosedin a narrow keel(in so far as the keelisadaptive,his isultimatelyaselectiverade-off).Thus,Collinsiaspp. cannot escapefrom the herkogamy-accuracytrade-offby usinghigherdimensionalspace(see below).Bycontrast,Stylidium specieshave maleand female tissues fused into asinglestructure. The flowers are thushighlycoordinatedincontactingthe pollinatorsin a consistentplacewith both theanthersandstigmassequentially.The remarkablyighaccuracyand precisiono Stylidiumflowersisat leastpartlya result ofthis integration.

Comparisonof the populationmean vsspeciesmean con-formance to thepostulated adaptivesurfacemay reveal theeffect ofgenetic/developmentalconstraints. This is becausegeneticconstraintswillusuallyhavestrongereffectson covari-ationwithinspeciesthanamongspecies,because,althoughtheG matrix isitselfa potentiallyevolvingtrait, divergencemayrequireconsiderable time. Thetrajectoryof among-speciescovariation ofGAD and GSD oDalechampia appearsto fitto the isometricadaptiveridge,asexpected(Fig.2a).However,a sample of South Americanpopulations of D. scandens

Fig.6 Therelationshipbetweengland-antherdistance(GAD)andgland-stigmadistance(GSD)across18 Mexicanpopulationsof twohypothesized cryptic speciesinthe Dalechampiascandenscomplex,where the two clusters ofpointsinmorphometricpace representhetwo hypothesized cryptic species.(Thedata presentedhere werenotincludedin Fig.2 or relatedanalyses.)It should benoted that onepoint(inthe brokencircle)did not clusterwithany other pointsandwas excluded from lateranalyses.Theopen circles arethe means ofthe twocryptic species(leftand rightclusters).Populationswithin acrypticspeciesdo notappearto track hehypothesizedadaptiveridge(straightbrokenline),althoughthe meansof the twocrypticspeciesmaydo so.Theparameterestimatesfor thisrelationshipare based onregressionof all18 populationmeans.

appearsto follow atrajectory(b= 0.54) closer tothe geneticregression(b= 0.67; measuredin one population)than thehypothesised adaptivetrajectory(b = 1.0) (Fig.2a; Hansenetal., 2003b). The analysisof two cryptic speciesof the

D. scandensomplexin Mexico showsa poorfit ofpopulationswithin each clusterhypothesizedrypticspecies)o theadaptiveridge.The predicted regressionvalueswere: intercept = 0,slope= 1.0,7?2= 1 0,but the observedvalues were1 77,0.36,0.31 (left cluster, facultative-selfing species), and 5.99,-0.09, 0.004 (rightcluster,facultative-outcrossingspecies),respectively.By contrast, the meansof the twosubspeciesconformedto theadaptiveridgereasonablywell(Fig.6).

Conflicting selectivepressures Selectionfor increasedout-crossingwill favourherkogamyin self-compatiblespeciesthatare notdichogamous(sexualfunctionsseparatedemporally),andresponseto thisselectionmayreducetheoptimalityof themean. Thisrelationshipcan be examinedby comparingtheoptimalityscores ofself-compatiblespeciesthatare facultativeselfers vs facultativeoutcrossers,becausefacultative selfersarepresumablynot understrongselectionforherkogamy(ormayevenexperienceelectionagainstherkogamy),whereasacultativeand obligateoutcrosserspresumablyare.

The predictedrelationshipin Dalechampiais forspecieswith high selfingrates and little orno herkogamyto havehigheroptimalityscores andpotentially higheraccuracies.Weused theanther-stigma distance (ASD)as a proxyfor the

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outcrossingate seeArmbruster,988),butdid not findanyrelationshipetween hismeasure ndoptimality.nCollinsiayhowever,herewasasignificantositive elationshipetweenhe

Fig. 7 Response of the mean departure from the optimum (circles)and imprecision stamen (triangles) and style (squares) length (/)to variation in the outcrossing index (calculated as the sum of therelativized corollalength and the relativized time ofself-pollination,where near four is mosthighly outcrossing and near zero is mosthighly selfing;see Armbruster etal., 2002) across 31 populationsof 22 species of Collinsieae (Plantaginaceae). See text for statisticalanalyses.

estimatedutcrossingateandmean-squaredcaleddeparturefrom heoptimumr= 0.75;ndependentontrast 0.20;Fig.7).Escaperom theconflict ofherkogamyThereseemsto beevidenceorescaperom heherkogamy-accuracyrade-offbysomepopulationsofD. scandens.Thismechanismsbestunderstoodyexamininghe blossomeometrynlateraliew(Fig.8).Onegroupofpopulationslustersn morphologicalspace(leftcluster;Figs6, 9)and conformso the blossomformdepictedn Fig.8a.Bycontrast,heotherpopulationsclustero therightnFigs6 and9andconform otheblossommorphologyepictednFig.8b.The leftclusterfpopulationshasthethree tigmasnd 10staminatelowersrrangedmoreor essn asingleplaneina lateraliew,hisplanesportrayedas aline;Fig.8a).Bycontrast,herightclusterutilizeshigherdimensionalpace,with thestylesdivergingutof theplaneformedbytheresinglandand staminatelowersin lateralview,heseplanesappear s twodivergingines;Fig.8b).

Theoptimalityonsequencesf thisgeometricalifferenceare hownnFig.9.There eemso be aninitial rendowardsdecreasingmeanoptimalityincreasingifferencebetweenGSD andGAD)withincreasingerkogamyASD),hat s,atrade-off,n thosepopulationsithone-plane eometryFig.9;leftpopulationluster).This trade-offisappearsompletelyin thepopulationswithtwo-plane eometryFig.9).

Fig. 8 Photographs and diagrammatic representations of the two different arrangements of flowers in two hypothesized cryptic species ofDalechampia scandens, which do not(a) and do (b) escape from the herkogamy-optimality trade-off by 'escape' into higher dimensional space.Symbols: Ar anthers; Grresin gland; S, stigma, (a) 'Left cluster' populations have smallanther-stigma distances and anthers and stigmas orientedin more or less the sameplane (in the lateral view, a line passing through the resin gland), hence experiencing the trade-off that ASD = GSD -

GAD, where ASD is theanther-stigma distance, GSD is the gland-stigma distance and GAD is the gland-anther distance, (b) 'Right cluster'populations have large anther-stigma distances and anthers andstigmas oriented in different planes (in the lateral view, lines passing throughthe resin gland), hence not experiencing the trade-off that ASD= GSD - GAD.

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Fig. 9 Relationship between mean departure from optimality (asmeasured by the difference between the gland-stigma distance andanther-stigma distance, GSD-GAD;y-axis) and herkogamy (as

measured by the anther-stigma distance, ASD;x-axis) across 17populations of Dalechampia scandens in Mexico. Points arepopulation means. There is apossible trend towards increasingdeparture from the optimum with increasing herkogamy in the leftpopulation cluster (broken line). However, in the right cluster, whichis of type 2 geometry, departure from optimality does not increasewith herkogamy, indicating escape from the optimality-herkogamytrade-off in higher dimensional space. The overall relationship of the17 population means is indicatedby the full regression line, withthe parameter estimates indicated abovethe graph. The distinctiveblossom geometries of the two population clusters are indicated bythe diagrams below.

Thereappears o be a similar trend acrossspeciesin the rest

of the genus.Specieswith stamens andstylefallingout on asingleplanewerecategorizedashavingJS JS JS

'hi)

I2n\

c JS JS JS I ,2(t .5 3 3 3 or, J=^ mi -3 - ^- es

I I IlsSsH ill

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Fig.10 Arepresentativeprunedmaximallyparsimoniousree ofDalechampiaspeciesshowingmultipleshiftsinblossomgeometry,representingescapefrom the herkogamy-accuracytrade-offbyexploitationof higherdimensionalspace.Forexplanationof thediagrams,see Fig.8. Thephylogeneticestimate isbased on maximumparsimonyanalysisof combined nuclear ribosomalITS-15,8S,ITS-2)andchloroplasttrnK ntron)DNAsequences(Armbruster&Baldwin, 1998;B.G. Baldwin &W. S.Armbruster,unpublished).

Table2 Classificationof Dalechampiaspeciesinto twotypesofblossomgeometry

Blossomgeometry Type1 Type2

Number ofspecies 26 17Averagemean2 scaled deviation from 24.66* 18.67*optimum(%) (standard error) (3.66) (4.21)Averagemean2 scaled male 5.71** 4.50**imprecision(%) (standard error) (1.07) (1.03)Averagemean2-scaled female 4.01*** 2.73***imprecision%) (standarderror) (0.57) (0.50)

Not allspeciesfit neatlyinto thesecategories.Types1 and 2 areillustratedn Fig.8. Differencessignificantunder the assumptionof speciesindependence(but see Fig.10): *, F= 64.8.0,P < 0.001;**,F= 217.8,P < 0.001;**\F = 275.8,P< 0.001.

governingthe placementof pollenon andreceiptfrompolli-nators(Fig.2).This observationsupportsour hypothesisthatfitness ishighestwhen reward-stigma and reward-antherdistances arenearlythe same,but it does not allow statisticalevaluation,asn = 3. Stylidiumspp.(Stylidiaceae),whichhavethe greatest structural integration and lowestpopulationinaccuracyvalues,fit much moretightlyto thehypothesizedridgethanDalechampiaspp. (Euphorbiaceae)and Collinsieaespp.(Plantaginaceae),ith lower structuralntegration.Indeed,

the structureofStylidiumlowers,with fused stamenandpistiltissues,almostguaranteesagoodfit to theridge,as thelengths

of the two tissues aremechanicallylinked.One question that arises whenmodellinga multispeciesfitness surfaceas aridgeis: what determineswhere individualpopulationsand speciesliealongthe ridge?One possibilityisthat geneticdrift and/or randomspeciation generatesthesedifferences(although,of course,the combinations remainadaptive).Anotherpossibilityis that theridgeis 'bumpy or acordilleraof peaks (dependingon howlow the'passes'are).Someecologicalinformationsuggeststhat this isprobablythecase for most flowers andcertainlythe three studiedhere.Inpollinationsystems,theadaptiveridgeislikelyto beextremelybumpy becausepollinator size (or behaviour)often has adiscontinuous distribution.For example,most Dalechampiaspeciesarepollinatedbybees of c.5.5-7.5 mm, 9-12 mm or20-26 mm inlength(Armbruster,1988;Hansenetai, 2000).Thisdiscontinuitywouldcreatea seriesofhighand lowpointsalongtheadaptiveidge:highwhere both GAD andGSD matchandoccupied pollinatorsizeclass,and low wheretheydo not.We wouldexpectlocalhighpoints alongthis ridgeto fall outroughlyat GAD= GSD= 3-5 mm (touchingthe abdomenofTrgonar Hypanthidium)yGAD= GSD= 5-7 mm (touchingthe thorax or abdomenof Euglossapp.), GAD= GSD = 8-14mm (touchingthe thorax or abdomenof Eufrieseapp.)

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and GAD= GSD= 16-22 mm (touchingthe thoraxorabdo-men of Eulaemaspp.).Indeed,the distributionof GAD andGSDacrosspeciesshowspeaksandtroughs n theirfrequencydistributions (see GSD, fig 2 in Hansen etaL, 2000).

Althoughtheremaybespeciesclusters at the first threepeaks,forunknown reasons he lastpeakisunoccupied by any studyspecies (Fig.2a);speciesutilizingEulaemaaspollinatorsappearto do so with'Eufrieseamorphology'(seeArmbruster, 1988,1993;Hansenetal, 2000).

We expected Dalechampia spp.,with the leaststructuralintegration,to fall fartherawayfrom theridge,on average,than Collinsieae,but the twogroupsofspecieswereactuallydistributedvery similarly(Fig.2). This may be because themorphologyof Collinsiaflowers,with stamens andstyleenclosedn alinearkeel,precludesescaperomtheherkogamy-accuracytrade-off, as appears to havehappened in someDalechampiaspecies.Instead,herkogamyas a proportionofflower

lengthis remarkably

arge duringmuchof the flowers

life in mostspeciesof Collinsiaseefig.4 in Armbrusteretal.,2002),presumablyontributingto population departureromthe localadaptiveoptimum.

The positionof thepopulationand speciesmeans near theisometricadaptive ridgein allstudy systemsdidnot appeartobesimplyan artefactof correlatedevolution drivenbyoverallflowerorpollinatorsize.Althoughthere wasapositive geneticcorrelationbetweenstigmaand stamenlengthsin one popu-lationofD. scandens,heslopewassignificantlynonisometricat 0.52. In addition, the correlation betweenspeciesmeanGSDandGAD remainedhighafterconditioningon GA(thesize trait bestpredictingpollinatorsize).Furthermore,GA wasnot averygoodpredictorof GAD afterthe effect of GSD had

been removed (Fig.3), suggestingthat overall blossom-pollinatorisometryis notthe sourceof the tight GAD-GSDrelationship.Additionalsupportacrossall threestudysystemscomesfrom aconsiderationof thestrengthand slopesof therelationshipsbetweenstigma-rewardand anther-rewarddis-tancesin comparisonwith other floraltrait relationships.Ingeneral,the correlationsand slopesof theASDs were muchcloserto theexpectedvalueof 1 0, and theinterceptclosertothe origin,asexpected,than other trait combinations.

That Stylidiumpeciesandpopulationsallfall outalongthecrestof theadaptive ridgecan alsobe viewed assupportof thehypothesisthat fitnessshighest alongthis isometrictrajectory.Indeed, the tighter relationshipin Stylidium(with greatest

structuralntegration,.e. fusionoffloralparts),comparedwithCollinsiawithintermediatestructural ntegration)and Dale-champia(withleaststructuralblossomintegration),suggeststhat the adaptiveridgeisindeednarrower,asexpected,in themostaccuratestudy system.

An alternativenterpretations that thetightrelationshipnStylidiummay simplyreflectamechanical/pleiotropiconstraint(seeSchluter, 1996): the fusionof staminate and pistillatetissuesthatmakeup thecolumn.Bythisreasoning,heperfectcorrelationis an automaticconsequenceof the structural

relationship.However,thisbegsthequestionof howandwhythis complexstructurecame tobe, and leads usback to theoriginal hypothesisthat it exists as aresult of selectionforcoordinatingthe positionsof theanthersand stigmasduring

the sequentialmaleand femalephases.Futurephylogeneticcomparativestudiesof theorigins,lossesandmodifications ofthe columnmayshedlighton the selectivepressuresnvolvedin itsevolution.

Adaptive accuracyThe flowers of the 11speciesof Stylidiumwere c.15 timesmoreaccuratethan the flowersand blossoms of the15speciesof Collinsieaeand 28 speciesof Dalechampia,respectively.Asexpectedthis pattern parallelsthe trend of structural andstatisticalintegration,with Stylidiumflowersbeingthe mostintegratedstructurally, ndDalechampiahe least.Stylidiumsalsomuch more

statisticallyntegratedhanthe other two

genera(Armbrusteretai, 2004, 2009). The relationshipbetweenintegrationand floralaccuracyn this case iseasyto interpret.The fusion of thestaminateandpistillateissuesn combinationwith thetemporal,ratherthan spatial,displacementof sexualfunctions hasallowedStylidiumo achievenearlyperfectmeanoptimality(i.e.tight correspondenceof wherepollenisplacedon andpicked upfrompollinators).This,incombination withhighprecision,leads tohighfloralaccuracy.

The correlationbetween femaleprecisionandmaleaccuracydetected in Collinsia could either be theresult of a causalinfluence of femaleprecisionon maleaccuracy,a causal influ-enceof maleaccuracyon femaleprecision,or the two variablesbeingsimilarlyinfluencedby a third. In thissystem,it seems

mostlikelythatstigmatraits nfluencestamentraitsrather hanviceversa,becausestigmapositionis programmed develop-mentallyto changewith flowerage(see below).This leadstoimprecisionin stigmaposition,observedparticularlyin theoutcrossingspeciesof Collinsia,

Causes ofdeparture from the optimumIt wasinterestingto note that reward-anther and reward-stigmadistances tendednot to covary isometricallyamongpopulationswithin aspeciesin Dalechampia, althoughtheydidsoquitestronglyat thelevelofspeciesmeans. Thissuggeststhat theremaybegeneticconstraints,such aspleiotropy,that

preventpopulationsfrom

divergingoptimally,even

thoughspeciesdo so.Indeed,the trajectoryobservedn onesampleofthe D. scandenspopulationswasverysimilarto the trajectoryof thegeneticcorrelation(0.54vs0.67),aswouldbeexpectedif pleiotropylimitedresponseto selection to thesubptimaltrajectoryof thegeneticregression(HansenetaL,2003a,b).The closerapproach to the adaptive trajectory byspeciesmeans thanby populationmeansis consistent withthe ideathatevolutionaryresponseoselectionat oddswiththegenetictrajectory akes more timethan does evolution inresponseto





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selectionthat is parallelto the genetictrajectory(Schluter,1996, 2000;Hansen &Houle,2008).This is seenin species-population comparisonsbecausepopulationshave lesstimeto divergethan do species;speciesusuallyrepresentmore

completeisolation anddeeper phylogeneticbranchesthan dopopulations.The differential'behaviour' ofpopulationsandspeciesis also consistent with the ideathat adaptiveridgetrackingrequiresdisruption of the geneticarchitectureofpopulations, which may (or may not) be associatedwithspeciation(Gould,2002).

Shallowerallometricslopesat lower levelsof nestedhierar-chies(e.g.populationsnestedwithinspecies)havebeennotedin previousstudies.Differencesin slopeshave beensuggestedto be statistical artefactsrelated to measurementerror (Pagel& Harvey,1988),but othershaveshown thatbiologicalexpla-nationsare much morelikely(Lande,1979;Burt, 1989; Riska,1989, 1991;Armbruster,1991;Hansen etaL,2008).Furtherevidence

againstthe artefact

problemin the

presentstudyis

that the slopesin questionarenearlyisometric,and isometricslopesdo not generatethe artefact(Pagel& Harvey,1988).

Alternativeresolutionsofconflictingselectivepressures?Selec-tion for increasedoutcrossingin self-compatiblespecieswithsimultaneous oroverlappingsexual functionswillgenerallyfavourherkogamy.Thispressurewill often selectdirectlyagainstoptimalityofthemean,becausecorrespondenceofthereward-antherandreward-stigmadistancesoften resultsn anthersandstigmas beingclosetogether(increasinghe likelihood ofself-pollination).Thisis almostcertainlyhe reasonwhyCollinsieaehave rather owaccuracyfor such anintegratedflower[withconnatepetalsand adnate(epipetalous)stamens].Apparentconflict in selectivepressuresseems to beespeciallystrongintheoutcrossing speciesof Collinsia,which showstrongherko-gamy(andlowoptimality)overa largeportionof the life of aflower,with reduced herkogamyonly towards the end offlower life(KaliszetaL, 1999;ArmbrusteretaL, 2002).Thisdevelopmentalpattern is reflectedin the strongcontributionof departurefrom the optimum and femaleimprecisiontoinaccuracy(the change in style length over the life of theflower contributes toplant-andpopulation-level imprecision;Fig.4b).

Lowaccuracyas a result ofherkogamyis alsoprobablyafactor n therelativelyowaccuracyofmanyDalechampiablos-soms. Thisrelationshipscomplicated,however,bythe three-dimensional

'escape'from the trade-off between

herkogamyand anther-stigma optimality in somespecies(see below).Stylidiumspp. do not face this conflict inselection becausetheyhaveescapedfromthe conflictthrough dichogamy(seebelowand ArmbrusteretaL, 1994,2004).

There are thus at least twopossibleroutes ofescapefromthe trade-off betweenaccuracyand herkogamy(whilstmain-taining outcrossing).One is illustratedbyStylidium:escapeintimebyseparatingsexual functionstemporally (dichogamy).Flowersnitiallydispense pollenfor acoupleof daysand then

subsequentlycollectpollenfrompollinators(ArmbrustertaL,1994).Thisescapefromthe trade-offmay,in part, explainthemuchhigheroptimalityand accuracyn Stylidiumcomparedwith Dalechampiaand Collinsia,which areself-compatible

and incompletelydichogamous.SomepopulationsofD. scandensndsomespecieso Dale-champiaappear,however,o escapefromthetrade-offbyusinghigher dimensionalspace.Rather than havingthe reward,stigmasandanthers n asingleline orplane,such thatthe dis-tances arenearlyadditive(forexample,ASD= GSD- GAD),as isthe casefor many populationsand species,somespecieshavethestylesandstaminateflowersdivergingfromtheglandin adifferentplaneor lineardimension.This 'solutionappearsto have beenemployedby a numberof Dalechampia speciesandevolvedat least fivetimes(Fig.10).Thissystemof herko-gamyactually onlyworks wellbecauseof partialdichogamy,however.In the pistillatephase (stigmasreceptive,no maleflowers

open),reward-collectingbeescontact thestigmasand

transfer llogamouspollen.In the bisexualphase (stigmasrecep-tive,one toseveralmaleflowersopen),bees aremuchlesslikelyto touch thestigmas,becausethe male flowersnow formanew platform (on a differentplane) on which thebeesareperched.Partialrather than fulldichogamyremains advanta-geous,as it providesthe possibilityof fail-safeselfingin theabsence ofpollinators at the end of the receptiveperiod(reproductiveassurance).

Speciesthat are facultativeor obligateselfers(forwhateverreason)are not subjectto the selectiveconflictbetweenout-crossing (herkogamy)and the accurate fit of anthersandstigmas.Thus,wemightexpectthemto showhigheraccuracy.However,thisexpectationscomplicatedbythe fact that selfers

maybeundermuch morerelaxed electionoraccuracy,lthoughthe covariance ofstamen-pistil may still be maintainedtopromote self-pollinationseeAnderson& Busch,2006).TherewasnodetectabletrendinDalechampiaorfacultativelyelfingspeciesto havesmallermeandepartures rom the optima.InCollinsieae, however,acultativeelfingpopulationsandspeciesshowed much lowerdeparturesfrom their optima than didthe facultativeoutcrossers(Fig.7).

Although dichogamyis commonamongfloweringplants(Faegri& van der Pijl, 1979),it is usually interpretedas anadaptation promotingoutcrossing. Althoughthis is certainlythe case,one wonderswhetherthe 'choice'ofdichogamyoverherkogamyas apromoter mightsometimesbe drivenbyselec-tion for

anther-stigmaaccuracy.Future

comparativestudies

could addressthisquestion by lookingat evolutionarytransi-tionsbetween the twotypesof outcrossingpromoter.

Althoughthe use ofhigherdimensionalspaceas awaytobreakout of theherkogamy-accuracyrade-offhasnot,to ourknowledge,been describedpreviously,we expectthere tobe many examplesbesidesDalechampia.Open chamberand'platform' lowers aregoodcandidates. ConsiderPassiflora,orexample.The upright, platformlowerscan achieveherkogamy(spatial separationof theanthers andstigmas)in horizontal





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spacebyhavingthe threestigmaspositionedbetween the fiveanthers,with room tospare.However,mean optimality isdeterminedin the verticaldimension,by the match betweenthe corona-stigmaand corona-anther distances(W. S. Arm-

bruster,unpublished).Heterostylyis anothertypeof escape,wherehavingtwo forms of flowers andintramorph ncompat-ibilitymeans thatoptimality(reciprocity)can behigh evenwhen there isstrong herkogamy(Sanchezetal.>2008).Inter-estingly,someheterostylousspecieshavealsoescapedintohigherdimensionalspace, apparentlyto improvefurther theefficiencyof intermorph pollentransfer(Armbrusteret al.,2006).

Concluding remarks and future research

Thecomparativenalysesofinterspecificandinterpopulationaldataon floralaccuracysupportedour hypothesisthat there isa fitness surfacegoverningthe interactionof reward-stigmaandreward-antherdistances atthe specieslevel.Indeed,con-formanceof speciesmeansand, to a lesserextent,populationmeans toa positiveisometric linepassing throughthe originstronglysupports our hypothesisof an isometricadaptiveridgegoverningthesize of structurescontrollingwherepollenisplacedon pollinatorsand wherestigmastouch pollinatorsto collectpollen.

In comparingthe threestudysystems,Dalechampia,Col-linsieae,and Stylidium,weobserved considerablevariationindegreesof accuracy(closenessof individualsand populationmeansto thehypothesizedadaptiveridge),with marked vari-ation in the relativeimportanceof phenotypic precisionvsmeanoptimalityingeneratingloral naccuracy.t appearshat

geneticconstraintson precision,asmanifestedthroughvary-ing degreesof floralintegration,imposeimportantlimits onDalechampiaaccuracy.Inaccuracyn Collinsiaappearsto belargelya productof conflictingselectivepressurepromotingherkogamy(spatialseparationofanthers andstigmas)duringmostofthelifeof theflower,which,in the contextof thelineararrangementof fertileparts,results n lowaccuracy.Stylidiumachieveshigh accuracyas a resultof escapingthe need forherkogamyby beingdichogamous(temporal separationofsexualfunctions)and byvirtueof the extremeintegrationoffloralparts,notablythe fusionof staminaland pistil tissuesinto amotile column.

We recommendthat futureinvestigationsconsiderin more

detailthe shapeof the

adaptivesurface

controllingthe coor-

dinatedevolutionof thepositionsof pollen placementandpickup.Althoughwemaybe correctin invokingan adaptiveridgethat runsalongan isometricdiagonal,we lack detailedinsightsinto theshapeof theridge.Underwhich conditionsis it broad,and underwhichis it narrow?This isimportantbecause,if theridgeisbroad,the adaptivecostof small devi-ationsfromthe optimumwill besmall andselectionweak.Ifthe ridgeisnarrow, he costwill belargeandselectionstrong.Is the top of theridgesmoothor bumpy? Bumpinessof the

adaptiveridgeseemslikelyto be the rule because thedistribu-tions ofpollinatorsize and/orbehaviour areusuallydiscontin-uous,asnoted above.

It should bepossibleto gainfurtherinsightinto theshape

of the adaptivesurfaceby examiningthe variancesof theoptima.Forexample,largeoptimumvarianceswouldsuggestbroaderridgeswith moregradual approach planes.It remainsto be determined how todeal with thisissuemathematically,however. Forexample,ifbroadridgesare associatedwithlargevariancein the optima, then maybethe optimum varianceshould actuallybe subtracted fromthe inaccuracyestimaterather hanadded to it(butcf.Armbrusteretal.,2009).Alter-natively,thevariancen the optimumcouldbeusedin a sepa-rate explicitstep of mapping relativefitness ontoaccuracy.Clearly,there are opportunities for further theoreticalandempirical development.

AcknowledgementsWe thankMark Rausher and twoanonymousreviewersforcommentson an earlierdraft,P. H. Olsen for thephotographsin Fig.2a and theNorwegianResearchCouncil,the NansenFund and the US National ScienceFoundationfor support(grantsDEB-9318640,DEB-9708333,DEB-0324808andDEB-0444745to W.S.A.,and DEB-0444157to T.F.H.).

ReferencesAndersonA,BuschJW. 2006. Relaxedollinator-mediatedelection

weakensloralntegrationn self-compatibleaxaofLeavenworthia(Brassicaceae).mericanournal f Botany3: 860-867.

ArmbrusterWS.1984.Theroleof resinnangiospermollination:ecologicalnd chemical onsiderations.mericanournal f Botany1:

1149-1160.ArmbrusterWS.1988.Multilevelomparativenalysisfmorphology,

function,ndevolutionDalechampialossoms.Ecology9:1746-1 761ArmbrusterWS.1990.Estimatingndtestingheshapesfadaptive

surfaces:hemorphologyndpollination Dalechampialossoms.American aturalist35:14-31.

ArmbrusterWS.1991.Multilevelnalysesfmorphometncata romnatural lantpopulations:nsightsntoontogenetic, enetic,andselectivecorrelationsnDalechampiacandens.volution5: 1229-1244.

ArmbrusterWS.1993.Evolution fplantpollinationystems: ypothesesand testswiththeneotropicalineDalechampia.volution7:1480-1505.

ArmbrusterWS.1996.Evolutionffloralmorphologyndfunction:nintegratedpproachoadaptation,onstraint,ndcompromisenDalechampiaEuphorbiaceae).n:LloydD, Barrett CH,eds.Floralbiology.ewYork,NY,USA:Chapman& Hall,241-272.

ArmbrusterWS. 2001. Evolutionf floral orm: lectrostaticorces,pollination,ndadaptive ompromise.NewPhytologist52:181-183.

ArmbrusterWS. 2002.Can ndirectelection ndgeneticontext ontributetotraitdiversification?transition-probabilitytudyof blossom-colourevolutionn twogenera. ournalf Evolutionaryiology5:468-486.

ArmbrusterWS,BaldwinBG.1998.Switchrom pecializedogeneralizedpollination.Nature 94:632-632.

ArmbrusterWS,EdwardsME,DebevecEM.1994.Characterisplacementgeneratesssemblagetructure fWesternAustralianriggerplants{Stylidium). cology5: 315-329.





18/19

616 ResearchNewPhytologist

ArmbrusterWS,HansenTF, PlabonC,Prez-Brrales,MaadJ. 2009.Theadaptiveccuracyf flowers:measurement ndmicroevolutionarypatterns. nnals f Botany03:1529-1545.

ArmbrusterWS,MartinP, KiddJ, StaffordR,RogersDG.1995.Reproductiveignificancef indirectpollen-tube rowthn Dalechampia(Euphorbiaceae).mericanournal f Botany2:51-56.ArmbrusterWS,MulderCPH,BaldwinBG,KaliszS,WessaB,uteH.2002.Comparativenalysisflate loraldevelopmentndmating-systemevolutionn tribeCollinsieaeScrophulariaceae,.\).Americanournal fBotany9: 37-49.

ArmbrusterWS,PlabonC,HansenTF, MulderCPH.2004.Floralintegration,modularity,ndprecision: istinguishingomplexadaptationsromgeneticconstraints.n:PigliucciM,PrestonK,eds.Phenotypicntegration:tudyingheecologynd evolutionfcomplexphenotypes.xford,UK:OxfordUniversityress, 3-49.

ArmbrusterWS,Prez-Brrales,Arroyo,EdwardsME,Vargas .2006.Three-dimensionaleciprocityf floralmorphsnwildflax{Linumsuffruticosum):new twistonheterostyly.ewPhytologist71:581-590.

ArmbrusterWS,SchwaegerleKE.1996.Causes fcovariation fphenotypicraits mongpopulations.ournal fEvolutionaryiology:

261-276.ArnoldSJ,BurgerR,HohenlohePA,AjieBC,JonesAG.2008.Understandinghe evolutionndstabilityf the G-matrix.Evolution 2:2451-2461.

ArnoldSJ,PfrenderME,JonesAG.2001. Theadaptiveandscapes aconceptual ridgebetweenmicro-and macroevolution.entica112/113:9-32.

Bell G.1989.Acomparativeethod.Americanaturalist33:553-571.BradshawD. 1991.Genostasis ndthe limits o evolution.Philosophical

TransactionsftheRoyal ociety fLondon 333: 289-305.BurtA.1989.Comparativeethodsusingphylogeneticallyndependent

contrasts. n:HarveyPA,Partridge ,eds.Oxfordurveysnevolutionarybioloev,ol.6.Oxford,UK: OxfordUniversity ress,3-53.

ConnerJ,ViaS.1993.Patterns fphenotypicndgeneticcorrelationsamongmorphologicalnd ife-historyraitsnwildradish,Raphanusraphanistrum.volution7: 704-711.

ConnerJK.1997.Floral volutionn wildradish:he rolesofpollinators,naturalelection,ndgeneticcorrelationsmongraits.nternationalJournal fPlantSciences58:S108-120.

Conner K.2002. Geneticmechanismsf floral rait orrelationsn anaturalpopulation.Nature 20:407-410.

DarwinC. 1877.Thevarious ontrivancesywhichorchids reertilised yinsectSynd edn.London,UK:Murray.

EndlerA.1986.Natural electionn thewild.Princeton,NJ,USA:PrincetonUniversityress.

Endler A.1995.Multiple-traitoevolution ndenvironmentalradientsnguppies.TrendsnEcologynd Evolution0:22-29.

FaegriK,van derPijlL. 1979.The rinciples fpollination cology,rdedn.Oxford,UK:Pergamon,44.

Felsenstein. 1985.Phylogeniesnd thecomparativemethod.AmericanNaturalist25: 1-15.

Gavrilets . 2004. Fitnessandscapesnd theorigin fspecies.rinceton,NJ,

USA:PrincetonUniversityress.GouldSJ.2002. Thetructurefevolutionaryheory. ambridge,MA,USA:Belknap/Harvardress.

GrantV. 1971.Plant peciation.ewYork,NY,USA:ColumbiaUniversityPress.

HansenTF,ArmbrusterWS,AntonsenL. 2000.Comparativenalysisfcharacterisplacementndspatial daptationss illustratedytheevolution Dalechampialossoms.American aturalist56: S17-S34.

HansenTF,ArmbrusterWS,CarlsonML,PlabonC.2003a.EvolvabilityandgeneticonstraintnDalechampialossoms:Genetic orrelationsndconditionalvolvability.ournal f

*Experimentaloology.Molecularnd

Developmentalvolution96B: 23-39.

HansenTF, CarterAJR,PlabonC.2006. Onadaptiveccuracyndprecisionn natural opulations.mericanaturalist68:168-181.

HansenTF, HouleD. 2004.Evolvability,tabilizingelection,ndtheproblemf stasis.n:PigliucciM,PrestonK,eds.Phenotypicntegration:studyingheecologynd evolutionfcomplexhenotypes.xford,UK:

OxfordUniversityress,130-150.HansenTF, Houle D. 2008.Measuringndcomparingvolvabilityndconstraintn multivariateharacters.ournal fEvolutionaryiology1:1201-1219.

HansenTF,PlabonC,ArmbrusterWS,Carlson,ML.2003b.EvolvabilityandgeneticconstraintnDalechampialossoms:omponentsfvarianceandmeasuresfevolvability.ournalf Evolutionaryiology6:754-766.

HansenTF, Pienaar ,OrzackSH. 2008.Acomparativeethodorstudyingdaptationo arandomly volvingnvironment.volution2:1965-1977.

HarderLD,WilsonWG.1998.TheoreticalonsequencesfheterogeneoustransportonditionsorpollendispersalyanimalsEcology9:2789-2807.

HeinrichB,RavenPH. 1972.Energeticsndpollinationcology.Science176: 597-602.

JohnsonSD,SteinerKE.1997.Long-tonguedlypollinationndevolution

offloralpur engthntheDisadraconisomplexOrchidaceae).volution51:45-53.JonesAG,ArnoldSJ,BurgerR.2003.Stabilityf the G-matrixn a

populationxperiencing leiotropicmutation,tabilizingelection,ndgeneticdrift.Evolution7:1747-1760.

JonesAG,ArnoldSJ,BurgerR. 2004.bvolutionandstabilityr theG-matrix na landscapeith amovingoptimum.Evolution8:1639-1654.

KaliszS,VoglerD,FailsB,FinerM,ShepardE,HermanT, GonzalesR.1999.The mechanismfdelayed elfingn Collinsiaerna(Scrophulariaceae)Americanournal f Botany6: 1239-1247.

LandeR. 1979.Quantitativeeneticanalysisf multivariatevolution,appliedo brain bodysizeallometry.volution3:402-416.

LandeR. 1980.Thegeneticcovariance etweenharacters aintainedypleiotropicmutations.GeneticsA:203-215.

LandeR,ArnoldSJ.1983.The measurementf selectionn correlated

characters.volution7: 1210-1226.LankinenA,Skogsmyr. 2001. Evolutionfpistil engthasa choicemechanismorpollenquality.Oikos2:81-90.

LiCC.1975.Pathanalysisa primer.PacificGrove,CA,USA:BoxwoodPress.

MaadJ. 2000.Phenotypicelectionnhawkmoth-pollinatedlatantherabifolia: argetsndfitness urfaces.volution4:112-123.

MaadJ,Alexandersson. 2004.VariableelectionnPlatantheraifolia(Orchidaceae):henotypicelectiondiffered etweenexfunctionsn adrought ear. ournal fEvolutionaryiology7: 642-650.

MulcahyD. 1983.Modelsotpollenubecompetitionn heramummaculatum.n:RealL,ed. Pollinationiology.ewYork,NY,USA:AcademicPress,151-161.

NesseRM.2005.Maladaptationndnatural election.QuarterlyeviewfBiology0:62-70.

NilssonLA.1988.The evolutionf flowerswithdeepcorolla ubes.Nature

334:147.O ConnellLM,JohnstonMO.1998.Maleand femalepollinationuccessinadeceptiverchid,a selectiontudy.Ecology9: 1246-1260.

OrzackSH,SoberE. 1994a.Optimalitymodelsand the testofadaptationism.mericanaturalist43: 361-380.

OrzackSH,SoberE.1994b.How(not)to testanoptimalitymodel.TrendsinEcologynd Evolution: 265-267.

PagelMD,HarveyPH. 1988.The taxon-levelroblemntheevolution fmammalianrain ize: actand artefacts.mericanaturalist32:344-359.

PlabonC,HansenTF. 2008.Ontheadaptiveccuracyf directionalasymmetryn insectwingsize.Evolution 2:2855-2867.





19/19


PollyD. 2008.Developmentaldynamicsand G-matrices: canmorphometricspacesbe usedto modelphenotypic evolution?EvolutionaryBiology35:83-96.

PurvisA,Rambaut A.1995.Comparative analysis byindependent contrasts(CA

macroevolutionary patters pollination accuracy

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