TheJournalofNeuroscience,August1,1996,16(15):4716–4732 The Analysis of Complex Motion Patterns by Form/Cue Invariant MSTd Neurons Bard J. Geesaman1 and Richard A. Andersen2 1DepartmentofBrainandCognitiveSciences,MassachusettsInstituteofTechnology,Cambridge, Massachusetts02139,and2DivisionofBiology216-76,CaliforniaInstituteofTechnology,Pasadena,California91125 SeveralgroupshaveproposedthatareaMSTdofthemacaque spirals. The different classes of stimuli included: coherently monkeyhasaroleinprocessingopticalflowinformationused moving random dot patterns, solid squares, outlines of intheanalysisofselfmotion,basedonitsneurons’selectivity squares, a square aperture moving in front of an underlying forlarge-fieldmotionpatternssuchasexpansion,contraction, stationarypatternofrandomdots,asquarecomposedentirely androtation.Ithasalsobeensuggestedthatthiscorticalregion offlicker,andasquareofnonFouriermotion.Whenaunitwas maybeimportantinanalyzingthecomplexmotionsofobjects. tuned with respect to motion patterns across these stimulus Moregenerally,MSTdcouldbeinvolvedinthegenericfunction classes, the motion pattern producing the most vigorous re- ofcomplexmotionpatternrepresentation,withitscellsrespon- sponse in a neuron was nearly the same for each class. Al- sibleforintegratinglocalmotionsignalssentforwardfromarea thoughpreferredtuningwasinvariant,themagnitudeandwidth MT into a more unified representation. If MSTd is extracting ofthetuningcurvesoftenvariedbetweenclasses.Thus,MSTd generic motion pattern signals, it would be important that the isform/cueinvariantforcomplexmotions,makingitanappro- preferredtuningofMSTdneuronsnotdependontheparticular priatecandidateforanalysisofobjectmotionaswellasmotion featuresandcuesthatallowthesemotionstoberepresented. introducedbyobservertranslation. Totestthisidea,weexaminedthediversityofstimulusfeatures andcuesoverwhichMSTdcellscanextractinformationabout Key words: area MSTd; optical flow; object motion; motion motion patterns such as expansion, contraction, rotation, and perception;form/cueinvariance;extrastriatecortex Two pathways for visual information processing in extrastriate shown to have relatively small receptive fields, rather similar in cortexhavebeenidentified(UngerleiderandMishkin,1982;Van sizetothosefoundinareaMTatthesameeccentricityandalso Essen and Maunsell, 1983; DeYoe and Van Essen, 1988). One similarintermsoftheirpreferencefortranslationalmotion.Cells stream,the“what”pathway,sendsinformationventrallyintothe in MSTd, on the other hand, have comparatively large receptive temporallobeandappearstobeinvolvedinprocessingthespatial fields that generally include the fovea and often extend across patternofthevisualscene.Theotherstream,projectingdorsally bothipsi-andcontralateralhemifields.Thesecellsareselectively intoposteriorparietalcortex,hasbeendescribedasthe“where” tuned not only for large-field translational motion, but also for pathway and is involved in localizing objects in space and the motion patterns such as expansion, contraction, and rotation related task of processing image motion. The best-studied area (Sakata et al., 1985; Saito et al., 1986; Tanaka et al., 1986, 1989; withregardtothelattertaskisareaMT,locatedontheposterior Tanaka and Saito, 1989). Our lab’s previous investigation in bankandfloorofthesuperiortemporalsulcus(STS),containing MSTd also showed that some units in this region have complex cells shown to respond to simple linear (translational) motion response characteristics, in many cases demonstrating a prefer- (Maunsell and Van Essen, 1983a,b; Albright, 1984). MT sends a ence for spiraling motion patterns over expansion, contraction, heavyprojectionforwardtoareaMST(medialsuperiortemporal androtation(Grazianoetal.,1994). region), an adjacent cortical region located on the floor and Becausethesecomplexmotionpatternsarebuiltupfromlocal anteriorbankoftheSTS.AreaMST,whichisalsobelievedtoplay regions of approximately straight motion, they can effectively an important role in the motion processing hierarchy, has been drivemanydirectionallyselectiveunitsinMT.Whatdistinguishes functionallysegmentedintoatleasttwodistinctregions,aventral a large proportion of MSTd cells, besides the increased size of lateral one (MSTl) and a dorsal one (MSTd) (Desimone and theirreceptivefields,isthattheirspecificityformotionpatternis Ungerleider,1986;Saitoetal.,1986;UngerleiderandDesimone, not sensitive to stimulus placement within a neuron’s receptive 1986a,b;KomatsuandWurtz,1988).ThecellsinMSTlhavebeen field(DuffyandWurtz,1991a,b;Grazianoetal.,1994),aproperty referredtoaspositionalinvariance.Theinvarianceiswithrespect ReceivedSept.20,1995;revisedMay7,1996;acceptedMay13,1996. topreferredtuningandislesspronouncedforresponseamplitude ThisworkwassupportedbyNationalInstitutesofHealthGrantEY07492,the OfficeofNavalResearch,theSloanFoundation,andtheHumanFrontiersScientific (DuffyandWurtz,1995)andtuningwidth.Tuninginvariancewith Program.WethankNingQianandDavidBradleyfortheirhelpfulcommentson respect to motion pattern is not found within MT, where even earlierversionsofthismanuscript,andGailRobertsonfortechnicalassistance.We minor positional shifts in the placement of the these stimuli can are also indebted to the two anonymous reviewers for their comments and suggestions. dramaticallyalter(evenreverse)aunit’spreferredtuning(Lagae CorrespondenceshouldbeaddressedtoRichardA.Andersen,JamesG.Boswell etal.,1994). ProfessorofNeuroscience,DivisionofBiology216-76,CaliforniaInstituteofTech- nology,Pasadena,CA91125. The types of complex motion stimuli to which MSTd cells Copyright(cid:113)1996SocietyforNeuroscience 0270-6474/96/164716-17$05.00/0 respondhavebeenassociatedwiththefullfieldpatternsprojected GeesamanandAndersen•Form/CueInvariantMSTdNeurons J.Neurosci.,August1,1996,16(15):4716–4732 4717 ontotheretinaduringobserverlocomotion,asfirstrecognizedby positional invariance. Based on these initial criteria, 190 cells were Gibson (1950). Many computational and psychophysical studies consideredforanalysis,71frommonkey89-1and119frommonkey90-2. The details of the recording procedure have been described previously haveshownthatbyanalyzingtheseflow-fieldmotionpatternsand (Grazianoetal.,1994).Briefly,ascleralsearchcoilandanacrylicskull detectingsuchfeaturesasthefocusofexpansion,theparameters cap were implanted 5 d before beginning training on a fixation task. of observer rotation and translation can be recovered (Prazdny, Training and subsequent behavior were reinforced by depriving the 1980;Andersen,1986;WarrenandHannon,1990).Thissuggests monkeysoffluidbeforeeachsessionandthengivingdropsofapplejuice aroleforMSTdinprocessingego-motionanddeterminingdirec- upon correct task completion. After mastery of the behavior, a second surgerywasperformedtointroduceacraniotomythatprovidedchronic tion of heading (DOH). At face value, the well documented accesstothebrainforrecordingpurposes.Becausewewereconfidentof positional invariance of MSTd units is puzzling—if the nervous our identification of area MSTd based on approximate location and system uses optical flow to guide navigation, we might expect response properties, we chose not to kill the monkeys for purposes of neurons performing DOH analysis to be sensitive to the retinal anatomy. These monkeys went on to become subjects in subsequent location of these patterns. However, positional invariance with investigations. Fixation task and data collection. The animal was placed 57 cm away respect to stimulus specificity does not preclude changes in the from a wide-field tangent screen projection monitor, which readily al- response amplitude with stimulus placement (Duffy and Wurtz, lowedstimuliaslargeas40(cid:56)indiametertobepresentedtothemonkey. 1995).Acoarse-codingschemecouldtakeadvantageofaspatial Trials were initiated by the appearance of a green (0.1(cid:56)) fixation point responsegradienttoencodethelocationofthefocusofexpansion directlyaheadoftheanimal.Themonkeywasrequiredtofixatethetarget bypoolinginformationoveralargenumberofunits. and pull a lever within 600 msec of target onset. After a 3 sec period, AlthoughthereisgoodevidencethatMSTdisimportantinthe which included the presentation of two stimuli and an intervening gap, the fixation point dimmed and the monkey was required to release the analysis of optical flow, the positional invariance of these units levertoreceiveareward.Throughoutthetrial,eyepositionwasmoni- withrespecttopreferredtuningsuggestsotherpossibleroles.An tored. If eye speeds exceeded 15(cid:56)/sec (as in a saccade), the trial was additional function for MSTd makes an analogy between MSTd terminatedwithoutareward.DatacollectionwascontrolledbyaPDP-11 andareaIT(inferotemporalcortex)inthetemporallobe(Grazi- computer,andstimuluspresentationwascontrolledbyaPC-compatible ano et al., 1994), which also demonstrates positional invariance. 386computer. Stimuli.Thedifferentvisualstimuliusedcanbedividedintodifferent Cells in IT have been found that are selective for such complex types and classes. A stimulus’s class refers to attributes of the stimulus spatial patterns as toilet brushes and faces (Gross et al., 1972; other than motion pattern; i.e., whether its features are composed of Desimoneetal.,1984).Thisselectivityismaintainedregardlessof random dots, lines (empty square), edges (solid square), aperture bor- stimulus placement within the units’ large receptive fields ders, or flicker. A stimulus’s type refers to the motion pattern these (Schwartz et al., 1983; Desimone et al., 1984). The positional featuresundergorelativetooneanother,namely,whethertheyexpand, rotate,contract,orspiral. invariance in cell tuning for both IT and MSTd suggests a func- Stimulus type is based on the concept of a spiral space (Fig. 1), tionalconnectionbetweenthetwoareas.WhereITisthoughtto originallyformulatedinGrazianoetal.(1994).Inthisspace,expansion analyze spatial pattern information in the image, MSTd could and contraction are on opposite sides of the same axis, and the two analyzemotionpatterninformation.Itshouldbeemphasizedthat directions of rotation are on opposite sides of the orthogonal axis. A thepossible“pattern”motionand“ego-motion”rolesforMSTd stimulus,theimagefeaturesofwhichhavetheirmotionvectorspointed 180(cid:56) away from the center of the display (expansion), is represented are not mutually exclusive. In fact, ego-motion analysis can be straight up in this space (0(cid:56)); contraction is represented straight down- consideredasubtypeofpatternmotionprocessing.MSTdmight ward (180(cid:56)). Moving from expansion to contraction is equivalent to alsobeimportantasanearlystageinanalysisofbiologicalmotion, rotating the velocity vectors of the features by 180(cid:56). If, instead, these such as that presented in Johansson dot displays (Hoffman and vectorsarerotated90(cid:56),globalrotationineitherdirectionisobtained.For Flinchbaugh,1982;PoiznerandBellugi,1981;Matheretal.,1992; example, rotating the velocity vectors of an expansion stimulus 90(cid:56) clockwise results in a clockwise rotation stimulus pattern. Intermediate Dittrich,1993;MatherandWest,1993). rotations, such as the 45(cid:56) rotations used in these experiments, result in ManyexperimentsstudyingareaMSTdhaveusedrandomdot spirals.Spiralscontainelementsofeitherexpansionorcontractioncom- (RD) stimuli with different types of global motion (expansion, binedwitheitherclockwiseorcounterclockwiserotation,givingfourbasic contraction,translationmotion,etc.)toprobetheresponseprop- typesofspiralpattern.Usingthisrepresentation,acontinuousspaceis ertiesofthesecells.Inthecurrentinvestigation,wehaveincluded formed,withexpansion,rotation,andcontractionbeingdiscretecardinal directionswithinthis“spiral”space(Fig.1). stimuli, the motion pattern of which is established by features Astimulus“movie”iscomposedof60consecutiveimageframeslasting other than random dots, such as edges, and then compare these a total of 1 sec. Six classes of stimuli were used, four of which are responses and tuning curves across classes. We also explore the representedinFigure2.TheRDclass(fordetails,seeGrazianoetal., effect of using cues other than luminance by creating motion 1994)consistsof150dotswithlimitedlifetimes(333msec,or20frames) patterns using “second-order” or nonFourier motion. These ex- andconstantvelocity.Attheendofitslifetime,eachdotisassignedanew random location within the 20(cid:56) diameter stimulus circle and given a perimentswillhelptoestablishhowgeneralthefeaturesandcues trajectory and speed appropriate for its new location. The dots are are that MSTd uses to extract motion pattern. This work is relocated asynchronously to avoid a coherent flickering of the stimulus partially motivated by studies of “form/feature/cue invariance” every 333 msec. If the dot moved outside the bounds of the display recently demonstrated in MT, V1, and IT (Albright and window,itwasimmediatelyassignedanew,randomlocationwithinthe Chaudhuri,1989;Albright,1992;Saryetal.,1993). displaycircleandgivenanewtrajectory.Forallstimulustypes(patterns), thespeedofeachdotwasalinearfunctionofitsdistancefromthecenter ofthedisplay,inthiscasegivenbytheformulaS(cid:53)0.2(cid:51)r,whereSisin MATERIALS AND METHODS (distanceunits)/secandrisindistanceunits.Thedirectionofmotionfor Animalpreparation.ThreehemispheresfromtwoRhesusmonkeyswere each dot is determined by the type of global motion desired (e.g., usedfortheseexperiments.Becausetheresultsweresimilarinthetwo expansionrequireseachdottobemovingdirectlyawayfromthecenter monkeys,thedatawerepooledforthepurposeofanalysis.Unitslocated ofthestimulus). inMSTdweretentativelyidentifiedbasedontheirlocationinthecham- RD stimuli are incompatible with the motion of a single object. For ber and depth relative to the dura. In each of the three chambers example,althoughthedotsintheexpansionstimulusmoveoutwardwith recordedfrom,wemappedoutbothMSTdandMTbasedonthetuning motionconsistentwiththeapproachofanobject,thecircularboundary characteristicsofcellsintheseregions.Particularlyhelpfulindistinguish- ofthisstimulusisstationary.Asthisluminanceboundaryisreadilyvisible ing MSTd from MT was the former cells’ large receptive fields and because of the relatively high density of dots within the stimulus, an 4718 J.Neurosci.,August1,1996,16(15):4716–4732 GeesamanandAndersen•Form/CueInvariantMSTdNeurons Figure1. Spiralspaceexplained.Inthisrepresentation,expansion/con- tractionareonoppositesidesoftheverticalaxis,andthetwodirectionsof rotationareonoppositesidesofthehorizontalaxis.Intermediateorien- tationsbetweenthesecardinalaxesrepresentspiralpatterns.Expansion (top) is assigned an angular value of 0(cid:56) by convention, with the angles increasingasonemovesclockwise.Distancefromtheoriginisameasure offiringrate;anglereflectsthetypeofmotionpattern.Datafromthetwo curvesdisplayedonthispolarplotwereobtainedfromasinglecellusing theRDstimulusclass.Withonecurve,thespacewassampledevery22.5(cid:56) (16 points), and with the other curve every 45(cid:56) (8 points). Each point plottedrepresentstheaveragefiringrateforthatstimulustype(motion pattern) pooled from repeated, randomly interleaved trials. Note the similarityofthetwocurvesobtainedatthetwosamplingfrequencies.The linesemanatingfromtheoriginrepresentthepreferredtuningdirections recoveredfromthisdataafterregressiontoGaussians.Thisparticularunit wastunedtoaspiralcontainingelementsofbothexpansionandclockwise rotation. The similarity of tuning curves for the two sampling densities enabledustousethelowersamplingfrequencysothatmoredatacouldbe collectedperrecordingsession. observer does not get the impression of a single approaching circular object.Instead,thedotsappearasindependentfeatures. AseconddistinguishingfeatureoftheRDstimuliisthattheydonot evolveduringtheir1secpresentations.Theinstantaneousvelocityfields Figure2. Fourofthesixstimulusclasses.Ashowsthevelocityvectorfield don’t change during the stimulus sequence. Psychophysical evidence for a spiral midway between expansion and counterclockwise rotation exists suggesting that such pure “velocity fields,” despite giving rise to (correspondingtoanangularlocationof315(cid:56)inspiralspace).Notethat some ambiguities, are sufficient in many cases to allow observers to thelengthsofthesevectorsincreasewithdistancefromthecenterofthe recoverDOH(WarrenandHannon,1988).Forthesereasons,wethink stimulus.B–Dshowrepresentativeframesfromdifferentstimulusclasses ofthisstimulusclassasbeing“flow-like”becauseitcapturesaspectsof attwopointsintime.Becausethesquaresrepresentedarebothrotating globalmotionpatternsufficientforego-motionwhileleavingoutstimulus andexpandingwithtime,theirmotionpatternisalsothatofaspiral.In attributes,whichmaybeimportantintheperceptionofmovingobjectsin theAPclass,thetextureelementsmakinguptheinteriorofthesquaredo theenvironment. notmovewiththeedgesofthestimulus.Thespacingandplacementof Twootherstimulusclasses,solidsquare(SS)andemptysquare(ES), thesetextureelementsremainunchanged.Althoughthepatternsareall werecreatedbyhavingthecornersofsquaresobeymotionrulessimilar represented as black against a white background, on the screen the to those established for the RD stimuli (Fig. 2). However, whereas the polaritywasreversed.TheluminancecontrastsoftheAPandSSclasses dotsoftheRDclasshavelimitedlifetimesandstraightpaths,theborders wereactuallymoresimilarthantheyappearinthisfigure.Twoadditional ofthesquaresarevisiblefortheentiremovieandhaveaccelerationand classes,FLandNF,alsowereusedinthisstudy,butthenatureofthese curvature consistent with their trajectories being updated every frame. stimulipreventedaconvenientstaticrepresentation. Thesestimulisimulatethemotionofasingle,rigidobject.Onlytheedges of the SS and ES stimuli contain information about the motion of the stimulus,whichisexactlyoppositethecasefortheRDstimulusclass.The The flicker (FL) stimuli were identical to the SS stimuli described inclusion of both the ES and SS classes was motivated by looming above,exceptthatinsteadoftheinteriorofthesquarebeingahomoge- detectors in other species, which respond well to SS type stimuli but neousgray,itconsistedofrandompixelsturningonandoffeveryframe, poorlytoESstimuli(SimmonsandRind,1992). creatingashimmeringinteriortothesquare.Dotdensitywasadjustedso The aperture (AP) stimuli were created by moving a virtual window, thattheluminancecontrastofthesquareagainstthebackgroundwasthe identicalinspatialextentandmotionpatterntothesquaresintheESand sameastheSScase.FortheES,SS,FL,andAPclasses,theminimum SSclasses,overastationarybackgroundofrandomdotswithunlimited size of the square is 5(cid:56) of visual angle as viewed by the monkey. This lifetime (Fig. 2). The background is hidden except where the square occursforthefirstframeofanexpansionpatternandthelastframeofa aperture window exposes the RD background underneath. The spacing contractionpattern.Maximumedge-lengthis20(cid:56).Thepresenceofflick- between the dots remains constant, and the dots themselves have no eringdotshasbeenshowntoinhibitthedirectionalresponseofareaMT motion,otherthantobeexposedoroccludedwithtime,dependingon (Snowden et al., 1991) cells, and we were interested in examining a themotionpatternspecifiedfortheaperture. similareffectinareaMSTd. GeesamanandAndersen•Form/CueInvariantMSTdNeurons J.Neurosci.,August1,1996,16(15):4716–4732 4719 ThenonFourier(NF)stimuluswasproducedbycreatinga20(cid:56)square variance. It is equal to the total variance less the within-trial fieldofsmallsquaresthateachhavea50%probabilityofbeingonoroff, variance.Thisvalueislargefortheflatmodeloncellsresponding with each square covering 0.1(cid:56) of visual angle. Pixel polarity does not preferentially to different types of motion pattern. It represents change from frame to frame unless the imaginary border of a square obeying motion rules identical to those established for the squares de- the model’s lack of fit with respect to the data that cannot be scribed above passes over the pixel in question. Where this occurs, the explained after the variance associated with randomness in cell polarityofthepixelreverseseveryframethatthevirtualsquareborderis responseissubtracted. overthepixel.Usingthismethod,themotionoftheborderwasreadily The quotient obtained by dividing this lack-of-fit variance by visibletohumanobserversattheeccentricitiesusedintheseexperiments. thewithin-trialvarianceisdistributedaccordingtoanFdistribu- Unliketheotherclasses,motionpatternisnotdefinedbyluminancecues, but by flicker in the stimulus. A study by Albright (1992) showed that tionwith7andN(cid:50)8df,whereNisthetotalnumberoftrialsfor units in MT can respond to translational motion defined by this cue the experiment (usually N is (cid:59)80). By determining where this reasonablywell,andwewereinterestedtoseewhetherthiswasalsothe quotient lies on the appropriate F curve, this value can be con- caseinMSTd. vertedintoaprobabilitythatisanunbiasedmeasureofhowwell In the discussion that follows, an experiment refers to data recorded usingasinglestimulusclass(RD,SS,ES,FL,AP,orNF)foreachofthe the data fits the model. The larger this value, the better the fit. eight motion types (expansion, contraction, two types of rotation, and Thisprobabilitymeasurewillbereferredtoastheflatindex(FI) four types of spirals) in multiple repeats (approximately eight) of each andhasaminimumvalueof0andamaximumvalueof1.TheFI stimulus. Figure 1 shows two superimposed tuning curves obtained by represents the probability that the observed lack of fit from the sampling 8 and 16 directions in spiral space. As demonstrated in this flat model can be explained by chance. Note that the variance figure,duringpreliminaryexperimentswedeterminedthatusing8evenly spacedstimulusdirectionsgavesimilarresponseprofilesas16directions. quotientislarge(andtheFIsmall)whenthelackoffitislargeand Wechosetosampleatthelowerdensitytosaverecordingtime.There- thewithin-trialvarianceissmall. fore,asingleexperimenthasapproximately64trials(8repeatsofthe8 Figure 3 shows data from eight representative experiments stimulustypes).Sometimeslessdatawerecollectedwhenwewereunable reflectingarangeofFIs.Asdescribedbelow,thissametechnique to hold the cell or when the monkey would not cooperate with the behavior.Weperformeduptosixdifferentexperimentsoneachcell,one is used to test the goodness of fit for the Gaussian models foreachstimulusclass.Thestimuliwereallgeneratedoff-linebeforethe recovered from these same data sets. We chose to be very con- experimentsanddisplayedduringthetrialsatarefreshrateof60Hz. servative and only excluded from further analysis those experi- ments in which the observed lack of fit would have occurred at ANALYSIS least 95% of the time by chance (i.e., an FI of (cid:46)0.95), assuming Regressionandhypothesistestingwasusedextensivelytoanalyze theflatmodelwasvalid. the data. Some of these techniques are strictly valid only when Theexperimentspassingtheabovetestwerethenregressedto linearmodelsareconsidered.Becausemuchofthetimethecurve a general Gaussian function with four parameters—floor, ampli- fitsarenonlinearintheirparameters(e.g.,Gaussians),theprob- tude,mean,andwidth,accordingtothegeneralformula: abilitiescalculatedareapproximations.However,forlargeN,the various indexes used approximate actual probabilities (Snedecor y(cid:53)a(cid:49)b(cid:51)exp(cid:50)(cid:126)x(cid:50)c(cid:33)2/d2, (2) andCochran,1989). One stage of the analysis involved plotting average firing rate wherethedependentvariableyisfiringrateandtheindependent againststimulusdirectioninspiralspaceforeachexperimentand variablexisstimulusdirectioninspiralspace.Thefouradjustable then fitting the data to a Gaussian function. For many experi- parametersareasfollows:aistheflooroftheGaussianfunction, ments,theresponseprofilewasessentiallyflat,makingtheGaus- b is the amplitude, c is the mean, and d is the variance (width). sian function inappropriate for modeling the data. A screening Thischoicewasmadefortworeasons.Ascanbeseeninthefinal processwasusedtoeliminatetheexperimentsthatproducedflat frameofFigure3,whenaunitinMSTdgivesastronglyselective responseprofiles.Thisinvolvedregressingthedataineachexper- response, the profile approximates a Gaussian quite well. Sec- iment to the horizontal line (response (cid:53) constant) and then ondly, the four Gaussian parameters effectively characterize rel- testingthehypothesisthattheobserveddataweregeneratedbya evantaspectsofaneuron’sresponse,suchaspreferredtuning. cellwitharesponseprofileadequatelydescribedbythisequation. ThestatisticspackageSystatwasusedtoobtainthesefits,along This “flat model” is the appropriate model for experiments in withconfidenceintervalsforeachparameter.Meansquareerror which stimulus type has no consistent effect on cell wasusedforthelossfunction.Hypothesistestingwasperformed responsiveness. as was done for the flat model above, substituting the best fit Totesttheflatmodel’sgoodnessoffitforthedata,anANOVA Gaussian model in place of the flat model. Lack of fit was wasperformedtodeterminethetwocomponentsoftheresidual calculated by subtracting the within-trial variance from the total variance.Thewithin-stimulustypevarianceisassociatedwiththe variance, then dividing by the within-trial variance. Where this intrinsicvariabilityofthedatacollectedandisobtainedaccording quotient fell along the appropriate F distribution recovered the totheformula: probabilitythattheobservedlackoffitoccurredbychance. (cid:79) (cid:79) 1 Anindexfordifferentialresponsestrengthwasneededforthe se2(cid:53)N(cid:50)n (cid:126)yij(cid:50)yi(cid:122)(cid:33)2, (1) analysis. Directional indexes that take into account only average preferred and anti-preferred responses are lacking in that they wheres2isanunbiasedestimateofthewithintrialvariance,Nis ignore aspects of the response profile provided by intermediate e thetotalnumberoftrialsfromtheexperiment,nisthenumberof stimulus directions. Furthermore, it is desirable for an index of stimulus types, y is the firing rate of the jth repeat of the ith responsestrengthtoreflectthewithin-typeresponsevariabilityof ij stimulus type, and y is the mean firing rate for the ith stimulus the data. The smaller this variability, the greater the representa- i(cid:122) type(recallthatstimulustypereferstothemotionpatternofthe tionalpowerofaunitforaparticularstimulusattribute.Whatwas stimulus in spiral space.) This variance could be calculated be- desired, in essence, was an index of “Gaussianness” that would cause data were collected for multiple repeats (6–10) of each reflect both response amplitude and variability. To do this, the stimulus. The remainder of the variance is the “lack of fit” observeddatawerestatisticallycomparedagainstanappropriate 4720 J.Neurosci.,August1,1996,16(15):4716–4732 GeesamanandAndersen•Form/CueInvariantMSTdNeurons Figure3. RawdatademonstratingvariousFIsandGIs.Movingacrossandthendown,thedataincreasinglytakeonamoreGaussian-shapedprofile. Thevariabilityofthedataalsodecreases.NoGIappearsforthefirstdatasetbecausetheFIexceeded0.95.Thesecondframeshowsdatafroman experimentnearourthresholdcriteriaforexclusionbasedontheFI.Multipledatapointswithinaparticulargraphforthesametuningdirectionrepresent repeatedtrials.Beforecurvescouldbefit,thedatawereshiftedsothatthepreferredstimuluswascenteredat(cid:59)180(cid:56).Thisfacilitatedregressioninan analysispackagethatdidnotprovideforcircularstatistics.Therefore,itwasnotthecasethattheunitsinthesixexperimentsallhadtheirpreferredtuning directionnear180(cid:56).Afterregression,themeanparameterwasshiftedbackintheoppositedirectionbyanequivalentamount. “flat” set of data. To obtain the flat data, the average firing rate Circular, nonparametricstatistics across all trials was determined for each individual experiment, Nonparametrictestsfromcircularstatisticswereusedtosupple- and then the data were shifted for each trial so that the average mentthepreviousanalysis(foradiscussionofthesemethods,see firingratewasthesameforalleightstimulustypes(Fig.4).Inthis DrewandDoucet,1991;Fisher,1993).Circularstatisticsaddress way,thedatawere“flattened.”Thewithin-trialvarianceremains problems specific to the analysis of data, where the measured unchanged after this transformation, allowing meaningful and quantity is a function of a variable confined to a periodic input powerfulcomparisonswiththeoriginaldataset. range. Nonparametric tests have the advantage of not requiring BasedontheGaussianmodelrecoveredfromtheoriginaldata, theshapeofthetuningcurvestoconformtoaparticularmodel. the lack-of-fit statistic was calculated twice for each experiment, Therefore, analysis of the data with these methods does not once on the original data and once on the flattened data. In all require previous screening of the experiments. The preferred cases,thelackoffitoftheGaussianmodeltotheoriginaldatawas tuning of a cell was calculated as the trigonometric mean of the notsignificant.Inmostcases,thelackoffitfortheflatteneddata datafromthefollowingequations: waslarger,particularlywhentheareaunderthemodelGaussian curve was large. For each experiment, the log ratio of the two (cid:79) (cid:79) n n probabilitieswascalculated.ThisGaussianindex(GI)agreeswell C(cid:53) F cos(cid:102), S(cid:53) F sin(cid:102), (cid:102)(cid:53)arctan(cid:126)S/C(cid:33), (3) i i i i with subjective assessments of the Gaussianness of the data, as i(cid:53)1 i(cid:53)1 seen in Figure 3, and is an excellent measure of differential response strength. This figure shows experiments representing a where(cid:102)(cid:35) isthepreferredtuningofthecell(adjustedtotheproper rangeofGIsandFIs.NotethataGIisnotcalculatedforthefirst quadrant based on the signs of S and C), n is the number of experiment;inthiscase,theFIwasabovethethresholdexclusion directionsinspiralspacesampled(inthiscase8),(cid:102)isdirectionin i criteriaof0.95. spiralspaceofthestimulus,andF istheaveragefiringrateofthe i GeesamanandAndersen•Form/CueInvariantMSTdNeurons J.Neurosci.,August1,1996,16(15):4716–4732 4721 Figure4. “Flattening”ofthedata.A,Therawdatafromoneexperiment(i.e.,onestimulusclass,multiplemotiontypes).Thisgraphisidenticalinform tothosedescribedinFigure3.Thehorizontalaxisrepresentsthemotionpatternoftheinducingstimulus.Theverticalaxisreportsthemagnitudeofthe response(inspikes/sec)tothestimulus.B,Thisplotshowstheconsequenceof“flattening”thedata,asoutlinedinthetext.Thewithin-trialvariance,as wellasthemeanfiringratewithrespecttotheentiredataset,remainsconstant,buttheaveragefiringrateisnowthesameacrossallstimulusdirections. Bystatisticallycomparingthetopandbottomdatasets,weachievedameasureofdifferentialresponsestrength. neuron in response to motion type i. According to the Rayleigh where the hypothesis of a common preferred tuning underlying test,thenullhypothesis(thatthedataaredistributeduniformly; experiments l and k with trigonometric means u and u was l k i.e., each motion type drives the cell by an equal amount) is rejected if Y (cid:46) 3.84. This limit corresponds to the upper 95% rejectedifp(cid:44)0.05accordingto: pointofthechi-squaredistribution(with1df). (cid:206)S2(cid:49)C2 RESULTS R(cid:53) (cid:79) , P(cid:53)exp(cid:126)(cid:50)NR2(cid:33), (4) The basic findings of this study are reported in Figure 5. This n diagramshowspolarplottuningcurvesfromasinglecellinwhich Fi eachofthesixstimulusclassesgavetunedresponses.Thisunitis i(cid:53)1 tuned for expansion regardless of the features and cues used to whereNisthetotalnumberoftrialsrunduringtheexperiment. define the motion patterns. For the AP class, although the re- (cid:35) R(thesamplecircularvariance)isameasureofacell’sselectivity sponse to expansion was strong, selectivity for stimulus pattern (widthoftuningcurve)andisrestrictedtovaluesbetween0and was somewhat less than for the other classes; a significant re- 1withhighernumbersreflectingwidertuning.Totestwhetherthe sponse to clockwise-rotating apertures was also recorded. Note preferredtuningoftwoexperimentsisequal,wecalculate: that response amplitude and width does not possess the same (cid:83) (cid:68) (cid:89) degreeofinvarianceaspreferredtuning. (cid:79) (cid:79) n n Thisunitissomewhatunusualinrespondingstronglytoallsix C (cid:53) 1 F F cos2(cid:102), stimulus classes. An example of a cell responding to a subset of 2 i i i i(cid:53)1 i(cid:53)1 theclassesisreportedinFigure6,whichshowstuningcurvesfor (cid:83) (cid:68) (cid:89) another unit tuned to expansion. Responses to FL, AP, and NF (cid:79) (cid:79) n n stimuliwere10timesweakerthantoRD,ES,andSSwithrespect S2(cid:53) 1 Fi Fisin2(cid:102)i, toaveragefiringrate.However,exceptfortheNFclass,inwhich i(cid:53)1 i(cid:53)1 little selectivity is observed, a preference for expansion is main- tained.Thisinvariancewithrespecttostimulusclasswasgenerally (cid:104)ˆ2(cid:53)C2(cid:49)R2, (cid:100)(cid:53)(cid:126)1(cid:50)(cid:104)ˆ2(cid:33)/(cid:126)2R2(cid:33), (cid:115)2(cid:53)(cid:100)/N, 2 2 observedforalltheMSTdneuronsrecordedfrom. C (cid:53)cosu /(cid:115)2(cid:49)cosu/(cid:115)2, S (cid:53)sinu /(cid:115)2(cid:49)sinu/(cid:115)2, Response strength and experimentscreening M k k l l M k k l l (cid:206) Although data from individual neurons strongly supports form/ RM(cid:53) CM2 (cid:49)SM2, Y(cid:53)2(cid:126)1/(cid:115)l2(cid:49)1/(cid:115)k2(cid:50)RM(cid:33), (5) cueinvarianceinMSTd,itwasimportanttoquantifyandformal- 4722 J.Neurosci.,August1,1996,16(15):4716–4732 GeesamanandAndersen•Form/CueInvariantMSTdNeurons Figure 7. FI distributions by class. This is a box plot showing the FI distributionsbystimulusclass.Eachofthesixplotsshouldbeviewedasa sortofcompacthistogramwithaGaussian-shapeddistribution.Thesolid black squares indicate the distribution means. The short horizontal lines bisectingtheverticalrectanglesrepresentthemediansofthedistributions. The vertical rectangle includes 50% of all index scores. The “whiskers” attachedtobothendsoftheserectanglesextendouttoinclude80%ofthe Figure 5. Comparison of tuning curves from a single unit for the six data.Thesixstimulusclassesfallfairlyneatlyintotwodifferentgroups. stimulusclasses.Thiscomesfromoneofthefewcells(B10800)inwhich TheFL,AP,andNFclasses,withhighFIscores,areplacedina“poor the FI and GI criteria were met for all six experimental classes. The responding” group. The remaining three classes gave more vigorous locationofeachdatapointinthesepolarplotsreflectsboththemagnitude responses,asreflectedintheirlowerFIdistributions. oftheresponseandthestimulustypeusedtoelicittheresponse.Distance awayfromtheoriginindicatesresponsestrengthinspikespersecond,and the angle is a function of the stimulus motion pattern inducing this cellsfrommonkey90-2and142frommonkey89-1).Thesebroke response.Thisparticularunitistunedforexpansion.Notethesimilarityin the six curves in terms of both orientation and shape, although there is downintostimulusclassesasfollows:190RD,119ES,184SS,119 somevariationwiththeAPclass.ComparedwithFigure4,tuningspeci- FL, 119 AP, and 50 NF. Many of these experiments were elimi- ficityislesspronounced;thisunitalsorespondsfairlystronglytoclockwise natedfromfurtherconsiderationherebecauseofalackofdiffer- rotationalmotion. ential response to motion pattern type, as indicated by an FI of (cid:46)0.95, leaving 158 (83%) RD, 116 (97%) ES, 152 (83%) SS, 57 (48%)FL,36(30%)AP,and26(52%)NF.ThepercentageofES experiments passing this test is deceptively high compared with the RD and SS classes. This is because the RD and SS patterns weretheonlystimulusclassesinvestigatedin89-1,andthismon- key’s responses in MSTd were not as vigorous as those for 90-2. Although we have no good explanation for this, differences in visual acuity cannot be ruled out; neither monkey’s vision was tested. If only 90-2’s data are considered, the proportion of experimentsthatremainedafterFIscreeningfortheRDandSS classesisnearthe97%foundfortheESclass.Allowingforthis, thesixstimulusclassescanbedividedintotwogroups:a“vigorous response” group made up of the RD, ES, and SS classes and a “weak response” group made up of the remaining stimulus classes. This distinction is clear in Figure 7, which looks at the distributionofFIbyclass. Data sets from experiments with an FI of (cid:44)0.95 were fit to Gaussian curves, and the lack of fit for each experiment was calculated, as detailed above in Materials and Methods. The Figure 6. Form/cue invariance of a single neuron. As with the cell in Gaussian model’s lack of fit was not statistically significant for Figure5,thisunitisalsotunedforexpansion.ResponsestotheFL,AP, any of the data sets examined. After calculating this same and NF classes are 10 times weaker than those to the RD, SS, and ES statistic on the data sets normalized for mean response rate classes. The responses to the NF stimuli were not well tuned; little (“flattening”thedata)asoutlinedabove,theGI(ourmeasure selectivityinresponseisdemonstrated.Thisislikelyafunctionofthepoor of response strength) was calculated for each experiment. If signal-to-noise ratio associated with the low firing rates obtained from thesestimuli. this measure of response did not exceed 0.1, the experiment wasdiscardedfromfurtheranalysis.A0.1thresholdvaluewas chosenbecauseitrepresentsthepointatwhichtherawdataset ize these findings over a population of MSTd units. We also andtheflatteneddatafittheGaussianmodelobtainedthrough wanted to compare response strength across stimulus class and regression equally well. relate this index to the degree of form/cue invariance. Because Figure 8 looks at the GI distribution as a function of stimulus this analysis depends on quantifying differential response class.Thestimulusclassesinorderofincreasingresponsestrength strength,thismeasurewillbeconsideredfirst. are as follows: AP, FL, NF, ES, SS, RD. The separation of the Atotalof781experimentswasperformedonthesecells(639on stimulusclassesintotwogroupsbasedonresponsestrengththat GeesamanandAndersen•Form/CueInvariantMSTdNeurons J.Neurosci.,August1,1996,16(15):4716–4732 4723 Table2.Experimentsbystimulusclassandresponsecategory Tuned Untuned NoResponse RD 156/190 0/190 34/190 (82%) (0%) (18%) ES 107/119 12/119 0/119 (90%) (10%) (0%) SS 143/184 30/184 11/184 (78%) (16%) (6%) FL 42/119 54/119 23/119 Figure8. GIdistributionbyclass.GraphisidenticaltothatofFigure7. (35%) (45%) (20%) Thesixstimulusclassesfallfairlyneatlyintotwodifferentgroups.TheFL, AP 23/119 48/119 48/119 AP, and NF classes, with low GI scores, are placed into the “poor responding”group,whereastheremainingthreeclassesmakeupa“strong (20%) (40%) (40%) responding”category. NF 20/50 20/50 10/50 (40%) (40%) (20%) Table1.Numberofexperimentsanalyzedforeachstimulusclassat Asexplainedinthetext,tunedexperimentsarethosewithGaussianindexes(cid:46)0.1; eachroundofscreening UntunedandNoResponseexperimentshaveGIs(cid:44)0.1.WithUntunedexperiments, at least one motion type produced a significant response. The table includes the #experiments FI(cid:44)0.95 GI(cid:46)0.1 FIaverage GIaverage fractionofexperimentsineachgroup,followedbythepercentage. RD 190 158 156 0.34 1.63 ES 119 116 107 0.23 1.39 SS 184 152 143 0.37 1.33 FL 119 57 42 0.78 0.34 AP 119 36 23 0.92 0.11 NF 50 26 20 0.75 0.32 Numbersinthefirstcolumnarethetotalnumberofexperimentsforwhichdatawas collected.Experimentswereexcludedfromfurtherconsiderationattwosequential stages.Atthefirststage,onlythoseexperimentswithanFI(cid:44)0.95wereregressedto aGaussianmodelwithsubsequentcalculationofaGIforthatdata.Ifanexperi- ment’sGIwas(cid:46)0.1,itwasusedinfuturecomparisons.Therighttwocolumnsgive averagesoftheFIandGIforallexperimentsinwhichtheywerecalculated.TheGIs forFL,AP,andNFclasseswouldhavebeenevenlowerhadnotasubstantialnumber oftheseexperimentsbeeneliminatedatthepreviousround. was seen for the FI is also seen in this graph. The difference between the two stimulus groups is actually under-represented because of the disproportionate number of experiments in the Figure9. HistogrambreakingdowntheTunedcategoryofexperiments poorrespondinggroupthatwerescreenedoutbeforethisround accordingtothenumberofmotiontypesforeachexperimentproducing a significant response. Note the large number of experiments for which of analysis. If the FI screening hadn’t eliminated a substantial multiplemotiontypesproducedasignificantresponse. numberoftheFL,AP,andNFexperiments,theirdistributionof GIswouldhavebeenshifteddownward.Withinthesetwogroups, the responses were similar, although sometimes statistically dif- represented an increase in firing above background. When we ferent. Particularly interesting is the poor response of the FL reexaminedtherawdatafromtheUntunedgroup,weconfirmed stimulus compared with the SS, because the mean luminance that these experiments did not have well defined tuning curves, contrasts and form for these two stimuli are identical. An exam- butinsteadhadfundamentallyflatresponseswithsomesporadic inationofthesignificanceofthisfollowsintheDiscussion.Table activity. 1 presents a summary of the screening, showing the number of Figure 9 is a histogram that further breaks down the experi- experimentsforthesixclassespassingeachroundofelimination. mentsintheUntunedgroupaccordingtothenumberofmotion Theprecedingscreeningprocedureeliminatedallexperiments typesthatgaveresponsessignificantlydifferentfrombackground. with nearly flat tuning curves. This strategy would exclude both Thebinwiththelargestnumberofexperimentswas“8:”forthese experimentsinwhichthecelldidnotrespondtoanyofthemotion experiments, all motion pattern types for a particular class gave typesandexperimentsinwhichthecellrespondednonselectively significant responses. There were also a large number of experi- to the different motion types. To distinguish between these two ments in which only a single motion type gave a significant possibilitiesfor“flat”experiments,ttestscomparingtheresponses response.Althoughmostofthesubsequentanalysiswillfocuson toeachmotiontypewerecomparedagainstthebackgroundfiring the Tuned group of experiments, in a later section both the rateofthecell.TheBonferronimethodformultiplettestsjudged Untuned and No Response experiments will be analyzed using significanceatthep(cid:44)0.05/8(cid:53)0.00625confidencelevel.Table2 nonparametrictechniquesthatdonotrequirefittingtuningcurves shows the six experimental classes broken down into three cate- tospecificfunctions. goriesbasedonthistest.“Tuned”experimentswereexperiments with GIs (cid:46)0.1. “Untuned” experiments had GIs (cid:44)0.1, but the Preferred stimuluspattern neurons give a significant response to at least one motion type. Figure10showsthedistributionsoftheGaussianmeanparame- Overall, 57% of the experiments with GIs (cid:44)0.1 fell into the tersforeachstimulusclass.Thisparameterreflectsthepreferred Untuned group. More than 95% of these significant responses stimulus type for the unit. The length of the vector in each box 4724 J.Neurosci.,August1,1996,16(15):4716–4732 GeesamanandAndersen•Form/CueInvariantMSTdNeurons Figure 10. Distribution of preferred tuning directions (Gaussian means) by stimulus class. An over-representation of units tuned to expansion is observed.Asecond,smallerpeakforcontractionisalsoevident.Forthisanalysis,spiralspacewasdividedintoeightequallysizedpieces,asshownin eachofthesixplots.Thesediagramsareorganizedinasimilarmannertothepolarplotsinprecedingfigures.Aresponseprofilewascharacterizedas beingcenteredaround“expansion,”forexample,ifthepreferredtuningdirectionrecoveredforanexperimentwasbetween(cid:50)22.5(cid:56)(sameas337.5(cid:56))and 22.5(cid:56).Eachbox,representingoneoftheeightstimulustypes,containsavector,theorientationofwhichpointsinthedirectionofspiralspacebeing considered,andthelengthofthevectorreflectsthenumberofunitswiththistuningpreference.TheinconsistencieswithregardtotheFL,AP,andNF classesarelikelyaconsequenceofsmallsamplesizes. corresponds to the number of units with preferred tuning direc- theGaussianmeans.Fifteenunique(30total)potentialpairwise tioninthatrange.Theboxesarearrangedaspertherepresenta- comparisons were possible between the different classes for a tion of “spiral space” discussed above. As has been observed in single unit. These comparisons, along with the number of com- other studies of area MSTd, there is a predominance of cells parisonsmade,areasfollows:(RDvsES:105,RDvsSS:126,RD tunedforexpansion.Thiswastrueacrossallstimulusclasses.For vsFL:35,RDvsAP:18,RDvsNF:19,ESvsSS:93,ESvsFL: theAPclass,nounitstunedtocounterclockwise(CCW)rotation 32,ESvsAP:17,ESvsNF:19,SSvsFL:31,SSvsAP:16,SSvs or contraction were found, and for the NF class, no cells were NF:17,FLvsAP:10,FLvsNF:9,APvsNF:2).Table3shows found tuned to clockwise (CW) rotation. This is likely a conse- the percentage of cases for each comparison in which the fitted quence of insufficient sampling because of the small number of Gaussian means of the classes under consideration fell outside unitsthatgavesufficientresponsestothesestimulusclasses. eachother’s95%confidenceintervals.Table4showstheaverage Form/cue invariance across the MSTd cellpopulation differenceinpreferredtuning(takenastheabsolutevalueofthe pairwise subtraction of Gaussian means) between each of these In Figures 5 and 6, the form/cue invariance of a single MSTd neuron was documented. Based on our analysis of response stimulusclasses.Clearly,thosecomparisonsinvolvingclassesthat strength,wecannowshowthatthisisapropertyoftheMSTdcell gave poor responses tended to show larger average differences. populationasawhole. Figure 11 is a series of box plots comparing the differences in Pairwiseanalysisofaunit’spreferredtuningdirectioninspiral these fitted means for each of the 15 comparisons. In each case, space with respect to each stimulus class was performed. All six exceptforthecomparisonofAPandNF(wheretheNnumberis stimulus classes (RD, ES, SS, FL, AP, and NF) were potentially only2),thedifferenceiscenteredaroundzero.Innocasewasthe considered,althoughinmanycellstheresponsestosomeclasses differencebetweenanytwostimulusclassessignificantlydifferent werenotstrongenoughtomakeallpossiblepairsofcomparisons. from zero (two-tailed t test, p (cid:44) 0.05). More importantly, the Toquantifytuninginvariance,wemadepairwisecomparisonsof range of values bracketed by the tips of the “whiskers” in these GeesamanandAndersen•Form/CueInvariantMSTdNeurons J.Neurosci.,August1,1996,16(15):4716–4732 4725 Table3.Percentageofpreferredtuningdirectionsstatisticallydifferent shown in Figure 13. Not surprisingly, this plot looks similar to betweenstimulusclasses Figure 8, which shows the distribution of GIs by class. Both responseamplitudeandGIreflectresponsestrength.Ashasbeen RD ES SS FL AP NF seen previously, the six classes of response can be divided into RD xxx 14.3 23 34.3 16.7 36.9 strongrespondingandweakrespondingclasses. ES 14.3 xxx 14 25 29.4 42.1 Asimilaranalysiswasperformedforthevariance(width)andthe SS 23 14 xxx 25.9 37.5 47.1 floor(estimateoffiringrateinanti-preferreddirection)inFigure13. FL 34.3 25 25.9 xxx 30 0 Thedataindicatesthatthewidthoftheresponsecurvesissomewhat AP 16.7 29.4 37.5 30 xxx 0 greater, on average, for the FL, AP, and NF classes, although this NF 36.9 42.1 47.1 0 0 xxx rarelyreachedstatisticalsignificance.However,therangeoftuning widthsismuchgreaterfortheseclasses.Themagnitudeofthefloor Aparticularcomparisonisrepresentedbytheintersectionofarowandacolumn parameter was, on average, greater for the three weak responding labeledwiththeclassesbeingcompared.Numbersarethepercentageofinstancesin whichthefittedmeansoftwoexperiments’tuningcurvesfelloutsideeachother’s classes than for the strong responding classes. The difference only 95% confidence intervals obtained during regression. Only experiments in which reachedstatisticalsignificancewhentheFLclasswascomparedwith boththeGIsexceeded0.1wereusedforthiscomparison. the RD, ES, and SS classes. A subpopulation of MSTd cells re- spondedstronglytoalltypesofmotionpatterndefinedundertheFL Table4.Averagedifferenceinpreferredtuningbystimulusclass class,explainingtheelevationofthefloorparameter.Anexampleof (indegrees) suchaunitisshowninFigure14,inwhichtheresponsestotheFL andRDclassesarecompared.Thistonicelevationinresponsewas RD ES SS FL AP NF notobservedinthemajorityofcases,andinasmallnumberofcases RD xxx 10.3 15.4 25.1 30.9 27.2 the opposite effect—tonic inhibition—was observed. However, ES 10.3 xxx 10.6 20.2 21.3 25.5 enough units responded like the cell in Figure 14 to significantly SS 15.4 10.6 xxx 24.9 40 32.9 affecttheaveragevalueofthefloorfortheFLclass. FL 25.1 20.2 24.9 xxx 31.9 16.7 AP 30.9 21.3 40 31.9 xxx 35.9 Circular and nonparametricanalysis NF 27.2 25.4 32.9 16.7 35.9 xxx A potential shortcoming of the preceding analysis is that a sub- ThistableisinthesameformatasTable3.Numbersrepresenttheaverageobserved stantial number of experiments with flat tuning curves were ex- differenceinpreferredtuningdirectionbetweenstimulusclassesforindividualunits. cludedatthefirststage.Thiswasdonebecauseflattuningcurves Numbersareallpositivebecauseabsolutevaluesofthesedifferencesweretaken.If cannot be modeled after Gaussian functions. As noted above, featureinvariancedidnotoccurinMSTd,theseaverageswouldallbedistributedat (cid:59)90(cid:56).Thus,aconsiderabledegreeofinvarianceisindicated.Notethatnumbersare (cid:59)60% of experiments with flat tuning curves had responses that smallerwhencomparisonsaremadebetweenclassesthatgavestrongresponses(RD, weresignificantlyabovethebackgroundfiringrateofthecell.Itis ES,SS). desirable to include these experiments in the analysis. In this section, we reanalyze all the data using nonparametric methods, which allows all the data to be compared and doesn’t require plots account for 80% of the variation in preferred tuning asso- fittingthetuningcurvestoaparticularmodel. ciatedwithstimulusclass.Therefore,thepreferredtuningdirec- As explained in Materials and Methods, the trigonometric tions established from different stimulus classes were generally within30(cid:56)ofeachother. meansforeachexperimentwerecalculated.Forexperimentswith well tuned responses, these numbers agreed closely with the We postulated that any difference between preferred tuning estimates of preferred tuning obtained through fitting Gaussian directions was a consequence of noise in the data used to fit the functions.BasedonthenonparametricstatisticdiscussedinMa- curves.Ifthiswasthecase,experimentsinwhichtheresponsesto terials and Methods, pairwise comparisons of preferred tuning the stimuli were more robust would be expected to have smaller were made between classes for each neuron. Table 5 shows the differences between their preferred tuning directions. Figure 12 frequency with which these estimates of preferred tuning varied plotsthemagnitudeofthesetuningdifferencesagainstthesumof betweenexperimentalclasses.Thistablefollowsthesameformat theGIsofthetwoexperimentscompared.Asdiscussedabove,a as Table 3, when this same comparison was performed on the totalof30(15unique)suchcomparisonsarepossible,eachofthe screened set of data with parametric methods. Unlike Table 3, sixstimulusclassesbeinginvolvedin5comparisons.(Wearenot Table 5 includes comparisons of experiments with flat responses consideringcomparingastimulusclasswithitself,whichobviously and consequently large degrees of uncertainty surrounding the always has a difference of zero.) Note that the long axis of the estimationofpreferredtuning. “wedge”-shaped data are along the x-axis, indicating that the Previously,onlypairwisecomparisonsofpreferredtuningwere distributioniscenteredaroundzero.Thevarianceassociatedwith madeonthedata.Alsoofinteresttocompareacrossclassesisthe the difference in preferred tuning direction is large at small GI selectivity (width) of the responses. Because previously the sumsbutsmallwithhighGIs.Thisisexactlywhatisexpectedwith screening step preferentially excluded experiments with broad astochasticdistributionofthedataaroundzero,withtheGIsas selectivity, pairwise comparisons of the remaining experiments a reflection of the randomness of the data. This correlation is would be unavoidably biased. To overcome this problem, the consistent with invariance of preferred tuning direction across sample circular variance, a nonparametric index from circular differentstimulusclasses. statistics (see Materials and Methods), was calculated for each Other modelparameters experiment.Thismeasureofresponsesselectivitycanbeobtained We also examined the relative magnitudes of the other three from experiments even with poor selectivity. A perfectly tuned Gaussian parameters, i.e., amplitude (in spikes/sec), variance (in neuron—one that fired only in response to the preferred stimu- degreesofspiralspace),andfloor(inspikes/sec).Thedistribution lus—isdefinedashavingacircularvarianceof“0.”Attheother of the amplitude parameter as a function of stimulus class is extreme,acircularvarianceof“1”describesaperfectlynonselec-