Journal of Experimental Psychology: Copyright 1996 by the …ivrylab.berkeley.edu/uploads/4/1/1/5/41152143/helmuth... · 2020-02-02 · When Two Hands Are Better Than One: Reduced

Journal of Experimental Psychology:Human Perception and Performance1996, Vol. 22, No. 2, 278-293

Copyright 1996 by the American Psychological Association, Inc.0096-1523/96/$3.00

When Two Hands Are Better Than One: Reduced Timing VariabilityDuring Bimanual Movements

Laura L. Helmuth and Richard B. IvryUniversity of California, Berkeley

Within-hand variability was reduced on a repetitive tapping task when individuals tappedwith 2 hands in comparison to single-handed tapping. When the total variability wasdecomposed into central timing and peripheral implementation components (A.M. Wing &A.B. Kristofferson, 1973), the bimanual advantage was attributed to decreased centralvariability. The improved consistency does not require that the movements involve homol-ogous muscles. However, unlike phase coupling, the bimanual advantage is not found whenthe 2 movements are produced by different individuals, but rather requires that the 2movements be produced by 1 individual. It is proposed that separate timing mechanisms areassociated with each effector. During bimanual movements, the outputs from these timingmechanisms are integrated prior to movement execution, and it is this integration that resultsin the bimanual advantage.

Many actions are performed in a cyclic fashion. Thehammering of a carpenter, the hand gestures of the trafficofficer, and the casts of the fly fisher all involve the repe-tition of a simple sequence of muscular actions. In theseactions, the cyclic movements are all performed with asingle limb. In other skills, such as walking or rowing, therepetitive gestures require temporal coupling between dif-ferent effectors. In the experiments reported in this article,we examined the temporal consistency of repetitive actions,comparing the timing of movements made with one effectorwith the timing of movements performed with twoeffectors.

The motivation for this research came from findingsobtained in the study of neurological patients on simpletiming tasks. Ivry and Keele (1989) examined three groupsof patients, each with lesions associated with a distinctneural system of the central motor pathways. They foundthat patients with lesions of the cerebellum were consis-tently impaired on motor and perceptual tasks that requiredprecise timing. These results suggested that one function ofthis neural system is to operate as an internal timingmechanism.

In a second study (Ivry, Keele, & Diener, 1988), a subset

Laura L. Helmuth and Richard B. Ivry, Department of Psychol-ogy, University of California, Berkeley.

We are grateful to Steven Keele, Liz Franz, Eliot Hazeltine, andAnn Lacey for their comments. Alan Wing, J. S. Kelso, andGregor Schoener provided helpful suggestions during the reviewprocess. The study was supported by National Institutes of HealthTraining Grant 5T32 MH 15860 and by National Institutes ofHealth Grant NS30256. Informed consent was obtained from allparticipants and the data were coded to protect the anonymity ofthe participants.

Correspondence concerning this article should be addressed toLaura L. Helmuth or Richard B. Ivry, Department of Psychology,University of California, Berkeley, California 94720. Electronicmail may be sent via Internet to [email protected] orivry @ gamet.berkeley .edu.

of the cerebellar patients was tested extensively on a repet-itive tapping task (Wing & Kristofferson, 1973), a task thatis the focus of this article. A tapping trial began with thepresentation of a tone every 550 ms. The participants wereinstructed to tap a response key in time with the tones. After12 synchronizing taps (paced phase), the tones stopped andthe participants attempted to continue tapping at die targetrate (unpaced phase). Of particular interest with this task hasbeen the variability of the unpaced intervals. Wing andKristofferson presented a model that decomposes the totalvariability into two independent components. One compo-nent reflects variability in the motor implementation sys-tem; the second component is assumed to reflect variabilityin central processes, including an internal timing mecha-nism (see also Ivry & Corcos, 1993).

Ivry et al. (1988) tested seven patients with unilateralcerebellar lesions, four in which the focus was in the lateralcerebellum and three in which the focus was more medial.Output from the cerebellum is doubly crossed, such that theleft half of the cerebellum influences the left half of thebody. This neuroanatomical arrangement allowed each pa-tient to serve as his or her own control: The patients couldperform the tapping task with either the ipsilesional, im-paired hand or the contralesional, unimpaired hand. Asexpected, the patients' performance was more variablewhen tapping with the ipsilesional finger in comparison towhen tapping with the contralesional finger.

A double dissociation was observed between patientswith medial cerebellar lesions and those with lateral lesions.Although the Wing-Kristofferson model (1973) attributedthe increased variability for the medial group to the imple-mentation component, the deficit for the lateral cerebellargroup was associated with the central component. Takentogether with the findings of problems on time perceptiontasks (Ivry & Diener, 1991; Ivry & Keele, 1989), we hy-pothesized that the cerebellum functions as a central timingmechanism.

278

TIMING VARIABILITY DURING BIMANUAL MOVEMENTS 279

Upon consideration, these results suggest a paradox. Onthe basis of these neuropsychological results as well asprevious correlational findings with normal individuals(Keele, Ivry, & Pokorny, 1987; Keele, Pokomy, Corcos, &Ivry, 1985), we postulated the existence of a cerebellartiming mechanism that is accessed in a range of motor andperceptual tasks (Ivry, 1993; Keele & Ivry, 1991). However,the results from the patients with unilateral lesions suggestthat separate mechanisms regulate the timing of differentlimbs. Thus, at a minimum, it would be necessary to pro-pose the existence of at least two timing mechanisms, onefor each side of the body. One resolution to this paradox isto assume that representing temporal information is a ge-neric property of the cerebellum (e.g., Braitenberg, 1967;Desmond & Moore, 1988; Grossberg & Schmajuk, 1989).However, the exact region of the cerebellum utilized for thiscomputation might vary, reflecting task-specific and effec-tor-specific properties.

The notion of separate timing regulation of differentlimbs is of interest in the investigation of bimanual move-ments. Indeed, the focus of most bimanual research hasbeen on describing the strong temporal coupling that occursbetween limbs. Kelso, Southard, and Goodman (1979) hadparticipants simultaneously reach for two targets, one lo-cated to the left of the midline and one located to the rightof the midline. Different sizes and distances were combinedsuch that some conditions required symmetric movementsand others required asymmetric movements. Regardless ofthe condition, participants always showed strong temporalcoupling, beginning the movements of each limb and end-ing them at approximately the same points in time. Thisconstraint implied that, in asymmetric conditions, the leftand right arms moved at vastly different velocities andforces. Nonetheless, temporal coupling was also evident inthe kinematic analyses with each effector achieving peakvelocity and peak acceleration at approximately the samepoint in time (but see Marteniuk, MacKenzie, & Baba,1984).

Temporal coupling can reduce control requirements (e.g.,Kelso & Scholz, 1985). For example, different muscles maybe grouped into a single coordinative structure whose actioncan be described with a small set of parameters. Thus, inrepetitive bimanual movements, both limbs move at a com-mon frequency, and their relative motions can be describedby a single phase parameter (Haken, Kelso, & Bunz, 1985;Kelso, 1984; Turvey, Rosenblum, Kugler, & Schmidt,1986; Zanone & Kelso, 1992). Kelso and his colleagueshave demonstrated that there are basically two stable phaserelations for repetitive bimanual movements: inphase move-ments, in which each effector simultaneously follows acommon trajectory, and antiphase movements, in which thetrajectories of the effectors are offset by 180°. Althoughother phase relations can be learned (Zanone & Kelso,1992), a large body of evidence shows performance to bevastly more stable for inphase and antiphase movements.

Stability in these studies is typically assessed in terms ofthe ability of the individuals to produce different phaserelations or in the variability of the phase differences be-tween the two limbs for a given phase relation. The indi-

viduals are given a target phase difference (e.g., 0° forinphase), and the deviation from this target is measured interms of constant and variable error. This dependent vari-able is quite different from that measured in the cerebellarstudies (Ivry & Keele, 1989; Ivry et al., 1988). In theneuropsychological studies the focus was on the variabilityof the intertap intervals produced by a single hand.

There have been studies exploring how within-hand vari-ability on repetitive timing tasks is influenced during bi-manual movements. Yamanishi, Kawato, and Suzuki (1980)focused on phase coupling, and they also briefly noted thatwithin-hand variability was reduced during inphase biman-ual movements. In a case study, Wing, Keele, and Margolin(1984) tested a Parkinsonian patient, in which the symptomswere more evident on her dominant, right side. Althoughthis patient was much more variable when tapping with theright hand in unimanual tapping, the difference between thetwo hands was greatly reduced during bimanual tapping,primarily because performance with the left hand becameworse. Vorberg and Hambuch (1984) as well as Wing,Church, and Gentner (1989) have provided assessments ofdifferent sources of variability by using an assortment ofbimanual tapping conditions. In all of these studies, theanalyses focused on models that postulated the operation ofa single timing mechanism during bimanual movements(see also Turvey, Schmidt, & Rosenblum, 1989).

Given the ubiquity of temporal coupling and theoreticalemphasis on single timer models of bimanual movements,we were motivated to study the performance of cerebellarpatients on a bimanual version of the repetitive tapping task(Franz, Ivry, & Helmuth, in press). As discussed previously,patients with unilateral lesions show large differences intiming accuracy between their impaired effectors and un-impaired effectors (Ivry et al., 1988), a result we interpretedas showing selective disruption of an internal timing mech-anism on the lesioned side. What would the performance ofthese patients be during bimanual tapping? Three outcomescan be considered. First, the patients' movements may notbe coupled in a normal manner, and thus the between-handdifferences observed in unimanual tapping would be main-tained in bimanual tapping. Second, the patients' perfor-mance might be limited by the accuracy of the impairedhand. If this were so, then in the bimanual condition, thevariability for the unimpaired hand would increase, a resultsimilar to that reported by Wing et al. (1984). Third, be-cause of some sort of coupling, tapping with the unimpairedhand might lead to improved performance in the impairedhand. For example, the output from the timing mechanismfor the unimpaired hand might provide a stronger signal.

The results were quite intriguing. Timing variability ofthe impaired hand was consistently improved in the biman-ual condition in comparison to the unimanual condition. Forexample, one patient with a unilateral right cerebellar lesioncompleted 30 trials each with the left hand alone, the righthand alone, and bimanually. In a replication of Ivry et al.(1988), a large difference was found between the hands inthe unimanual condition. Based on the Wing-Kristoffersonmodel (1973), the central timing variability estimates were29 and 13 ms for the impaired and unimpaired hands,

280 HELMUTH AND IVRY

respectively. Performance with the unimpaired hand wasunchanged in the bimanual condition. Most interesting,however, the patient's performance with the impaired handwas significantly better in the bimanual condition. In thiscondition, her timing variability estimate dropped to 21 ms.The improvement in bimanual tapping is also evident in theoverall variability scores.

Taken together, the patient results suggest a number ofproperties concerning the timing of repetitive movements.The unimanual results pointed to separate timing mecha-nisms for different effectors (Ivry et ah, 1988). Our recentbimanual results, however, indicate that the processes in-volved in timing bimanual movements interact. The sourceof this interaction remains unclear. It may be that underbimanual conditions, the timing mechanisms themselvesinteract. Alternatively, the output from these mechanismsmay be constrained (i.e., coupled).

To explore these issues, we assessed performance onunimanual and bimanual tapping tasks in normal individu-als. There have been previous studies comparing left-handand right-hand performance, but this research has beendirected toward questions of hemispheric specialization(Sergent, Hellige, & Cherry, 1993; Truman & Hammond,1990; Wolff, Hurwitz, & Moss, 1977). In the current ex-periments, we were interested in comparing within-handvariability under unimanual and bimanual conditions. Spe-cifically, is within-hand variability reduced in normal indi-viduals when they are simultaneously tapping with the otherhand? If so, understanding this phenomenon should provideuseful information regarding the nature and interactions ofinternal timing mechanisms.

Experiment 1

Experiment 1 is a variation of the standard repetitivetapping task designed by Wing and Kristofferson (1973).Participants in this task are asked to repetitively tap at afixed interval, first in time to a synchronizing signal andthen in a self-paced continuation phase. In the current study,participants performed this task under three conditions: lefthand only, right hand only, and both hands. In the bimanualcondition, the two hands tapped biphase.

Method

Participants. Thirty undergraduate students at the Universityof California, Berkeley participated in this experiment in partialfulfillment of psychology course requirements. All of the partici-pants were right handed as assessed by self report.

Apparatus. A desktop computer was used to control stimuliand collect responses. A response board (20 cm X 30 cm) with twopiano-type keys (2 cm X 10 cm), one on the right and one on theleft, was used to collect the data. Minimal force was required todepress the response board keys (e.g., passive weight of 25 gwould activate the microswitch). Responses were recorded asdigital interrupts with temporal resolution of 1 ms.

Procedure. Participants were seated in front of a computerterminal in a quiet room. They were told to place their hands on theboard in a comfortable position and to move only the index finger

of the appropriate hand(s). In the single-hand condition, the par-ticipants rested the inactive hand at the side of the response board.

Participants initiated each trial by typing the "ENTER" key on astandard keyboard. Following a 1-s pause, the computer generateda series of 50-ms tones, separated by 400 ms. Participants begantapping once they were ready to synchronize their responses withthe tones. After 12 paced intervals, the tones were discontinued.The participants continued tapping in an unpaced phase, attempt-ing to maintain the target interval. After 32 unpaced responses, theend of the trial was signaled by a loud, long tone.

After each trial, the computer screen presented the participantwith feedback. The mean interval duration, in ms, was presented aswell as the standard deviation. The target rate of 400 ms was alsoprinted on the screen so that participants could compare their meaninterval duration with the target duration. In the both hands con-dition, data for the left and right hands were presented. Participantswere encouraged to use the feedback to help them improve theirperformance. The experimenter emphasized that consistency, asmeasured by the standard deviation, was an important measure oftheir performance.

Design. Trials were grouped into blocks of eight. There werethree blocks of each of three conditions: right hand only, left handonly, and both hands at once. Each time the participant encoun-tered a condition for the first time, two practice trials preceded theblock of eight test trials. Practice trials were not analyzed.

To counterbalance the order of presentation of the three condi-tions, there were six possible sequences of blocks. For example,Participant 1 completed a block of right hand only (r), then left (1),then both (b); 1, b, r, b, 1, r. Participants were randomly assignedto one of the six sequences. The experiment lasted approximately50 min.

Data analysis. The primary data for analysis were the final 30intervals produced during the unpaced phase of each trial. Themean and standard deviation for each trial was computed. Inaddition, a transformed measure of variability was obtained bycalculating the standard deviation from a trend line fitted throughthe 30 data points for each trial. The transformation has been usedin previous studies of repetitive tapping (Ivry et al., 1988; Keele etal., 1985) and removes any global changes in tapping rate that mayhave occurred during the trial.1 The mean and transformed stan-dard deviation scores were averaged over each block of eight trials.Trials in which a participant tapped an interval of less than 200 msor more than 600 ms were excluded from analysis and repeated atthe end of a block. Such trials generally were the result of partic-ipants failing to activate the microswitch.

We further analyzed the standard deviation scores using theWing-Kristofferson model (1973). As stated previously, thismodel decomposes the total variability into two components: vari-ability associated with response implementation (motor delay) andvariability associated with central processes. Wing and Kristoffer-son proposed that a central timing mechanism determines when thetarget interval has elapsed. At this point, a command to tap isissued. However, the actual tap occurs only after delays introducedby peripheral implementation processes. A central assumption oftheir model is that the central command processes and implemen-tation processes are independent. Moreover, the activation of eachprocess occurs in an open-loop mode (feedback free). Specifically,the timing on Interval j + 1 begins as soon as the timing mecha-nism issues the command signaling the end of Interval j, indepen-

1 The transformation facilitates the covariance analysis requiredfor the Wing-Kristofferson (1973) decomposition of total variabil-ity. However, calculations based on the raw data are very similarto those obtained from the transformed data.


dent of any variability in the implementation of preceding move-ment commands.

Formally, the duration Interval j can be expressed as

I = C + (1)

in which I, C, and MD represent the durations of the interval,clock, and motor delays, respectively. Given the assumption ofindependence, the variances associated with each component areadditive:

a-,2 = <rc2 + 2crM (2)

The open-loop assumption allows an estimate of the peripheralvariability to be given by

2 = -autocovar,(l), (3)

where autocovar(l) is the covariance between Intervals j and j +1 (Lag 1). Because the total variability is obtained from the rawdata, an estimate of the clock variance can be obtained fromEquation 1 by using subtraction.

Wing and Kristofferson (1973) referred to all of the variance notassociated with response implementation as clock variance. In thisarticle, we refer to this source as central variance. This moreinclusive term acknowledges that there are other processes in-volved in motor planning in addition to a timing mechanism andthat these may be expected to affect performance on this task (seeIvry & Corcos, 1993, for further discussion of this issue andjustification of the model's assumptions).

Results and Discussion

Performance was quite stable on this task and there wasno difference on any of the measures across blocks. There-fore, in the following analyses, the data were combinedacross the three blocks. A subset of trials was repeated(14%) because there was an excessively short interval(<200 ms) or long interval (>600 ms) within the run. Foralmost all of these trials, the problem was that on oneresponse the participant failed to produce sufficient force toactivate the microswitch. This problem was especially evi-dent for three of the participants who failed to produce atleast 20 trials without an aberrant interval.

Participants generally were accurate in maintaining thetarget pace. In the unimanual conditions, the mean intertapinterval was 392 ms for the right hand. For the left hand, thecomparable figure was 389 ms. During bimanual tapping,the movements of the two hands were tightly coupled, andthe mean interval for each hand was 391 ms. The meanphase difference, averaged for all participants, was —0.7 ms(SD = 4.95 ms), with the negative value indicating aminuscule lead time for the left hand. Because there is nota priori reason to expect one hand to consistently lead theother, individual phase differences are more meaningful.The largest mean phase difference for an individual was12.1 ms. Ignoring the sign of the mean phase differences,the median value for the 27 participants was 3.9 ms. Thiscorresponds to a phase difference of 3.5° when converted topolar coordinates.

Our focus in this experiment is on the variability of theintertap intervals. Participants were more consistent whentapping with their dominant, right hand, F(l, 26) = 8.20,

p < .01. The mean variability for the right hand was 20.1ms, and for the left hand it was 21.3 ms. Although Wolff etal. (1977) found no asymmetry on a similar task, the currentresults are in accord with more recent reports of lowervariability when individuals tap with their dominant hand(Sergent et al., 1993; Truman & Hammond, 1990). Wereturn to this point when we discuss the Wing-Kristofferson(1973) decomposition of the total standard deviation.

The critical finding of Experiment 1 is that total variabil-ity was significantly lower in bimanual tapping in compar-ison to unimanual tapping. That is, within-hand perfor-mance was more consistent when the participants weresimultaneously tapping with their other hand. This bimanualadvantage was present for both the right and left hands.Variability dropped from 21.6 ms unimanually to 18.7 msbimanually for the right hand, and from 22.3 ms unimanu-ally to 20.3 ms bimanually for the left hand. The interactionwas not significant.

We used the Wing-Kristofferson (1973) model to deter-mine whether the reduction in total variability could beattributed to a change in either the central or peripheralcomponents, or both. Before presenting these data, it isnecessary to verify that the predictions of the model hold inboth the unimanual and bimanual conditions. Figure 1 pre-sents the covariance functions for Lags 0-5. Note that thesquare root of the autocovariance at Lag 0, autocovart(0)gives the total variability score for each condition. The mostbasic prediction of the Wing-Kristofferson model was sup-ported in that the autocovariance between successive inter-vals was negative. Indeed, the Lag 1 covariance was nega-tive in 107 of the 108 conditions (27 participants X 4Conditions each).

However, although there was no consistent correlation atLag 2, the covariance function at Lags 1-5 tended to alter-nate between negative and positive values for all four con-ditions. For example, the Lag 3 covariance was smaller thanthe Lag 2 covariance for 81 of the 108 conditions. Signifi-cant nonzero correlations at lags greater than 1 indicateviolations of the basic Wing-Kristofferson model (1973).Wing (1977) discussed possible mechanisms that mightyield such covariance functions. In particular, the covari-ance function is expected to have a sawtooth pattern if eithersuccessive timing signals are negatively correlated, or suc-cessive implementation delays are negatively correlated.Wing (1977; see also Wing, 1979) has shown how estimatesof variability in the timing and implementation componentscan be obtained given these possible dependencies. Thus,we chose to calculate the two components using both thebasic Wing-Kristofferson model and the two models assum-ing negative dependencies.2 It should be noted that, unlikethe sawtooth pattern observed in the present experiment,Wing (1977) reported a covariance function suggesting a

2 We used the method described by Wing (1977) to test the twoalternative models in which either successive timing or implemen-tation signals are assumed to be negatively correlated. For eachmodel, we minimized a least-squares goodness-of-fit measure byiteratively adjusting one free parameter corresponding to the mag-nitude of the correlation between successive samples.

282 HELMUTH AND FVRY

600

Figure 1. Covariance functions for Experiment 1. A: Covari-ance functions for the right hand, tapping alone and bimanually. B:The values for left-handed tapping.

positive correlation between successive motor delays (butsee Wing et al., 1989). Although the reasons underlying thisdifference are unclear, it may reflect the fact that Wing(1977) provided individuals with a feedback signal duringthe unpaced portion of each trial.

The mean estimates of the central and implementationcomponents are shown in Figure 2. Analysis with the basicWing-Kristofferson model (1973) reveals a striking disso-ciation. The estimate of central variability is lower duringbimanual tapping in comparison to unimanual tapping, F(l,26) = 49.87, p < .0001. There was no difference in themotor delay estimates between the unimanual and bimanualconditions, F(l, 26) < 1.0. Thus, the component analysisindicates that the bimanual advantage reflects a reduction incentral variability for each hand when the two hands tapsimultaneously.

The analysis of the hand effect was more problematic.The estimate of implementation variability was lower for

the right hand in comparison to the left hand, F(l, 26) =10.94, p < .01. This result suggests that the advantage intapping with the dominant hand is because of reduced noisein the peripheral implementation system. This finding wasreported by Sergent et al. (1993) in a study investigatinginteractions of verbal processing and tapping. However, inthe current study, the basic model showed that the estimateof central variability was significantly lower for the lefthand in comparison to the right hand, F(l, 26) = 6.10, p <.05. Although this result was not found in the Sergent et al.study, the trend is in the same direction—clock variabili-ty—was lower for the left hand in comparison to the righthand (see Figure 1 of Sergent et al., 1993).

A less ambiguous pattern of results emerged when wemade the central and peripheral estimates using the alterna-tive models that account for the observed sawtooth covari-ance functions. First, we estimated the components underthe assumption that successive clock signals were nega-tively correlated. This phenomenon might be expected toemerge if the timing mechanism operated as an oscillator or

Right Left

B 14

Right Left

Figure 2. Components of total variability for Experiment 1. A:central variability, B: implementation variability.


limit cycle (Schoener, 1994). A double dissociation wasobserved with this model. The bimanual advantage wasagain attributed to a reduction in central variability, F(l,26) = 25.74, p < .0001, with estimates of 15.4 ms and 12.1ms for the unimanual and bimanual conditions, respectively.The less consistent performance with the left hand wassolely attributed to the implementation component, F(l,26) = 5.06, p < .05. The central variability estimate did notdiffer between the two hands, F(l, 26) < 1.0. This samepattern of results was obtained when the data were fit usingthe alternative model that assumed a negative correlationbetween successive motor delays. Again, the lower variabil-ity during bimanual tapping was associated with the centralvariability estimate, F(l, 26) = 45.71, p < .0001 (uni-manual = 13.5 ms; bimanual = 10.7 ms), and the handeffect was linked to the peripheral variability estimate, F(l,26) = 6.94, p < .05. For both alternative models, theinteraction terms were not significant.3

The current experiment provides a direct comparison ofwithin-hand timing variability during unimanual and biman-ual tapping. In previous studies, covariance analyses havebeen applied to bimanual data to examine whether the twoeffectors share common sources of variability. Vorberg andHambuch (1984) assumed that a single timing mechanismwas involved during bimanual tapping. Given this assump-tion, an estimate of the implementation variance can beobtained by calculating the asynchronies in the left and rightkey presses. In brief, these asynchronies are assumed toreflect effector-specific variability because the commandsto each effector are issued at a common point in time. Thus,the variability of the timer is estimated by the covariance ofthe intervals produced by each hand. By this procedure, theestimate of central variability averaged for all 27 partici-pants was 12.15 ms (SD = 3.83 ms). By definition, thisvalue is identical for both hands. Although this methodcannot be used to provide a comparison with unimanualtapping, the bimanual estimate is close to that obtained withthe models provided by Wing (1977; Wing & Kristofferson,1973).

Starting with a similar assumption of a single timer, Wing(1982) provided a further method for decomposing imple-mentation variability into two hypothetical sources. Onesource is effector specific; the other is assumed to reflect animplementation process that is shared by both effectors.Wing (1982) found the shared source of variability to benegligible. In contrast, the estimate of this component wasconsistently greater than zero in the present study. For allparticipants, the estimate of the effector-independent imple-mentation variability was 3.45 ms (SD = 6.17 ms). Thelarge standard deviation is primarily due to a single partic-ipant with a large negative estimate. Of the 27 participants,23 had a positive value (sign test, p < .05). There aresubstantial methodological differences between the currentstudy and that of Wing (1982). For example, in Wing(1982), successive key presses by each hand were made ondifferent keys.

In summary, the results of Experiment 1 show that forparticipants performing a task of motor timing ability, twohands are better than one. Timing variability within each

hand is reduced during bimanual repetitive tapping in com-parison to unimanual tapping. Moreover, based on theWing-Kristofferson model (1973; also Wing, 1977), thesource of the improvement in the bimanual condition isentirely attributed to a reduction in variability associatedwith central processes. This result is similar to mat obtainedin our research with cerebellar patients (Franz et al., inpress). These patients show an asymmetry in performanceunder unimanual conditions because of the unilateral pa-thology. However, this asymmetry is reduced during biman-ual tapping, and this reduction was also attributed to thecentral component.

Contrary to models which assume the operation of asingle timing mechanism during bimanual movements(Vorberg & Hambuch, 1984; Wing, 1982), we hypothesizedthat the reduced central variability may reflect an interactionbetween separate timers associated with each hand. Anelaboration of this model is presented in the General Dis-cussion. However, there are other processes that contributeto the estimate of central variability (Ivry & Corcos, 1993;Ivry & Hazeltine, 1995). In the following two experiments,we test hypotheses that attribute the bimanual improvementto factors other than interactions between central timingmechanisms.

Experiment 2

The first experiment demonstrated that within-hand vari-ability was reduced when participants were asked to pro-duce simultaneous movements with both hands. The biman-ual movements involved homologous muscles: Themovements were all produced by flexion and extension ofthe index fingers of each hand. An important question iswhether the bimanual advantage requires that the move-ments be homologous. To answer this, the two movementsin Experiment 2 were produced by nonhomologous actions.For one limb, the movement was again flexion and exten-sion of the index finger; for the other limb, the movementnow involved forearm flexion and extension. If the biman-ual advantage were obtained with nonhomologous move-ments, then it would suggest that the underlying mechanism

3 It could be argued that one model might be appropriate forcertain participants and a different model for other participants. Toallow for individual differences, we also used a procedure in whichthe variability estimates from the best fitting model for eachparticipant was used. For this analysis, the correlation parametercould be either negative or positive. Because these alternativemodels contain an extra parameter, they are guaranteed to provideat least as good a fit as the basic two-parameter model, and in mostcases, a better fit. To offset this, we replaced the variabilityestimates from the basic model only if the least-squares measurewas reduced by 70% with an alternative model. For the 108 fits (27participants X 4 Conditions), 23 of the scores were revised ac-cording to this arbitrary criterion. For the most part, the revisedscores were similar to the original scores. When an analysis ofvariance was run with the new estimates substituted in those placeswhere a substantial change was found, the lowering of the centralvariability estimate under bimanual tapping was still obtained, F(l,26) = 33.72, p < .0001.


may arise at a level that is independent of particular com-binations of response implementation systems.

The use of nonhomologous movements can also providea test of an attentional account of the bimanual advantage.Suppose that in the planning of a movement, people repre-sent an abstract goal they hope to achieve, for example, todrink from a mug or type a word. At some level of process-ing, this goal must be translated into a specific movementplan. One hand must be selected to pick up the mug; a fingermust be specified to strike the keyboard. It is possible thatinitially, multiple actions are generated, each of which couldachieve this goal. However, over time, one of these potentialactions is selected. People rarely find themselves simulta-neously reaching for a mug with both hands or pecking akey with more than one finger.

This scenario suggests that in producing unimanualmovements, there may be a need to inhibit alternative ac-tions. With bimanual movements, this requirement wouldbe reduced. Applied to our tapping task, it may be that thebimanual advantage is the result of reduced selection de-mands in comparison to unimanual tapping. In the lattercondition, the selection of one finger may require an inhi-bition of activation of the homologous finger on the otherhand. In bimanual tapping, this selection process would beeliminated.

Although the selection hypothesis may appear counterin-tuitive, it merits exploration for a number of reasons. First,consider some neurological evidence. Patients who havesuffered a unilateral stroke resulting in hemiparesis fre-quently show mirror, or associated movements. When thesepatients attempt to perform a task with their affected limb,homologous muscles are sometimes activated on the unim-paired side. Curiously, the patients report that they are notconsciously attempting to move the ipsilesional limb andare generally surprised to observe this phenomenon (e.g.,Zulch & Muller, 1969). Second, neuroimaging studies withhealthy adults suggest bilateral activation during unilateralmovements. Using positron emission tomography Roland,Meyer, Shibusaki, Yamamoto, and Thompson (1982) foundbilateral activation of many cortical and subcortical areaswhen individuals performed a series of ballistic movementsunilaterally. In particular, supplementary and premotor ar-eas showed bilateral metabolic increases compared withresting rate, whereas the primary motor hand area showedcontralateral activation. They suggest that a motor programis initially elaborated bilaterally, and only at final corticalprocessing stages does the activation become asymmetric.Similarly, Kim et al. (1993) observed bilateral activationduring die production of unilateral finger movement se-quences. The activation was not symmetric, with only theleft hemisphere showing comparable activation for bothleft-hand and right-hand sequences.

Bilateral activation rarely has obvious behavioral conse-quences. However, homologous errors have been observedin typing (Lessenberry, 1928, cited in Rumelhart & Nor-man, 1982). These errors occur when the person intends totype a key with a particular finger and movement butinstead executes the mirror symmetric action with the otherhand.

These examples demonstrate not only that there is bilat-eral activation in preparing movements, but also that there isa special status for the activation of homologous muscles.According to the selection hypothesis, the bimanual advan-tage may thus result from the fact that processing demandsare reduced during bimanual tapping because there is noneed to inhibit homologous muscles of the inactive hand. Ifthis were so, then the bimanual advantage should be lostwhen the movements involve nonhomologous movements.This follows because with nonhomologous movements, theselection process would have to operate twice. For example,consider an individual who is using the right index fingerand the left forearm. In this case, the selection processwould have to inhibit activation of the left index finger andinhibit activation of the right forearm. Thus, in comparisonto unimanual movements, the demands on this processwould be increased. Not only should the bimanual advan-tage disappear, but we might expect to see an increase invariability during bimanual tapping.

Method

Participants. Twenty-eight participants from the University ofCalifornia, Berkeley psychology subject pool participated in thisexperiment.

Procedure and design. The standard repetitive tapping taskwas modified slightly for Experiment 2. For one limb, participantstapped as in the preceding experiments by simple flexion-extension of the extended index finger. For the other limb, partic-ipants tapped by moving their forearm at the elbow. The hand inthis condition was clenched into a fist, and the wrist was kept inline with the forearm. The elbow rested on the table in front of theresponse board, and a response was made by lowering the entireforearm, bringing the ulnar side of the fist into contact with thekey. The experimenter demonstrated the technique to the partici-pants and observed their practice blocks to ensure correct perfor-mance. Participants were randomly assigned to perform the taskwith either the right finger and left forearm or the left finger andright forearm.

Participants completed three conditions: two involving uni-manual tapping (finger only or forearm only) and one involvingbimanual tapping (finger and forearm). All trials consisted of 12paced responses and 32 unpaced responses. Trials were groupedinto blocks of seven, and three blocks of each condition werepresented. The order in which the blocks occurred was counter-balanced across participants.


The data from 1 participant were excluded from the finalanalysis because of high variability. For the remaining 27participants, 285 trials (13%) were repeated because of anextremely short or long response. The estimates of centraland implementation variability were obtained by averagingover the 21 trials per condition to obtain the most stablemeasure of performance.

The interresponse intervals did not differ among condi-tions, averaging 396 ms for unimanual conditions and 393ms for bimanual conditions. For both finger and forearmtapping, the mean interval was 395 ms.


Unlike in the previous experiment, there was no signifi-cant reduction in total variability during bimanual tapping,F(l, 26) = 1.59, p > .05. However, there was a significantinteraction of this factor and the effector used, F(l, 26) =7.03, p < .05. When tapping with the finger, total variabilitywas 21.3 ms under unimanual conditions in comparison to19.1 ms under bimanual conditions. In contrast, when par-ticipants tapped with the fist, total variability was slightlyhigher under bimanual conditions (unimanual: 19.2 ms;bimanual: 20.3 ms).

We used the Wing-Kristofferson model (1973) to exam-ine the sources of the changes in total variance. The covari-ance functions for the four conditions (unimanual fist tap-ping, unimanual finger, bimanual fist, and bimanual fingertapping) are shown in Figure 3. Of 108 Lag 1 estimates (27participants for each of 4 conditions), 107 were found to benegative. As in Experiment 1, there was a consistent saw-

500

400

300

200

100

-100

1 -»- Unimanual

j\ -•- Bimanual

V ̂0 1 2 3 4 5

Lag

B 500

-200

Lag

Figure 3. Covariance functions for Experiment 2. A: Covari-ance functions for finger tapping alone and bimanually. B: Co-variance functions for the forearm tapping.

tooth pattern across Lags 1-5. Thus, the data were againevaluated with both the basic Wing-Kristofferson model(1973) and the two alternative models that predict thispattern of responses. However, the alternative models led tono changes in the basic conclusions and are not consideredfurther.

The estimates of central timing and implementation vari-ability derived from the Wing-Kristofferson model (1973)are presented in Figure 4. As in Experiments 1 and 2, theestimate of central timing variance drops significantly whenparticipants tap during bimanual conditions, F(l, 26) =20.28, p < .0001. This effect is apparent for both limbs: Thereduction is 4.4 ms and 3.2 ms for the finger and forearm,respectively, when comparing unimanual and bimanualtapping.

There was a main effect of limb, F(l, 26) = 7.2, p < .05,for the estimate of central variability. This estimate waslower when participants tapped with their forearm in com-parison to the finger. This result was unexpected, and is, tosome extent, at odds with previous results reported by Wing(1977). Using only unimanual conditions, Wing found thattotal variability was greater for finger movements in com-parison to forearm movements. This trend is also evident inthe current experiment (SDs of 21.3 ms vs. 19.2 ms for thefinger and forearm, respectively). However, Wing (1977)attributed this difference to lower implementation variabil-ity for the forearm, whereas we fund the difference to be inthe estimate of central variability. In addition to this dis-crepancy in the component estimates, the covariance func-tions were quite different. Whereas Wing (1977) found asignificant negative covariance at Lag 2, the covariancefunctions in Experiments 1 and 2 in the current study weresawtooth in shape with a positive Lag 2 covariance. Aspreviously noted, an important methodological difference isthat Wing (1977) provided a feedback tone after eachresponse.

The estimate of implementation variability was found toincrease during bimanual tapping, F(l, 26) = 4.92, p < .05.Whereas Figure 4 indicates that this increase is predominantfor the forearm, the Limb X Mode interaction was onlymarginally significant, F(l, 26) = 3.74, p < .07. Theincrease in implementation estimate may be related to aphenomenon reported by Turvey et al. (1989). In that study,participants rotated their arms while holding pendula ofdifferent masses. As the difference between the masses heldby the two arms became greater, the Lag 1 covariancebecame more negative (e.g., larger estimate of implemen-tation variability). Combining two effectors of differentmasses, the finger and the forearm, might produce an anal-ogous effect. It may be that when the two limbs require verydifferent forces, peripheral variability increases because ofcross talk between the effector systems.

In summary, two important conclusions can be drawnfrom the results of Experiment 2. First, the bimanual ad-vantage is not dependent on homologous movements. Theeffect generalizes to situations in which the movementsinvolve nonhomologous effector combinations. Second, theresults do not support the attention hypothesis. This hypoth-esis predicted that the bimanual advantage would be re-

286 HELMUTH AND FVRY

Finger Forearm

B

Finger Forearm

Figure 4. Components of total variability for finger and forearmtapping. A: central variability, B: implementation variability.

versed, or at least eliminated, if participants tapped withnonhomologous muscles. This prediction was based on theassumption that this form of bimanual tapping would in-crease attentional demands because a selection processwould have to operate twice (i.e., for each limb). However,the data show that the bimanual advantage persists evenwhen the movements are made with different groups ofmuscles. A comparison of Figures 2 and 4 suggests that thereduction in the central variability estimate appears to be aslarge in this experiment as in the Experiment 1. No formalstatistical comparisons, however, were made because ofvarious methodological differences.

Experiment 3

As noted in the introduction, previous research on biman-ual movements has emphasized constraints on phase rela-

tions that can be adopted by the two effectors. New insightsinto the level at which these constraints are imposed areprovided by the findings of Schmidt, Carello, and Turvey(1990). These researchers examined whether similar con-straints would emerge in multieffector movements producedby two people. Specifically, 2 participants were seated nextto each other and asked to swing one leg in synchrony witha metronome signal. On some trials, the participants wererequired to produce inphase movements by coordinatingflexion and extension cycles with their partner's move-ments. On other trials, the participants attempted to producetheir movements in an antiphase mode: When 1 participantwas extending his or her leg, the other was to flex his or herleg. These two modes were tested at different frequenciesranging from 0.6 Hz to 2 Hz.

The striking result from this study was that many of thedynamical phenomena found in multieffector movementsproduced by a single participant also were evident when thetwo limbs were moved by two different participants. Forexample, the relative phase of the two limbs was maintainedmore accurately and consistently in the inphase mode incomparison to the antiphase mode. Moreover, this differ-ence became amplified at higher frequencies with partici-pants showing a tendency for phase shifts from antiphase toinphase mode at the highest frequencies tested. Schmidt etal. (1990) argued that the dynamical system producing thecoupling phenomena need not require any sort of materiallinkage, but rather could be the result of an informationallinkage. In particular, they emphasized that the linkage mustresult from the visual information afforded each individualconcerning his or her own movements and those of thepartner. No interindividual coupling was observed when theindividuals were prevented from viewing the moving limbs.

The provocative results of Schmidt et al. (1990) led us toask whether the bimanual advantage described in the currentExperiments 1 and 2 would also be found when the move-ments were produced by two individuals. Specifically,would the within-hand variability (associated with themovements of a single individual) be reduced when thosemovements were coordinated with those produced by an-other individual? If this were so, it would suggest that thewithin-hand bimanual advantage reflects processes similarto those that constrain between-hand phase relations.

Another motivation for the current Experiment 3 is that itprovides a test of one source of feedback that might con-tribute to the bimanual advantage. In particular, duringbimanual tapping, visual and auditory feedback may helpparticipants maintain the consistency of the movements ofeach limb. For example, if one limb were to produce anaberrant cycle, feedback from the other limb might help theparticipant reinstate the proper frequency. In unimanualtapping, no such information would be available (other thana participant's internal model of the interval). Note that theopen-loop assumption of the Wing-Kristofferson model(1973) is based on how a single limb might be affected byfeedback from its own action. It remains possible that feed-back from a different limb might be important. Experiment


3 provides an assessment of whether visual or auditoryfeedback from a different limb (individual) contributes tothe bimanual advantage.4

Method

Participants. Forty-four participants from the University ofCalifornia, Berkeley psychology subject pool participated in thisexperiment.

Procedure and design. Participants were tested in pairs inExperiment 3. At the beginning of the session, the participantswere seated side by side in front of the computer. A keyboard wasplaced in front of each participant, and the two keyboards wereadjacent to one another. Each participant tapped with only the rightindex finger. There were three conditions. Two conditions in-volved unimanual tapping. For one condition, the participant onthe right tapped alone. For the second unimanual condition, theparticipant on the left tapped alone. The participant who was nottapping simply rested.

The third type of trial was the bimanual condition. Here, the twoparticipants were asked to tap in synchrony. Each participanttapped with the right index ringer as in the unimanual condition.The participants were instructed to watch the movements of theirown and their partner's fingers. In addition, the sounds from bothkeyboards were clearly audible to both participants.

All other aspects of the design were as in Experiments 1 and 2.Each trial consisted of 12 paced responses and 32 unpaced re-sponses. The initiation of the paced responses began with the firstkey press detected from either participant. On almost all trials, theother participant began tapping within one response. A block oftrials was composed of seven error-free trials, and each conditionwas repeated for three blocks. The order in which the blocksoccurred was counterbalanced across participants. Thus, within apair, there were instances in which both participants performed ablock of unimanual tapping prior to the bimanual blocks. In otherinstances, one or both participants performed in the bimanualcondition prior to the first unimanual block.


Eleven percent of the 1,539 trials were repeated becauseintervals were either shorter than 200 ms or longer than 600ms. Most of these trials occurred during the bimanual con-dition, perhaps resulting from interference that arose be-tween the 2 participants as they attempted to coordinatetheir responses. As before, the central and implementationestimates were made after combining the analyses over the21 trials per condition.

The mean interresponse intervals for the unimanual con-ditions were 391 ms and 384 ms for the participants on theright and participants on the left, respectively. The compa-rable values for bimanual tapping were 389 ms and 385 ms.Note that unlike in the single-person Experiments 1 and 2,the mean intervals were not identical for the two-personexperiment during bimanual tapping. Nonetheless, themovements in the bimanual condition were coupled. Thephase differences between the two fingers were not uni-formly distributed but rather tended to cluster around asmall range. For some pairs of participants, this range wasnear 0 ms (e.g., tapping in synchrony); for others there was

a consistent phase difference between the participants. Thisconsistent phase difference might reflect the use of differentforces by the participants to depress the response key.

The critical comparison in this experiment is whethereach participant's within-hand variability is reduced whenparticipants tapped with a partner in comparison to whenthey tapped alone. The results show that this is not the case.Neither the total variability nor the central estimate, ascalculated by the Wing-Kristofferson model (1973), de-creased when 2 participants tapped together. In fact, forboth of these measures, variability increased during thebimanual condition. During unimanual tapping, the meanstandard deviation of the interresponse intervals was 21.6ms. In the bimanual condition, this value rose to 24.4 ms,F(l, 21) = 38.15, p < .001. Unexpectedly, there was amarginally significant effect of person, with the participantsseated on the right being more consistent, F(l, 21) = 4.02,p < .10.

The covariance functions were in accord with the predic-tions of the Wing-Kristofferson model (1973). The Lag 1covariance was negative for all but 4 of the 88 data points(44 Participants X 2 Conditions each). Moreover, the co-variance functions for all lags greater than 1 were notsignificantly different from 0.

The estimates of central and peripheral variability areshown in Figure 5. As with the total variability, the estimateof central variability during bimanual tapping increased to16.5 ms from 14.6 ms, F(l, 21) = 6.48, p < .05. For thiscomponent, the values were comparable for the groupsseated on the right and left. For the implementation esti-mate, there was no significant difference between the uni-manual and bimanual conditions. However, the interactionwas significant, F(l, 21) = 7.43, p < .05. As shown inFigure 5, the implementation estimate rose for the person onthe left during bimanual tapping. No change was found forthe person on the right. It is possible that the higher imple-mentation estimates for the person on the left occurredbecause these participants had to adopt a less natural postureto watch the two hands.

The results from this experiment clearly indicate that thebimanual advantage does not emerge when the two effectorsare controlled by different individuals. In other words, the

4 We have also explored whether the bimanual advantage mightresult from enhanced auditory feedback available during bimanualtapping. In brief, we hypothesized that each hand might provide apacing signal for the other hand. If this source of information isimportant, we reasoned that participants should benefit from hav-ing a perfect auditory pacing signal. To test this idea, we comparedunimanual and bimanual tapping when the pacing signal wasmaintained for the entire trial. Because this manipulation providesa perfect auditory model in both conditions, the bimanual advan-tage would disappear if auditory feedback was important. Contraryto this prediction, the bimanual advantage was as large duringpaced tapping as unpaced tapping (2.3 ms and 1.7 ms, respective-ly). In addition, participants were actually more variable duringpaced tapping (21.0 ms) in comparison to unpaced tapping (19.6ms). These results provide further evidence that timing on this taskis not improved by external feedback.


24

20

16

12-

8 -

4 -

B

• Tapping AloneD Tapping Together

Personon right

Personon left

Personon right

Personon left

Figure 5. Components of total variability for Experiment 3. A:central variability, B: implementation variability. Participantsseated on the left and right performed the tapping task either aloneor with their partner.

improvement during bimanual tapping requires that a singleindividual produce both movements. This finding suggeststhat different mechanisms may underlie the dynamics ofphase relations in rhythmic movements and those related tothe within-effector consistency hi bimanual movements. Forexample, as shown by Schmidt et al. (1990), visual feedbackmay be sufficient to produce certain stable phase relations inrepetitive movements produced by different individuals. Incontrast, visual feedback does not appear to be a relevantsource of the bimanual advantage. In fact, the results sug-gest that the consistency of an individual's movements isdisrupted when observing synchronized movements pro-duced by another person.

General Discussion

In Experiments 1-3 we examined the timing of repetitivemovements under unimanual and bimanual conditions. Un-like previous studies of bimanual movements (e.g., Kelso,1984; Zanone & Kelso, 1992), our primary interest was tocompare within-hand variability under the two conditions.Temporal variability was consistently reduced during bi-manual movements.

Experiment 2 showed that the bimanual advantage doesnot require that the two movements be produced by homol-ogous effectors. The bimanual reduction was also foundwith nonhomologous movements involving the finger andforearm. This result provides an important generalization ofthe phenomenon.

In addition, Experiment 2 provides an evaluation of anattentional account of the bimanual advantage. The biman-ual advantage is counterintuitive from the perspective ofresource theories of cognitive capacity (e.g., Kahneman,1973). Such theories predict that when task demands in-crease, performance on a given task should deteriorate, or atbest remain unchanged. In the current experiments, weobserved a situation in which performance (e.g., right-handtapping) improved when the task became more complex(e.g., performed simultaneously with left-hand tapping).Moreover, the results of Experiment 2 rule out a specificattentional hypothesis of the bimanual advantage. Neuro-logical, neurophysiological, and behavioral evidence sug-gests that, at some stage of processing, unimanual move-ments are represented bilaterally. On the basis of this, wehypothesized that unimanual movements may be more vari-able because of increased demands required to inhibit ho-mologous actions with the contralateral effector. This hy-pothesis led to the prediction that the bimanual advantagewould be lost, or perhaps reversed, if the movements wereproduced by nonhomologous effectors. This prediction wasnot confirmed.

Experiment 3 demonstrated that there is no reduction inwithin-hand variability when the two movements are pro-duced by different individuals. This result provides twoinsights. First, there appear to be differences between themechanisms that underlie within-effector variability andthose that influence between-effector coupling. This hy-pothesis is based on the finding that between-effector cou-pling appears to be similarly constrained whether the twomovements are produced by one or two individuals(Schmidt et al., 1990). In the current study, the bimanualadvantage was found only when the two movements wereproduced by a single individual. Second, Experiment 3demonstrates that visual and auditory feedback are notsufficient to produce the bimanual advantage. A feedback-based hypothesis might be that, during bimanual tapping,each effector provides a "model" of the target interval forthe other effector. In unimanual tapping, such a model is notavailable. This hypothesis, however, leads to the predictionthat the bimanual advantage should emerge in the two-person experiment.

Note that it remains possible that somatosensory feedbackcould be contributing to the bimanual improvement. How-


ever, previous studies with both normal and neurologicalindividuals (see Ivry & Keele, 1989) indicate that feedbackprocesses play a minimal role in the repetitive tapping task.

Given that feedback and attentional hypotheses cannotaccount for the bimanual advantage, we now turn to adiscussion of how internal timing mechanisms might pro-duce this effect. We used the Wing-Kristofferson model(1973) to evaluate whether the reduced variability wasattributed to changes in central processes or motor imple-mentation processes. In both experiments, the results wereclear: Lower estimates of central variability for each effec-tor were obtained during bimanual tapping.

The use of covariance functions to estimate componentsources of variability during bimanual movements has beenused by a number of investigators (Turvey, et al., 1989;Vorberg & Hambuch, 1984; Wing, 1982; Wing et al., 1989).These investigators have consistently concluded or assumedthat a single timing system regulated the movements of thedifferent limbs. That is, the time at which the movementsshould occur was attributed to a shared process, althoughthe times at which responses were made were influenced byadditional processes that might be effector specific. It is notclear how this form of analysis could account for the bi-manual advantage. Why would a single timing mechanismbecome more consistent when its output is directed tomultiple effector systems? An alternative approach is topostulate different timing signals associated with each limb.Perhaps the bimanual advantage (and temporal coupling)reflect an interaction between these two signals.

Different hypotheses can be generated regarding the typeof central interactions that could produce this effect. It hasbeen hypothesized that rhythmic movements reflect theoperation of internal oscillators (see Schoener & Kelso,1988). In bimanual movements, two oscillators are postu-lated, one associated with each effector. However, theseoscillators are coupled, and the dynamics of bimanualmovements will reflect the strength of this coupling. Thisform of analysis has previously been used to account for thestability of certain phase relations during bimanual move-ments (Kelso, 1984; Yamanishi et al., 1980; Zanone &Kelso, 1992).

Little attention has been given to how coupling may affectwithin-effector variability. However, it seems reasonable toexpect that within-effector variability might be reduced ascoupling strength increases. An analogy might be to con-sider the stability of two pendula of different mass. Thesmaller pendulum can represent the unimanual condition.The larger pendulum can represent the bimanual conditionwhere two small pendula have been strictly coupled (andthus form the larger mass). A perturbation of a given sizewill have unequal effects on these two dynamical systems.The larger pendulum will show less displacement from itslimit cycle than the smaller pendulum. The coupled systemwill have reduced variability. It is important to note that,although the preceding metaphor draws on a physical ex-ample, similar interlimb coordination dynamics are found inintraindividual and interindividual movements (Schmidt, etal., 1990). Thus, the "larger" pendulum must emerge at anabstract, nonbiomechanical level.

A different version of a coupling hypothesis may alsoaccount for the bimanual advantage. As shown in previousresearch, patients with unilateral cerebellar lesions showincreased central variability when tapping with their ipsile-sional hand (Ivry et al., 1988). This within-subject dissoci-ation suggests that different effectors engage the operationof different timing mechanisms. However, these patientsalso show a strong frequency and phase coupling whenperforming bimanual movements (Franz et al., in press).One way to account for this is to assume that the outputsfrom separate timing mechanisms are integrated. Perhapsthis integration reflects a response bottleneck: Output toperipheral motor pathways cannot occur at arbitrary pointsin time, but is constrained. For example, when two handsare moving in phase, motor commands for each hand areissued simultaneously. By this model, the coupling does notreflect any interactions between the timing mechanisms perse, but rather a process receiving the output from thetimers.5

There are many possible forms that an output constraintcould take. We explored a set of models in a series ofsimulations. The models share the following properties:First, in each, separate timing mechanisms are associatedwith each effector (hand-hand or hand-forearm). For thecurrent discussion, random samples from each timing mech-anism are assumed to form a normal distribution. Onenormal distribution is used to represent samples from the"left" timer, and a different normal distribution is used torepresent the "right" timer. The means of these distributionswere set to the means of the interresponse intervals pro-duced during the unpaced tapping phase. The standard de-viations were set to the estimated central variability com-ponents as derived from the Wing-Kristofferson model(1973). Thus, the means and standard deviations are notequal for the two distributions. Our decision to use only thecentral estimates is motivated by the assumption that thebimanual advantage reflects central interactions. This isfurther justified by the experimental results showing that themotor delay estimates did not decrease during bimanualtapping.6

To simulate the central variability in a unimanual tappingtrial, we took 30 samples from one of the distributions ofintertap intervals and calculated the mean and standarddeviation of the samples. This procedure was repeated sep-arately for the left and right timers. For bimanual trials,separate sets of 30 samples were obtained, one from thedistribution of the left timer and one from the distribution ofthe right timer. These samples were then combined (see

5 The current model does not require the two timing mechanismsto be associated with the different sides of the body. Indeed, wewould expect within-effector variability to be reduced duringfinger-foot movements that involved effectors on the same ordifferent sides of the body.

6 The qualitative pattern of results would be the same if totalvariability scores were used in the simulations. However, the useof these values would distort any quantitative comparisons. This isbecause the motor component is unaffected by the couplingconstraint.


below) to simulate the hypothesized output constraint. Themean and standard deviation of the new, integrated distri-bution were then calculated to obtain an estimate of centralvariability during bimanual tapping for that trial. Theseprocedures were repeated for 24 unimanual and 24 biman-ual trials for each of the 27 participants.

Six different models were tested. To repeat, the modelsshare two primary assumptions. First, each model is basedon the assumption that mere are separate timing mecha-nisms associated with each effector. Second, in each modela coupling mechanism constrains bimanual movements sothat a single central output is sent to both effectors simul-taneously. The models differ in how the samples from thetwo timing distributions are combined. Table 1 presents thesimulated mean interresponse interval and estimate of cen-tral variability for each model calculated for the 27 partic-ipants. The unimanual estimates are an average of right- andleft-hand performance. We also ran large-scale simulationsby taking 3,000 samples from each of two distributions: onematched to the estimate of central variability for the righthand averaged across participants and the other matched tothe left-hand estimate. These simulations yielded essentiallythe same results as those shown in Table 1.

The null models are essentially identical to the unimanualconditions. Null right would mean that during bimanualtapping, performance is completely determined by the out-put of the samples from the right timer. For null left,bimanual tapping would be completely determined by theoutput of the samples from the left timer. Given that there isno real integration of the different timers, the simulationsfail to produce a reduction in variability during bimanualtapping.

The random model provides the simplest form of integra-tion. Prior to each response, the output integrator randomlyselects one of the two timing signals. This model actuallypredicts a slight increase in variability, resulting from thefact that the means of the two distributions are not identical.

For the first model, the samples of the combined distri-bution are based on whichever timer provides the first input.That is, central commands to tap are sent to both effectorsas soon as one of the timers indicates that the target time haselapsed. The combined distribution will include samples

Table 1Six Models by Which Two Timing MechanismsCan Be Integrated

Models

NullRightLeft

FirstLastRandomWaiting

RightLeft

Average

Experimental results

Mean interval

392389383399391

399399391

391

Central variability

13.7712.3510.9411.2813.68

17.1117.439.41

9.68

from both the right and left distributions because of theirconsiderable overlap. The last model is the converse. In thiscase, the central command is delayed until both the right andleft timers indicate that the target time has elapsed. Inter-estingly, both models predict reduced central variabilityduring bimanual tapping. However, these models also pre-dict a change in the mean of the intertap intervals. The firstmodel predicts that participants tap faster, and the lastmodel predicts that participants tap slower.

The waiting model is a more complicated version of thefirst and last models. Rather than have the coupling occur bymeans of the commands to the periphery, coupling in thewaiting model is in terms of the restarting of the two timers.That is, after each timer indicates the target time haselapsed, the associated hand makes a response. Restartingthe timers, however, must occur simultaneously and is de-layed until both timers have completed timing the previousinterval. With this model, separate variability estimates areobtained for each hand. However, neither estimate providesa good fit to the data, both in terms of the means andstandard deviations.

The final model discussed in Table 1 is the averagemodel. For this model, the intervals in the combined distri-bution are calculated by taking the average of the twosamples for each bimanual response. The simulation of thismodel provides an excellent fit to the data. First, the meanof the combined distribution falls halfway between themeans for the left and right distributions. More impres-sively, the simulated standard deviation is 9.41 ms. InExperiment 1, the average central variability of the right andleft hands during bimanual tapping is 9.68 ms. On the basisof the empirical estimates of central variability, the averagemodel predicts a bimanual advantage of about 29%, a valueclose to the observed value of 26%. Note that the 29%reduction by the averaging model can be obtained analyti-cally. The standard deviation is reduced by a factor of thesquare root of 2 (or 29.3%) when a new distribution isformed by averaging two independent samples from a nor-mal distribution.

Large-scale simulations based on the mean data for Ex-periment 2 also were conducted. The two unimanual distri-butions were based on the mean finger and forearm esti-mates. Again, the average model clearly provided the bestfit. The simulated central variability in the bimanual condi-tion was 9.7 ms, and the observed value, averaged overfinger and forearm, was 9.8 ms.

The average model may seem at first to be implausible inreal time. In this model, a sample is taken from each timer,and the integrated central output occurs at the average ofthese two samples. It seems illogical that an averaged outputcould be sent prior to the time at which the integratorreceives the second input component. How could it beknown when this input would arrive?

However, if timing mechanisms are conceptualized asproducing a continuous signal, an averaging integrator isnot unreasonable. A sketch of how averaging might occurfor a single bimanual response is given in Figure 6. Theactivation of each timing mechanism is represented by acontinuous activation function. The peak of this function


B5 - -

4 -

3 -

2 -

1 • •

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Time

CombinedThreshold

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Tims

Figure 6. Hypothetical distributions representing the activation of timing mechanisms over time.A: Representation of a single timing mechanism. B: Two timing mechanisms are integrated, leadingto a more precise signal.

may be thought of as corresponding to the value for thissample of the target interval. Alternatively, there may besome threshold that corresponds to this value, and the timersignals that the target interval has elapsed once this thresh-old is crossed.

In the bottom of Figure 6, two activation functions areshown in thin lines. These correspond to two independentsamples, one associated with the left timing mechanism andone associated with the right timer. For bimanual tapping, asingle, integrated activation function is derived by summingthese two activation functions. If the two samples have areasonable amount of overlap, the peak of this new functionwill fall between the peaks of the two input functions andwill even be at the average if the input functions have thesame variance. (In the threshold version of this mechanism,there would need to be an increase in the threshold duringbimanual tapping.)

It remains to be seen if the bimanual advantage emergesas a result of some sort of neural averaging process. Weoffer the current example to demonstrate that this form ofcoupling could occur in real time.

The idea that outputs from separate timers are integratedis not necessarily at odds with the dynamical perspective ofcoupled oscillators. Indeed, the output constraint hypothesiscould be viewed as one specific version of how couplingarises. However, there are potential areas of difference thatcan be explored in future research. Theoretical work oncoupled oscillators has offered important insights into anumber of interlimb phenomena, such as the stability spaceof different phase relations and hysteresis effects mat ac-company phase transitions (see Haken et al., 1985). Thecurrent focus of the averaging model has been restricted tothe effects on within-hand variability (although the modeldoes predict phasing constraints). It will be useful to explore


the implications of an output bottleneck on other aspects ofbimanual coupling.

Finally, the averaging model makes quantitative predic-tions concerning the magnitude of the bimanual advantageacross different experimental conditions. For example, cen-tral timing variability is proportional to the target interval(e.g., Ivry & Corcos, 1993; Wing, 1980). The averagingmodel predicts that across tapping rates, the standard devi-ation during bimanual tapping should be reduced by approx-imately 29%. An experiment to test this prediction wouldalso provide an important test of the generalizability of thebimanual advantage.

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Received November 8, 1993Revision received June 8, 1994

Accepted January 17, 1995 •

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