dow el by theexper ime nte r. In hal f of thetrial s, thehand wasmovedfrom the starting position to the closest dowel placed at a viewing distance of 12. 5 cm (to war d pos itio n; Fi g.1

B

).In th e ot he r ha lfof thetri al s,the ha nd was moved from the starting position to the far wall of the box located at a viewing distance of 50 cm (away position; Fig. 1

C

). When performing hand movement s, partic ipants were instruc ted to rotate their forea rm without lifting their elbow. This manipulation did not deform the per- ceived shape of the afterimage that was persistently reported as circular. On eac h tria l, par tici pan ts wer e ins truc tedto reg iste r theperce ive d sizeof the afterimage at the end position and match it to one of the numbered circles presented on the LCD monitor. After the size-matching task and between each presentation of the stimulus, participants were instructed to close their eyes to prevent any incident light induced by the experi- menter activity. Trials were initiated once the previous afterimage disap- peared. Participants were also given four practice trials before testing began.

Procedures for experiment 1: the role of efference copy.

The experiment consisted of 28 trials in total with two repetitions for every condition, as described below. Conditions differed depending on the type of arm movements being made and the location of eye fixation during the exe- cution of these movements. Four control judgments were also collected without any movement of the arm to provide measurements of baseline. To study the effects of efference copy in size perception, trials were div ide d intotwo blo cks : oneblock of act ive mov eme nts andone blo ck of passive movements ( Carey and Allan, 1996 ; Bross, 2000 ) . The order of these two blocks was counterbalanced across participants. The logic was to see whether or not in the active condition—in which participants are actively moving their hand—the corollary discharge of the motor com- mand to the hand might influence the perceived size of afterimages. Under passive condit ions, there should be no motor comman ds to the hand, given that the experimenter, not the participant, is moving the hand. Therefore, the main difference between active and passive condi- tions was efference copy (i.e., feedforward motor command) that was avail able during active movem ents only ( Carey and Allan , 1996 ) . The order of presentation of the two blocks was counterbalanced across par- ticipants. In the active condition, participants moved their hand them- sel ves , cue d by aud ito ry ins truc tion s. In the pas siv e con dit ion , the experimenter, cued by auditory instructions, moved the participant’s hand. In this condition, participants were completely unaware in which direction the experimenter would move their arm from trial to trial, and wer e ins truc tedto kee p the ir armrelax ed andrefra in fro m hin der ing any movement of their limb. To study the effects of vergence on size percep- tion, three different types of fixation conditions were tested for every direction of hand movement, as follows: (1) “central fixation,” whereby the small red fixation light was turned on in the center of the hand-held rin g aft er theprese nta tionof theinduci ng stim uluslightand par tici pan ts were instructed to keep their eyes fixated on the small light and follow it as the hand was moved; (2) “no fixation,” whereby only the inducing stimulus light was presented without any fixation cue ever being pro- vid ed,and;(3) “la ter alfixati on, ” whe reb y thefixat ionlightwas pre sen ted next to the hand at 14.8° eccentricity from the body’s midline (25 cm from the eyes), and participants were instructed to fixate on this station- ary light immediately after the generation of the afterimage while the hand was moving. The order of these types of fixation was randomly determined for each of the “active” and “passive” blocks. In short, par- tici pan ts com ple ted24 exp eri men taltrial s (i.e ., 2 kin ds of mov eme nt



2 hand directions



3 fixation types



2 repetitions) and 4 control trials (baseline).

Pro ced ure s for exp eri men t 2: the rol e of ver gen ce andpropr ioc ept ion .

The protocol was similar to that of experiment 1, with the following two excep tions:(1) parti cipant s alwaysperformedactive movem ents;and (2) verge nce eye movem ents were record ed using a head- mounte d eye tra cke r to ens ure par tici pan ts wer e, in fac t, fix atin g app rop ria tel y, as wel l as to inv est iga te furt her the rel atio nsh ip bet wee n ver gen ce and per cei ved size of the afterimage. The experiment consisted of 48 trials in total (i.e., 2 hand directions



3 fixation types



8 repetitions). Trials were pre- sented in a random fashion.

Proce duresfor experi ment 3: misma tch betwe en vergen ce and propr iocep - tion.

To invest igate the effect of verge nce–p roprio ceptiv e mismatc h ( Ram sayet al. , 200 7 ) , par tici pan ts wer e tes tedwith con gru entand inc on- gru ent tri als . In thecongru ent con dit ion , the fix ati on lig ht was mov ed by the experimenter in the same direction as the observer’s hand. In the inco ngr uen t con diti on,the fix ati on lig ht was mov ed by theexper ime nte r in the opposite direction to the observer’s hand. Participants were asked to fol lowthe fixa tionlightwith the ir eye s andto mov e the ir han d acco rd- ing to the cued direction. Eye movements were recorded for all partici- pan ts. The exp eri men t con sist ed of 32 trials in tot al (i. e., 2 han d directions



2 conditions



8 repetitions). Trials were presented in a random fashion.

Data analyses.

For the pur pos es of sta tist ica l ana lys is, the sel f-re por ted dat a of per cei vedsize wer e firs t nor mal ize d to all ow mea nin gfulcompa r- ison between conditions and provide measures of individual susceptibil- ity to the illusion. This “susceptibility index” was calculated as follows: (perceived size of the afterimage at the away position



perceived size of the afterimage at the near position)/the sum of the perceived size of the afteri mages at each of these two positions ( Chouinard et al., 2013 ) . To ens urethat theillus ionhad bee n ind uce d, a

t

tes t aga ins t 0 wasperfo rme d on the mea n susc ept ibi lit y ind ice s for eac h con dit ion . A rep eat ed- measures ANOVA was also performed on these values with hand direc- tion (toward vs away), movement type (active vs passive), and fixation typ e (ce ntr al fix atio n vs no fix ati on vs lat era l fix ati on)as mai n fact ors . All results were corrected for multiple comparisons using the Bonferroni method (i.e.,

p

corrected



P

uncorrected



the number of comparisons). For experiments 2 and 3, vergence was determined from eye position in a head-centered reference frame with saccades removed, in a manner sim- ilar to that descr ibed in a recen t study by Frey and Ringach (2011) . To mea surethe cha ngein ver gen ce aft er lim b mov eme nt,the mea n ver gen ce angle at the end of the trial was subtracted from the mean vergence angle at the beginning of the trial. These two mean angles were determined by averaging vergence across 100 ms windows (25 data points). In this way, convergence eye movements (i.e., simultaneous inward rotation of both eyes to fixate at a near distance) were associated with positive values, while divergence eye movements (i.e., simultaneous outward rotation of both eyes to fixate at a far distance) were associated with negative values. These values were then correlated with the subjective ratings of the per- ceived afterimage size. Pearson correlation coefficients (

r

) were calcu- lated , and signifi cance from these corre lationcoefficients was establ ished using one-tailed criteria. This was deemed to be appropriate given that we already know on the basis of Emmert’s law that perceived afterimage size increases with viewing distance. More importantly, we were inter- ested in testing the hypoth esis that changes in perce ived size would al- ways be completely predicted by changes in vergence ( Taylor, 1941 ; Mon-Williams et al., 1997 ) . A repeated-measures ANOVA with fixation type (central fixat ion vs no fixation vs later al fixation) as a main factor (experiment 2) or a paired

t

test (experiment 3) was performed on the correlation coefficients.

Post hoc

pairwise comparisons were adjusted using the Bonferroni correction. Two-tailed criteria were used for all the pairwise comparisons.

Additional analyses based on maximum likelihood estimation.

To mea- sure the relative contribution of vergence and proprioceptive cues to the Taylo r illusio n, the maximu m likel ihoodestimation(MLE) princip le was applied to estimates of distance for the no-fixation condition of experi- ment 2. Previous research has demonstrated that human multisensory per cep tio n of dep th, hei ght,size, and spa tia l loc ati on fol low s pre dic tion s based on the MLE model ( Landy et al., 1995 ; Ernst and Banks, 2002 ; Gepshtein and Banks, 2003 ; Alais and Burr, 2004 ) . According to this model , verge nce and propr iocep tive estima tes are optima lly combin ed to yield the lowest variance in an integrated (multimodal) estimate. By using the MLE rule, distance estimates from vergence and proprio- ceptive signals are weighted by their reliability such that the signal with lower variance (i.e., higher reliability) is given more weight than the signal with higher variance (i.e., lower reliability). The statistical strategy for cue combination is a weighted linea r summation of each independent estimate:

S ˆ

VP



w

V

S ˆ

V



w

P

S ˆ

P

, ( 1 )

Sperandio et al.

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S i z e C h a n g e a n d N o n v i s u a l S i g n a l s i n D a r k n e s s J . N e u r o s c i . , O c t o b e r 2 3 , 2 0 1 3

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