Introduction

Sense of body ownership is no longer considered an invariant of human experience [1]. One fruitful paradigm that investigates its flexibility is the rubber hand illusion (RHI) [2], in which an artificial hand comes to be experienced as the participant’s own after a period of simultaneous brush stroking of the participant's hidden real hand and a visible dummy hand. The spatiotemporal coherence of stimulation appears to be a crucial condition for divergent visual, tactile, and proprioceptive signals to be integrated, and, consequently, for a sense of ownership over a fake limb to arise [3].

The exact way in which multisensory integration processes lead to the emergence of the rubber hand illusion remains a subject of heated debate (for a discussion see [4, 5]). One influential family of models are Bayesian causal inference models, which propose that the presence of the illusion depends on whether the brain infers that the visual and somatosensory signals stem from a common cause (for neurophysiological evidence of causal inference processes in non-human primates’ premotor cortex see [6]). Associations between sensory signals previously learned to frequently co-occur establish the prior probability of their shared origin, while likelihood is determined by the spatiotemporal congruence of visual, tactile, and proprioceptive signals. When the signals converge in space and time, the increased likelihood of observing such signals (given the assumption that they have a common cause) boosts the posterior probability of their common cause and thus supports the inference (and, as a result, the experience) of ownership over a fake hand. In a recent computational account [7], visuo-tactile synchrony and distance between the real and rubber hands are two major factors determining the inference of the commonality of signals. The distance between the hands accentuates the role of proprioception in the rubber hand illusion: greater discrepancies between visual and proprioceptive cues about the hand’s location weaken or break the RHI, particularly when the proprioceptive signals are of high precision. In other words, “the illusion is stronger the nearer the fake and real hand are to each other, [and] the noisier the proprioception modality is” [7, p. 19].

In our previous study [8], we aimed to experimentally examine these predictions. To manipulate the distance, we subliminally moved the participant’s hand at a very slow pace from the starting position (16cm between the real and rubber hands) to positions either closer (8cm) or farther away from (24cm) the rubber hand. RHI turned out to be comparably vivid at both distances, regardless of the participant’s individual proprioceptive precision (which was operationalized as the inverse variance of errors in an active arm reproduction task [9]). For a subjective measure of RHI strength, Bayes factor analyses provided substantial evidence for the null hypotheses, both when fitting unifactorial and full regression models. These results throw into question the relevance of 1) the degree of convergence of visual and proprioceptive spatial estimates and 2) proprioceptive precision for RHI induced visuo-haptically at distances shorter than 30cm (for reports of attenuation of RHI at larger distances see [10, 11]).

According to the extended Bayesian model of the RHI [5], the relevance of proprioception-laden factors may be diminished in the presence of touch. In the process of causal inference, cognitive systems use various sources of information, depending on their availability, reliability, and relevance for the task at hand. As for relevance, touch directly demarcates one’s body boundaries, as its receptor surface (skin space) is “physically co-extensive with the body itself” [12, p. 12]. Additionally, given that the skin space constitutes a high-resolution spatial map, the presence of spatiotemporally congruent visuo-tactile stimulation provides highly reliable sensory evidence for the hypothesis that the rubber hand is actually one’s own. Therefore, even if there is a noticeable discrepancy between visual and proprioceptive spatial estimates, visuo-tactile coherence renders it insignificant due to the superior precision of signals originating on the skin space. However, in the absence of tactile stimulation—when the RHI is elicited through the mere observation of a dummy—the inference should rely on the degree of visuo-proprioceptive convergence and the precision of unimodal visual and proprioceptive estimates (in line with the causal inference model of the RHI as proposed in [7]). On this basis, it could be hypothesized that, in the presence of touch, the convergence of visuo-proprioceptive estimates is still a ‘working’ factor, but due to its minimal influence on the final inference (favoring the separate causes hypothesis), it becomes virtually non-determinative of illusion strength. Visuo-proprioceptive convergence ceases to be a causal factor only in the case of complete absence of the proprioceptive input. Then, body attribution processes may be driven solely by visual body information, as shown by the studies carried out among patients suffering from spinal cord injuries at the cervical level [13, 14].

Furthermore, this compensatory effect of tactile information should depend on its complexity. Decreased complexity of spatiotemporal patterns of brush stroking—for instance, repetitive single-finger taps—renders visuo-tactile co-variance over space and time less informative (as illustrated by the fact that irregular and unpredictable stimulation patterns give rise to a more vivid illusion) [15]. Thus, we hypothesize that the magnitude of the effect of spatial distance on RHI strength will be proportional to the relative influence of proprioception, which should be greater when tactile information is more limited. Also, we expect to observe that the effect of spatial distance will be more pronounced for individuals with better proprioceptive abilities, but only when tactile information is absent or simplified. In the case of complex tactile stimulation, which is supposed to render the impact of visuo-proprioceptive estimates negligible, proprioceptive precision has been shown not to be predictive of RHI strength [8].

Finally, the relation between subjective reports of illusion strength and one of its classic behavioral proxies—proprioceptive drift [2]—should also depend on the availability and complexity of tactile information. Once the illusion has been induced, proprioceptive estimations of the position of one’s own hand are shifted towards the rubber hand and the magnitude of this shift tends to correlate with subjective RHI strength [10, 16]; however, the absence of such correlations is also frequently reported [17–21]. On this basis, it was argued that correlations are found only with the use of a particular measurement technique, that is, with the contralateral hand pointing at the position directly over the ipsilateral hand [22], or that proprioceptive drift may be a behavioral proxy of RHI only under specific circumstances, namely in experimental designs in which the participant’s hand is not displaced [23]. Alternatively, it might reasonably be argued that questionnaire ratings and proprioceptive drift capture different aspects of the RHI phenomenon [20]. From the perspective of probabilistic multisensory integration, determination of ownership (‘what are the parts of my body’) and location (‘where are the parts of my body’) are two different tasks for a cognitive system. While touch is relevant for the former, the latter is based only on visuo-proprioceptive estimates. Therefore, we hypothesize that correlations between subjective body ownership and drift should be particularly pronounced in the ‘no touch’ mode of RHI elicitation (i.e., when one is simply looking at a rubber dummy without receiving tactile stimulation) [7], because in this case the cognitive system uses the same visuo-proprioceptive estimates for both tasks.

In order to examine the previously-discussed predictions of the extended Bayesian model of the RHI [5], the subliminal displacement procedure [8, 23] was used to manipulate the distance between the participant’s hands (8 and 24 cm) and the RHI was elicited under conditions differing in terms of the availability and complexity of tactile stimulation (none, simple, complex). Additionally, we measured individual proprioceptive acuity. To ensure that the potential lack of effect of proprioception (cf. [8]) would be due to its irrelevance rather than an ill-chosen task, we decided to assess passive proprioception, as it is the most relevant in the conditions under which the RHI is generally assessed. The activation of several functionally distinct proprioceptive sensors, such as muscle spindles (major sensors of limb position and movement) or joint and skin mechanoreceptors, may differ depending on the kind of proprioceptive task used [24]. For example, in passive proprioceptive tasks, sensory feedback from cutaneous receptors is enhanced at the cost of input from muscle spindles. Therefore, active joint position reproduction (JPR) tasks may measure different aspects of proprioception than passive methods [25]; indeed, performances in threshold position/movement detection tasks and active reproduction tasks do not correlate [26], which suggests that ‘passive’ and ‘active’ proprioception subsystems should be distinguished. Therefore, while we used an active reproduction task (including arm flexions and abductions at the glenohumeral joint) in our previous study [8], in the present study we decided to use one which measures the elbow joint’s position sense threshold. In this task, the participant’s initial arm position is matched with the position of the arm during RHI elicitation and the experimenter moves the participant’s arm passively to the testing positions. We thereby ensured that the task assessing proprioceptive skills (precision) is maximally relevant to the sensory conditions accompanying RHI.

To sum up, we aimed to test three hypotheses concerning the interactions between visual, tactile, and proprioceptive cues in the shaping of body ownership. First, we expected that the attenuating effect of distance on RHI will be absent in the presence of complex tactile stimulation, diminished under the condition of limited tactile information, and most pronounced in the absence of touch. Second, we hypothesized that proprioceptive precision will be inversely related to RHI strength in the no touch and simple touch conditions—specifically, at the far distance between hands—whereas it will not have predictive value for the complex touch condition (at both distances) [8]. Third, we expected that the magnitude of correlation between proprioceptive drift and RHI strength will be inversely proportional to the amount of tactile information available.

Materials and methods

Setup and tasks

Proprioceptive acuity assessment.

Proprioceptive acuity was measured with a modified version of the psychophysical threshold method [26], which assesses the ability to differentiate between arm positions on a horizontal axis (angles of elbow joint flexion). Participants were blindfolded, sat in an upright position, and asked to place their right arm on a movable armrest. During each trial, the arm was initially placed in the starting position (elbow flexion = 90^o; Fig 1A–upper panel). The starting position of the arm during the task was matched with the position of the arm during RHI elicitation. The trained experimenter moved the armrest toward the midline of the participant’s body in a circular motion (allowed by the manipulandum) to the two following positions in a counterbalanced order: 1) the reference position (elbow flexion = 80^o; Fig 1A–bottom panel) and 2) the comparison position (ranging from 80^o to 86^o in 0.1^o steps). Each position was denominated by the experimenter as either the ‘first’ or the ‘second’. Then, the participant provided a verbal response (in a two-alternative forced choice task) indicating which of the two positions was closer to the body. No feedback was given to the participant. To ensure that the participants understood the task, two trial runs with easily noticeable differences between positions were conducted prior to the assessment.

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Fig 1. Experimental setup.

(A) Proprioception assessment. The experimenter moved the armrest from the starting position (90^o) to the two following positions: 1) the reference position (80^o) and 2) the comparison position (ranging from 80^o to 86^o in 0.1^o steps). The participant’s task was to indicate which one of the two positions was closer to the body. (B) Distance manipulation. Before the illusion elicitation, the participant's real hand was displaced at a very slow pace (under the detection threshold) to position either close to or far from the rubber hand. (C) Elicitation conditions. In the no touch condition, the illusion was elicited through the sole observation of the rubber hand. In the two remaining conditions, RHI was induced with tactile stimulation. The brushstrokes varied with respect to their spatiotemporal complexity–were either repetitive and spatially limited (simple touch condition) or temporally jittered, unpredictable and spatially extended (complex touch).

https://doi.org/10.1371/journal.pone.0244594.g001

Based on the correctness of the response, the psi-marginal adaptive staircase method [29] (as implemented in Python by [30]) determined the comparison position for each subsequent trial by increasing stimulus intensity (the difference between positions) after a wrong answer and decreasing it after a correct one. In this way, the adaptive algorithm converged towards the participant’s just-noticeable-difference (JND) threshold [31]. A uniform threshold prior and initial stimulus intensity (difference) set to 2.8^o were fed into the algorithm. To ensure that the participants maintained mental alertness throughout the task, breaks of one minute were taken after the 13^th and the 26^th trials (cf. [32]). After 40 trials, the algorithm outputs a logistic function fitted to the response data as well as just-noticeable-difference thresholds and estimates of the variability of the participant’s responses (represented as the slope of the logistic function) [31]. Proprioceptive accuracy was operationalized as being inversely related to just-noticeable-difference threshold and proprioceptive precision as being inversely related to the slope of the distribution. The assessment procedure lasted from 15 to 20 minutes.

Rubber hand illusion elicitation.

For illusion elicitation, a realistic, life-sized, right male rubber hand was used (in our previous study, no differences in illusion strength were observed between genders when a male hand was used) [8]. Depending on the distance (D) condition, the participant’s real hand was subliminally moved from the starting position (16 cm away from the rubber hand) either to the close (8 cm away from the rubber hand; Fig 1B–upper panel) or far (24 cm away from the rubber hand; Fig 1B–bottom panel) position with the use of a displacement sheet. Then, the illusion was elicited in three touch-related (T) conditions: a no touch condition (visuo-proprioceptive, Fig 1C–upper panel) and two visuo-tactile conditions (consisting of the synchronous stimulation of the real and the rubber hands with a brush): simple touch (Fig 1C–middle panel) and complex touch (Fig 1C–bottom panel). The simple and complex conditions differed in the number of stimulated fingers (simple: one finger; complex: three fingers stimulated in a random sequence), temporal structure (simple: steady, regular stimulation with a frequency of 0.5 Hz; complex: irregular stimulation with beep onsets jittered by adding Gaussian temporal noise with a mean of 0 seconds and standard deviation of 0.2 seconds) [33], and spatial patterns of stimulation (simple: repetitive brushstrokes extending from the proximal to the middle phalanx of the finger; complex: brushstrokes of varying length extending from the proximal to the distal phalanges). The stimulation in all conditions lasted 90 seconds and was standardised by using auditory beeps, audible only to the experimenter, to signal the timings of the strokes. As in the previous study [8] we used the audio tracks developed by Fuchs et al. [33] with slightly extended beep durations.

Rubber hand illusion questionnaire.

To measure the subjective strength of the illusion, a six-item questionnaire was used. The questionnaire was based on that of Longo et al. [34]. All questions began with the phrase “During the block I felt as if…” and answers were given on a seven-point Likert-type scale from -3 (I didn’t feel like that at all) to 3 (I felt like that very strongly). We had to exclude the conventional illusion items concerning tactile experiences (e.g., “…the touch I felt was caused by the paintbrush touching the rubber hand”)—even though their mean values are usually the highest (cf. [34])—as they would not relate to the no touch condition. Instead, to measure the illusion strength with the same items across all conditions, the three non-touch-related items with the highest loadings on the embodiment factor were selected. Control items were used in order to account for the potential tendency of participants to assent to the given statements. The selection criterion here was the lowest mean ratings of the rubber hand illusion strength in Longo et al.’s [34] study, given that the chosen illusion items do not tend to yield particularly high scores (average ratings tend to oscillate around 0). The selected items were translated into Polish and pre-tested during a pilot study (N = 10) to ensure that they yield comparably low mean ratings. The items were read aloud to the participant in a randomized order. All items are presented in Table 1.

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Table 1. Illusion strength questionnaire items.

https://doi.org/10.1371/journal.pone.0244594.t001

Proprioceptive drift assessment.

For proprioceptive drift assessment, a modified version of the procedure from Holle et al. [35] was used, adapted to our rubber hand illusion elicitation setup. From a variety of proprioceptive drift measures (cf. [22]), a visual judgment task was identified as being the most suitable, given that our hypotheses dealt with visuo-proprioceptive integration. Using, for instance, a contralateral matching task would solely engage proprioception. In our task, the participant’s hand was placed on the bottom surface of the shelf and the rubber hand was hidden with a wooden cover. A ruler was placed at the farthest edge of the top surface. The participant’s task was to verbally indicate the number under which they felt (cf. [36]) the middle finger of their real hand was placed (with 0.5 cm accuracy). Proprioceptive drift was measured twice in each condition: before (pretest) and after (posttest) elicitation of the illusion. In order to avoid the participant having been primed by the pretest number, the ruler’s posttest position was randomly shifted relative to its pretest position. The position of the middle finger for both the close and far conditions was marked on the wood on the experimenter’s side of the shelf so as to compare the participant’s answer with the correct number without the experimenter’s gaze indicating the actual position of the hand. The illusion-induced proprioceptive drift value was calculated as the difference between the posttest and the pretest drifts.

Results

The questionnaire items were found to have been appropriately chosen because: 1) the illusion scores were much greater than the control scores in all conditions (all ps < .0032) and 2) averaged control scores did not significantly differ across conditions, as shown by Friedman’s test: χ²(5, N = 46) = 3.51, p = .622 (descriptive statistics and bar plots are presented in S1 Table and S2 Fig).

The influence of the interplay between distance and touch availability on RHI strength: Non-parametric analyses

Non-parametric analyses revealed a pattern of results close to the hypothesized interaction (Fig 2). When the RHI was elicited through mere observation (T1), the illusion was weaker at the larger distance between hands (D2: Me = -1) than at the smaller distance (D1: Me = 1): Z = -2.57, p = 0.010, r = 0.500, BF₁₀ = 7.94, δ = 0.416 [95% CI: 0.123, 0.724]. Similarly, in the simple touch condition (T2), attenuation at the larger distance was observed relative to the shorter position: Z = -2.45, p = 0.014, r = 0.464, BF₁₀ = 7.41, δ = 0.411 [95% CI: 0.119, 0.710] (D2: Me = 1.33; D1: Me = 2). However, in case of complex tactile stimulation (T3), there was no evidence for differences in RHI strength between the distance conditions: Z = -1.48, p = 0.138, r = 0.312, BF₁₀ = 0.47, δ = 0.218 [95% CI: -0.064, 0.508] (D2: Me = 2; D1: Me = 2). Obtained Bayes factor values indicated moderate evidence for the alternative hypothesis in the case of no touch (BF₁₀ = 7.94) and simple touch (BF₁₀ = 7.41) conditions, and weak evidence for the null hypothesis in the case of complex touch condition (BF₁₀ = 0.47). There remains some degree of uncertainty regarding effect sizes in the no touch and simple touch conditions, given the relatively wide extents of corresponding 95% credible intervals (weak-to-medium effect size).

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Fig 2. Changes in the effect of distance between hands on RHI strength due to the amount of tactile information present during RHI elicitation.

The boxplots depict medians of subjective RHI strength (bold horizontal lines), upper values of the first and third quartiles (lower and upper sides of the box), and interquartile ranges for different elicitation conditions. The illusion was attenuated at the farther distance only in the conditions of absent or simplified tactile stimulation; no significant differences were observed for complex stimulation patterns. * p < 0.05.

https://doi.org/10.1371/journal.pone.0244594.g002

Across a wide range of Cauchy prior widths, Bayes factors appeared to be relatively stable. In the no touch (T1) condition, we observed moderate evidence for the alternative hypothesis under all prior specifications–narrow prior: BF₁₀ = 8.69, δ = 0.365 [95% CI: 0.075, 0.681], wide prior: BF₁₀ = 7.15, δ = 0.437 [95% CI: 0.126, 0.725], ultrawide prior: BF₁₀ = 7.00, δ = 0.450 [95% CI: 0.150, 0.764]. Similarly, moderate evidence for RHI attenuation at the larger distance was found in the simple touch (T2) condition–narrow prior: BF₁₀ = 5.89, δ = 0.353 [95% CI: 0.055, 0.659], wide prior: BF₁₀ = 7.07, δ = 0.425 [95% CI: 0.128, 0.728], ultrawide prior: BF₁₀ = 4.64, δ = 0.428 [95% CI: 0.126, 0.732]. In the complex touch (T3) condition, we obtained inconclusive results when the narrow prior was used: BF₁₀ = 0.82, δ = 0.178 [95% CI: -0.081, 0.472]. However, under wider priors, the evidence in favor of the null hypothesis was more decisive–wide prior: BF₁₀ = 0.39, δ = 0.231 [95% CI: -0.065, 0.525] (weak evidence), ultrawide prior: BF₁₀ = 0.30, δ = 0.235 [95% CI: -0.054, 0.539] (moderate evidence).

The influence of the interplay between distance and touch availability on RHI strength: Linear quantile mixed models analysis

An LQMM model for three quartiles of RHI strength— 25^th percentile: illusion logit = 0 (score = 0); 50^th percentile: illusion logit = 1.25 (score = 1.67); 75^th percentile: illusion logit = 2.08 (score = 2.33)—conditional on distance separating hands (D1: close; D2: far), touch availability during illusion elicitation (T1: none; T2: simple; T3: complex), and their interaction (model 1), was fitted on individuals with a random intercept:

We observed main effects of distance for the 25^th and 50^th percentiles, which means that, when no touch was applied during illusion elicitation (T1), RHI was significantly attenuated at the far distance (D2) relative to the near distance (D1), but only among weak and moderate responders. For the 75^th percentile (strong responders), the effect of distance balanced on the edge of statistical significance. The magnitudes of expected decrease (on the seven-point scale) for the groups were as follows: -2.57 [95% CI: -2.93, -0.95], p = 0.009 (for the weak responders), -2.30 [95% CI: -2.85, -0.53], p = 0.017 (for the moderate responders), and -1.86 [95% CI: -2.72, 0.17], p = 0.069 (for the strong responders). Similarly, the LQMM revealed main effects of touch complexity, but only for the two lower distribution ranges (among the weak and moderate responders) where the illusion was significantly stronger when elicited by tactile stimulation. The gradients of expected increase in RHI vividness at the shorter distance (D1)—as compared to the baseline no touch condition (T1)—were similar for simple (T2) and complex (T3) touch conditions. For simple touch, they amounted to 2.34, [95% CI: 0.66, 2.86], p = 0.013 (weak responders, T2), 1.86 [95% CI: 0.30, 2.62], p = 0.023 (moderate responders, T2), and 1.54 [95% CI: -0.61, 2.61], p = 0.15 (strong responders, T2), whereas for complex tactile stimulation they equaled 2.52 [95% CI: 1.12, 2.90], p = 0.004 (weak responders, T3), 2.08 [95% CI: 0.43, 2.75], p = 0.019 (moderate responders, T3), and 1.85 [95% CI: -0.92, 2.83], p = 0.174 (strong responders, T3).

Importantly, in line with our first hypothesis, a significant far distance–complex touch interaction was observed (Fig 3), which means that the decrease of RHI strength at the farther distance was lower when the illusion was elicited by complex tactile stimulation. Again, this effect surfaced only among weak and moderate responders, whereas it was not significant in the case of strong responders. The attenuation caused by increased distance—as compared to the T1 condition—was diminished, respectively, by 2.35 [95% CI: 0.51, 2.88], p = 0.019 (weak responders), 2.12 [95% CI: 0.19, 2.80], p = 0.034 (moderate responders), and 1.55 [95% CI: -0.80, 2.67], p = 0.184 (strong responders). The far distance–complex touch interaction showed an analogous pattern, but did not reach statistical significance in either of the tested percentiles: 2.08 [95% CI: -0.34, 2.85], p = 0.083 (weak responders), 1.93 [95% CI: -0.35, 2.79], p = 0.09 (moderate responders), and 1.60 [95% CI: -0.98, 2.73], p = 0.211 (strong responders).

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Fig 3. Effects on subjective RHI strength of distance, touch availability/complexity, and their interaction.

Effects were estimated by a linear quantile mixed model (LQMM) at three tested percentiles (25^th–weak responders; 50^th–moderate responders, 75^th–strong responders). For main effects, coefficients represent expected change in the outcome variable (RHI strength) for each unit of change in the predictor when the interacting variable is at the baseline level (e.g., expected change with increased distance (D2) when no touch (T1) was applied during illusion elicitation). For interactions, the coefficients reflect the difference in the change of RHI strength with distance (D2), compared to the change when the interacting variable is at the baseline level (T1) [44]. For example, at the 25^th percentile, attenuation of the RHI with distance in the complex touch condition (T3) is 0.22, compared to 2.57 at the baseline level (T1)—a decrease of 2.35 (as shown by the D2:T3 coefficient). Taken together, these results show that complex tactile information counteracted the attenuation of RHI strength caused by increased distance only among weak and moderate responders. The simple touch condition showed similar yet non-significant tendencies, which suggests that simplified tactile stimulation may be less potent in counteracting the attenuating effect of increased distance. Bold lines show significant effects. ** p < 0.01, * p < 0.05. (Note that the unequal confidence interval bounds are due to the non-linear back-transformation to the original scale).

https://doi.org/10.1371/journal.pone.0244594.g003

Discussion

In the present study, we examined how sense of body ownership is determined by the spatial properties of visual, tactile, and proprioceptive signals. For this purpose, the RHI was elicited in different conditions varying with respect to the distance separating the hands (i.e., the extent of visuo-proprioceptive spatial divergence) and the informativeness of tactile stimulation (i.e., the presence and complexity of tactile spatial information). We aimed to verify three hypotheses derived from the extended Bayesian model of the RHI [5]. First, we expected that the RHI will be less vivid with increasing distance between hands (i.e., increasing divergence of visual and proprioceptive estimates), but only when tactile information is simplified or altogether absent during illusion elicitation. In line with this hypothesis, we found that the RHI was attenuated with distance only when the illusion was induced either through passive observation of the hand or repetitive (simplified) tactile stimulation. When complex tactile stimulation was applied, the RHI was comparably vivid at both distances, which is in line with our previous findings [8]. The LQMM analyses revealed the diminishing of RHI in the no touch condition to be significantly greater than in the complex touch condition and only marginally greater than in the simple touch condition. This pattern of tactile-dependent reduction of distance effects surfaced in participants generally less prone to the RHI (among the weak and moderate responders), but was not observed in those more susceptible to the illusion (the strong responders).

These findings suggest that the degree of visuo-proprioceptive convergence is a relevant factor for RHI, but its relative impact diminishes in the presence of highly informative tactile stimulation. In our interpretation, increasingly complex visuo-tactile stimulation rigidifies the high likelihood of a common cause of visual and somatosensory signals (leading to RHI), regardless of the exact scale of the visuo-proprioceptive discrepancy (within coupling prior bounds). However, when tactile information is absent or simplified, the proprioceptive modality becomes a valuable source of information for the causal inference processes which identify the boundaries of one’s body (cf. [7]). This pattern of results was explicitly predicted by the extended Bayesian model of the RHI [5], but seems to be hardly accounted for in other competing models. Traditional theoretical approaches to the RHI [48] state that the visuo-proprioceptive recalibration of tactile coordinates to the rubber hand (the “visual capture” of proprioception) occurs prior to visuo-tactile integration, either allowing or preventing this integration in advance. If visuo-proprioceptive recalibration operated in such a bottleneck fashion, complex tactile stimulation could not compensate back for visuo-proprioceptive discrepancy. On the other hand, approaches attributing formation of sense of body ownership to cumulative multisensory integration processes [3] conceive of such processes as arising out of different combinations of available sensory information, without the principal dominance of any particular sense. While no sensory domain has been shown to be necessary for body transfer phenomena to occur (cf. [3]), our results suggest that relatively unconstrained tactile signals override proprioceptive ones due to their affiliation to a modality of higher spatial resolution. If the multisensory processes which determine body ownership were simply additive, visuo-proprioceptive divergence should also attenuate the RHI elicited by complex tactile stimulation, which was not observed in the present study (see also [8]).

Additionally, LQMM analyses showed that complex tactile information compensates for visuo-proprioceptive divergence only among individuals ranking lower in the distribution of RHI strength–in the 25^th and 50^th percentiles, that is, among weak and moderate RHI responders. For strong responders, the presumably robust effects of distance and tactile stimulation complexity (as well as their interaction) decline, which indicates that, for such individuals, even imperfect multisensory convergence triggers a convincing illusion. We speculate that strong responsiveness results from strong priors coupling visual and somatosensory signals (for a discussion see [5]), promoting RHI occurrence as long as multisensory stimulation properties do not exceed the spread of the coupling Gaussian (when the distance transcends 30cm or the rubber hand is placed outside trunk-centred peripersonal space, the ownership significantly decreases [10, 11, 27]. However, in more ‘inferentially conservative’ participants, a higher degree of visuo-proprioceptive and/or visuo-tactile convergence (within the coupling prior spread) is needed to tip the inferential balance in favor of the illusion. Therefore, when there is a large distance between hands, the RHI might be triggered only through (complex) tactile stimulation boosting the likelihood of a common cause of the incoming signals.

Our second hypothesis predicted that illusion strength would decrease with greater precision of one's proprioception, but only under the conditions of absent or simplified tactile stimulation (when proprioceptive signals have increased inferential importance). To assess individual proprioceptive competence, we used an elbow joint angular position detection task with sensory conditions mirroring those used in RHI induction. Contrary to our hypothesis, proprioceptive acuity was not correlated with RHI strength in any of the six elicitation modes. Small positive correlations were insignificant for both indicators, that is, for both the just-noticeable-difference threshold (proprioceptive accuracy) and the variability of one’s responses (proprioceptive precision). These results converge with our previous findings [8] and generalize them to another (passive) form of proprioception and a wider range of RHI elicitation conditions. Thus, an accumulating body of evidence suggests that a drop in RHI strength attributable to increased visuo-proprioceptive discrepancy is not weighted by the precision of one’s proprioceptive signals, even if their relative reliability (informativeness) is higher. This seems to contradict Bayesian accounts of body perception, although an alternative explanation might also be offered: since visual spatial acuity is superior to proprioceptive acuity by an order of magnitude [7], the effect exerted by proprioceptive signals on the result of causal inference may be relatively stable regardless of individual proprioceptive abilities. It is also worth noting that proprioceptive measurement paradigms are based on the questionable assumption that task performance reflects signal properties (precision). The question of the role of the signals' reliability in determining body ownership should perhaps be addressed more decisively through direct manipulation of signal properties, such as the addition of visual noise (cf. [49]), thereby enhancing the relative impact of proprioception. Such methods would also yield causal rather than merely correlational evidence.

Finally, we predicted that the strength of the positive association between proprioceptive drift and subjective RHI ratings will be inversely proportional to the amount of available tactile information. Contrary to our hypothesis, we found no associations between these two measures of RHI strength, regardless of the exact mode of RHI induction. This might seem peculiar given the established position of the proprioceptive drift as a “behavioral proxy of RHI” in the literature [22]. However, such results are not uncommon, as no relation between proprioceptive drift and subjective RHI is frequently reported [17–21] and the prevalence of such findings may be underestimated, given that a number of studies do not give information about the relation of these two measures (e.g., [50, 51]). It is also worth noting that, originally, proprioceptive drift was found to be a correlate of illusion prevalence time during a 30 minute period (in %) rather than its vividness [2].

This inconsistent picture of the relation between subjective ratings of RHI and proprioceptive drift might spring from the fact that the latter does not simply reflect a multisensory estimate of the location of one’s hand, but rather is a heterogeneous phenomenon determined by a multitude of extraperceptual factors. Associations between proprioceptive drift and subjective RHI tend to be found with the use of a particular measurement method: the contralateral matching task (i.e., when one reaches towards a position above an ipsilateral hand with a contralateral hand) [22]. The drift has also been shown to be hand-specific, as its magnitude is greater for one’s non-dominant hand [52]. Moreover, it is highly dependent on the way the instruction is phrased [36] and individual hypnotic suggestibility [53, 54], which suggests the involvement of higher-order cognitive processes. Thus, the methodological choices made on the basis of our hypotheses (i.e., choosing a visual judgment task involving the cognitively-mediated assessment of one’s hand’s position) might have actually promoted lower correlations between the two indices of RHI strength.

However, one could reasonably ask whether our main findings could also have been driven by cognitive mediation, given that subjectively assessed RHI strength has also been shown to increase with one’s suggestibility [53, 55] Moreover, when participants are asked about their expectations regarding the experience on an RHI questionnaire, they reproduce the typically-observed pattern of results for synchronous and asynchronous conditions without actually experiencing the illusion [56]. On this basis, it has been suggested that most RHI-based findings (or even the RHI phenomenon itself) are simply driven by demand characteristics [56]. We believe that, in the case of the presented study, this is unlikely for both methodological and theoretical reasons. First, the participants were actually not aware that their hands had been displaced and that the illusion was being elicited in two different locations. Second, our hypothesized interaction pattern was far too specific to be identified by a person without academic training in the body ownership field (unlike, for instance, the expected differences between synchronous and asynchronous stroking). Our methodological precautions notwithstanding, we agree that one should not draw far-reaching conclusions based on self-reports alone. Interestingly, a new methodological avenue for RHI research has just been opened: Chancel and Ehrsson [57] used a psychophysical (two-alternative forced-choice) task to determine which of two simultaneously stimulated rubber hands felt more like the participant’s own hand and found a preference for rubber hands placed just 5 cm closer to the participant’s hand. While this finding converges with the attenuation reported in our study (their tactile stimulation patterns would be considered “simple” in our design), it also shows that the spatial constraints of the RHI may be much tighter than previously thought. We believe that this psychophysical approach can be fruitfully coupled with methodological paradigms masking experimental manipulations (i.e., subliminal hand displacements) [23] to further reduce potential suggestibility effects and increase the sensitivity of methods examining the multisensory determinants of body ownership.

In conclusion, we found that the use of complex tactile stimulation during RHI elicitation counters the attenuating effect of increased distance between hands on the strength of the illusion. Our results indicate that the relative impact of proprioception on body attribution processes depends on the availability and informativeness of tactile signals, and is rendered ineffective by complex-structured spatiotemporal visuo-tactile correlations [5]. These findings augment our understanding of body ownership as being dynamically shaped by various combinations of multisensory inputs [3] by showing that feelings of ownership are primarily determined by informative signals from the most relevant sensory domains, rather than an unconstrained accumulation of all sensory evidence.

Supporting information

Acknowledgments

We would like to thank Jürgen Konczak, Arash Mahnan, and Jinseok Oh from the School of Kinesiology at the University of Minnesota for providing the elbow joint’s position sense threshold measurement device along with the guidelines on its implementation.