Experiment 1: Looming and receding results in neutral no-illusion context

The mean RTF in Experiment 1 was analyzed by a two-way ANOVA with the within-subject factors direction (two levels: looming, receding) and distance (six levels: 0.3 m, 0.6 m, 0.9 m, 1.2 m, 1.5 m, 1.8 m). This revealed a significant main effect of direction (F(1, 21) = 12.27, p =.002, ηp2 = 0.37), a significant main effect of distance (F(5, 105) = 2.95, p =.016, ηp2 = 0.12), and a significant interaction between direction and distance (F(5, 105) = 2.32, p =.048, ηp2 = 0.10). To further understand this interaction (see Fig. 3a), we analyzed the simple main effect of distance on RTF separated by direction. While there was a significant main effect of distance for looming stimuli (F(5, 105) = 5.03, p <.001, ηp2 = 0.19), there was no main effect of distance for receding stimuli (F(5, 105) = 0.33, p =.892, ηp2 = 0.02). Additionally, post-hoc comparisons between looming and receding stimuli for each distance level revealed that RTF was significantly greater for looming compared to receding stimuli at 0.3 m (V = 215, padjusted =.014, r =.61), as well as at 0.6 m (t(21) = 3.78, padjusted =.007, d = 0.81), while this comparison was not significant at the other distance levels (padjusted >.05).

Taken together, the results for Experiment 1 show that in a neutral no-illusion context, there is a distance-dependent modulation of multisensory facilitation for looming stimuli, with greater multisensory facilitation close to the physical body, whereas there is no distance-dependent modulation of multisensory facilitation for receding stimuli. This is in line with findings showing that PPS around the physical body responds preferably to looming compared to receding stimuli (Fogassi et al. 1996; Graziano et al. 1997; Bufacchi and Iannetti 2018) and there usually being no (or a weaker) distance-dependent modulation of multisensory facilitation for receding stimuli (e.g., Serino et al. 2015; de Haan et al. 2016; Kandula et al. 2017).

Fig. 3

Plots of RTF results from Experiment 1 (neutral no-illusion context) and 2 (with FBI induction) by key experimental factors, as well as ownership scores in Experiment 2. (a) RTF as a function of direction and distance in Experiment 1. (b) Box and whisker plot showing ownership scores by stroking condition in Experiment 2. RTF as a function of stroking condition and distance for looming (c) and receding trials (d) in Experiment 2. For the RTF plots, negative RTF signifies a quicker reaction time in visuo-tactile compared to unimodal tactile trials, error bars show ± 1 standard error of the mean, and the location of the participant and avatar/neutral object are shown on each end of the x-axis. For the box and whisker plot, the line in the middle of the box shows the median, the box represents the first and third quartile, and the whiskers represent the lowest value within 1.5 × IQR below the first quartile and the highest value within 1.5 × IQR above the third quartile. An asterisk represents a significant difference between directions in plot (a), whereas in plots (b-d) an asterisk represents a significant difference between stroking conditions. The hashtag in plot (d) represents a marginally significant (padjusted =.051) difference between stroking conditions

Experiment 2: Looming and receding results under induction of FBI

As a manipulation check, ownership scores between the synchronous and asynchronous stroking condition were compared using a Wilcoxon signed-rank test. This revealed significantly greater ownership ratings in the synchronous compared to the asynchronous condition (V = 219, p <.001, r =.78), suggesting that synchronous stroking successfully elicited a stronger FBI effect compared to asynchronous stroking (see Fig. 3b).

A three-way ANOVA with the within-subject factors direction (two levels: looming, receding), stroking condition (two levels: synchronous, asynchronous), and distance (six levels: 0.3 m, 0.6 m, 0.9 m, 1.2 m, 1.5 m, 1.8 m) was used to analyze the mean RTF. This revealed a significant main effect of stroking condition (F(1, 21) = 4.76, p =.041, ηp2 = 0.19), a significant two-way interaction between direction and distance (F(5, 105) = 8.81, p <.0001, ηp2 = 0.30), and a significant three-way interaction between direction, stroking condition, and distance (F(5, 105) = 2.93, p =.016, ηp2 = 0.12).

To investigate the three-way interaction further, we conducted additional two-way ANOVAs on RTF split by direction with the factors stroking condition and distance. For looming stimuli we found a significant main effect of stroking condition (F(1, 21) = 4.69, p =.042, ηp2 = 0.18) and a significant main effect of distance (F(3.27, 68.71) = 4.04, p =.009, ηp2 = 0.16), but no interaction between stroking condition and distance (F(5, 105) = 0.79, p =.558, ηp2 = 0.04). This signifies a distance-dependent modulation of multisensory facilitation relative to the physical body (as in Experiment 1) and a difference in multisensory facilitation between stroking conditions, showing stronger multisensory facilitation in the synchronous than asynchronous condition; however, these effects were independent of each other for looming stimuli, such that the distance-dependent modulation of multisensory facilitation did not differ between stroking conditions (see Fig. 3c).

On the other hand, the two-way ANOVA for receding stimuli revealed a significant interaction between stroking condition and distance (F(5, 105) = 2.64, p =.027, ηp2 = 0.11), which shows that the distance-dependent modulation of multisensory facilitation differed between stroking conditions. To better understand this interaction for receding stimuli we analyzed the simple main effect of distance on RTF in both stroking conditions. This revealed a significant main effect of distance in the synchronous (F(5, 105) = 2.98, p =.015, ηp2 = 0.12), but not in the asynchronous condition (F(3.31, 69.43) = 1.62, p =.189, ηp2 = 0.07). Post-hoc comparisons at each distance level between synchronous and asynchronous stroking found a significantly greater RTF for synchronous stroking at 1.5 m (t(21) = 3.82, padjusted =.006, d = 0.82) and a marginally significant difference at 1.2 m (t(21) = 2.82, padjusted =.051, d = 0.60). No significant differences were found at the other distance levels (padjusted >.05). These results (see Fig. 3d) suggest that the FBI, elicited in the synchronous condition, resulted in a distance-dependent modulation of multisensory facilitation for receding stimuli in proximity to the avatar.

Taken together, the results of Experiment 2 imply that induction of the FBI leads to a transfer of PPS to the avatar.

Experiment 3: Receding results under induction of FBI between YAs and OAs

Separate Wilcoxon signed-rank tests (due to comparing paired Likert scale data) for both YAs and OAs were used to compare ownership scores between the synchronous and asynchronous condition. This revealed significantly greater ownership ratings for synchronous compared to asynchronous stroking for both YAs (V = 329.5, p <.0001, r =.75; see Fig. 4a) and OAs (V = 213, p =.005, r =.57; see Fig. 4c). However, Wilcoxon rank-sum tests (due to comparing independent Likert scale data) revealed that ownership ratings in the synchronous condition were significantly lower for OAs compared to YAs (W = 559.5, p <.001, r =.51) and that the difference in ownership ratings between synchronous and asynchronous stroking (calculated as synchronous scores - asynchronous scores) was significantly smaller for OAs than for YAs (W = 496, p =.010, r =.36). This indicates that we were successful in creating stronger FBI effects in the synchronous compared to the asynchronous condition for both YAs and OAs, but that this effect was weaker and not as differentiated for OAs.

Note that when visualizing the ownership results, to follow standard box-plot conventions, ownership scores falling more than 1.5 × IQR below the first quartile or above the third quartile were visualized as individual grey dots. One OA participant had an ownership score exceeding this threshold in both the synchronous (2.00 × IQR above third quartile) and asynchronous (2.02 × IQR above third quartile) condition (see Fig. 4c). However, given that large inter-individual variability is expected for subjective ratings, these values were only marked for visualization purposes but were not removed from analysis.

For the analysis of mean RTF in Experiment 3, we conducted a three-way ANOVA with the between-subject factor age (two levels: young, old), and the within-subject factors stroking condition (two levels: synchronous, asynchronous) and distance (six levels: 0.3 m, 0.6 m, 0.9 m, 1.2 m, 1.5 m, 1.8 m). We found a significant main effect of age (F(1, 51) = 10.22, p =.002, ηp2 = 0.17), a significant main effect of distance (F(3.56, 181.48) = 7.59, p <.0001, ηp2 = 0.13), and a significant interaction between age and distance (F(3.56, 181.48) = 4.88, p =.001, ηp2 = 0.09). The three-way interaction between age, stroking condition, and distance was however not significant (F(4.10, 208.99) = 0.79, p =.534, ηp2 = 0.02). Note that to control for potential factors that could influence the age comparison in our setup, we conducted a covariate analysis with measured tactile thresholds, as these are known to increase with age (Verrillo 1980; Ekman et al. 2021), as well as the time spent in VR and gaming environments. As adding these factors as covariates did not affect the main patterns and interpretations of results, we here reported the ANOVA results without these covariates (for further details and results of the covariate analyses see text, Table S3 (gaming and VR questionnaire in German), and Table S4 (gaming and VR questionnaire translated into English) in the Supplementary Materials).

Despite the three-way interaction not being significant, we proceeded to conduct additional two-way ANOVAs on RTF with the within-subject factors stroking condition and distance separately for YAs and OAs. This was decided due to the exploratory nature of the factor age in our analysis. For OAs we found a significant main effect of distance (F(3.24, 80.97) = 5.41, p =.001, ηp2 = 0.18), but no main effect of stroking condition (F(1, 25) = 0.89, p =.355, ηp2 = 0.03), or interaction between distance and stroking condition (F(3.39, 84.64) = 0.95, p =.428, ηp2 = 0.04). To reaffirm the absence of an interaction between stroking condition and distance in OAs and to allow a comparison to the results for YAs, we ran post-hoc comparisons of RTF between stroking conditions at each distance level and found no significant results (padjusted >.05). These results (see Fig. 4d) show that in OAs there was no FBI induced distance-dependent modulation of multisensory facilitation for receding stimuli, suggesting that there was no transfer of PPS to the avatar in this age group.

Conversely, the same analysis in YAs revealed a significant main effect of distance (F(3.23, 84.02) = 7.91, p <.0001, ηp2 = 0.23) and a significant interaction between stroking condition and distance (F(5, 130) = 2.37, p =.043, ηp2 = 0.08). To further investigate this interaction, we analyzed the simple main effect of distance on RTF in both stroking conditions. This revealed a significant main effect of distance in the synchronous (F(3.67, 95.47) = 6.72, p <.001, ηp2 = 0.21) and asynchronous condition (F(5, 130) = 3.85, p =.003, ηp2 = 0.13). Post-hoc comparisons of the RTF at each distance level between stroking conditions showed a significantly greater RTF for synchronous compared to asynchronous stroking at 1.2 m (t(26) = 2.90, padjusted =.045, d = 0.56), while the other distance levels did not show a significant difference (padjusted >.05).

Given that a simple main effect of distance was found in both stroking conditions, we conducted an additional analysis to examine the difference in strength of the distance effect between stroking conditions in YAs. For this we fit simple linear models of RTF across distance for each YA in both stroking conditions. The resulting individual model slopes in each stroking condition were then compared, showing significantly steeper negative slopes in the synchronous (M = − 10.93, SD = 12.00) compared to the asynchronous (M = -5.26, SD = 9.83) condition (t(26) = 2.71, p =.012, d = 0.52). This indicates a stronger increase in multisensory facilitation with increasing proximity to the avatar for synchronous compared to asynchronous stroking.

The pattern of results for YAs (see Fig. 4b) shows that the FBI led to a significant increase in multisensory facilitation for receding stimuli in proximity to the avatar, thus replicating the distance-dependent modulation of multisensory facilitation for receding stimuli observed in Experiment 2.

Taken together, the results of Experiment 3 replicate the implied transfer of PPS to the avatar under induction of the FBI observed in Experiment 2. However, this effect was only found in YAs and was not present in OAs.

Fig. 4

RTF and ownership score results for YAs (top panel) and OAs (bottom panel) in Experiment 3. Box and whisker plot showing ownership scores by stroking condition for YAs (a) and OAs (c). RTF as a function of stroking condition and distance for YAs (b) and OAs (d). For the RTF plots, negative RTF signifies a quicker reaction time in visuo-tactile compared to unimodal tactile trials, error bars show ± 1 standard error of the mean, and the location of the participant and avatar are shown on each end of the x-axis. For the box and whisker plots, the line in the middle of the box shows the median, the box represents the first and third quartile, and the whiskers represent the lowest value within 1.5 × IQR below the first quartile and the highest value within 1.5 × IQR above the third quartile. Following standard box-plot conventions, values more than either 1.5 × IQR below the first quartile or 1.5 × IQR above the third quartile are visualized as grey dots. Importantly, the two values shown exceeding this threshold in plot (c) were not removed from analysis. Across all plots, a significant difference between stroking conditions is represented with an asterisk