All the formulated specific hypotheses have received support in the experiment, although some of them have been supported only partly. In particular, in support of Hypothesis-1, we observed strong positive correlations across participants between VUCM computed at the higher (FTOT) level and VORT computed at the lower (FHAND) level across all the visual feedback conditions (Fig. 8 in Results). While the correlation does not necessarily imply causation, these effects are expected from Hypothesis-1. Note that these conditions were associated with broadly varying values of the synergy index. Additional support for Hypothesis-1 was received by observations of FTOT-stabilizing synergies across conditions with FTOT feedback, while in conditions with FHAND feedback, we observed FHAND-stabilizing synergies, as reflected in the inequality VUCM > VORT and ∆V > 0. In contrast, no such synergies (∆V ≈ 0) were seen in conditions when a particular force variable, FTOT or FHAND, received no visual feedback, even when its magnitude was indirectly constrained, as was the case for FTOT in the condition with FHAND feedback (Figs. 4, 5 and 6 in Results; cf. Hypothesis-2). Overall, these results can be seen as a reflection of a trade-off between synergies at different hierarchical levels illustrated in Fig. 1 in the Introduction (see also earlier studies by Gorniak et al. 2007, 2009).

Analysis of inter-sample variance indices within single trials with the sharing pattern close to the one preferred naturally by the subjects (50:50), provided support for Hypothesis-4. The synergy index under this condition was lower compared to the inter-trial analysis (Fig. 9 in Results). These results corroborate the hypothesis that VUCM can be viewed as produced by two contributors, inter-trial sharing differences (VUCM,SH) across trials, which is obviously absent in the within-a-trial analysis, and within-a-trial covariation constraining the variability of the elements to the UCM that takes place over time during individual trials (VUCM,CoV), and both play an important role in defining the structure of variance (see also Abolins et al. 2025a, b).

Our Hypothesis-3 was related to the role of continuous vs. intermittent (i.e., off-target) visual feedback. In line with this hypothesis, we observed significantly higher VORT values in the “off-target” feedback condition, contributing to the smaller ∆V indices. These effects were significant only in the within-hand analyses, not as a main effect in the between-hand analyses. Interestingly, the data were tightly clustered across subjects in the off-target feedback condition compared to the continuous condition (Figs. 5, 6 and 7), suggesting that allowing errors in performance smaller than the target size can lead to higher consistency across subjects. The differences in VUCM between the continuous and intermittent feedback conditions were relatively small, however, suggesting that the feedback type affected primarily only one of the variance components, namely, along the ORT direction (as shown in Fig. 5 in Results).

Although variance within the UCM, by definition, has no effect on the magnitude of the salient performance variable, it reflects the stability of that variable by showing how efficient the CNS is in channeling unavoidable variations in elemental variables into the UCM. The importance of VUCM has been demonstrated in studies of neurological patients with impaired control of action stability. In particular, changes in the index of action stability during steady-state performance (∆V) between patients with multiple sclerosis and age-matched controls have been shown to reflect differences in VUCM, not VORT (Jo et al. 2016). In that study, the group differences in the magnitude of anticipatory synergy adjustments (ASAs, cf. Olafsdottir et al. 2005) in preparation for a quick action were also associated with differences in the changes in VUCM. Patients with Parkinson’s disease on- and off- dopamine-replacement drugs showed pronounced differences in the characteristics of VUCM, not VORT (Falaki et al. 2017). Along similar lines, training in conditions challenging action stability led to a significant increase in VUCM in both young and older persons, whereas VORT dropped in both groups (Wu et al. 2012, 2013).

Earlier models related the structure of inter-trial variance to both feedback-based and feed-forward circuits (Latash et al. 2005; Goodman and Latash 2006). Both possibilities have been combined into a scheme on the production of multi-element actions (Martin et al. 2009, 2019). Recent studies have offered a method to quantify the contributions of two components to VUCM (and ∆V), which have been tentatively associated with the feed-forward and feedback circuitry, by separating the effects of inter-trial variation of the sharing pattern and intra-trial co-variation of elemental variables (Solnik et al. 2015; Abolins et al. 2025a, b). We built on those studies to explore how this scheme can handle tasks where each of the effectors represents a combination of lower-level elements, and by expanding the range of feedback conditions, in particular by contrasting behaviors under continuous and intermittent (off-target) feedback.

Our findings can be interpreted within the scheme of control with two basic commands, reciprocal and coactivation (R and C), at different levels of a task-specific control hierarchy (reviewed in Latash 2010; Feldman 2015). This scheme is presented schematically in Fig. 9 for the task of producing forces with the index and middle fingers of each hand, as in our experiment. Note that there are two kinds of back-coupling loops in this scheme to the control levels: From peripheral sensory endings reflecting the performance (primarily visual feedback in our study, with possible contributions from force-sensitive endings in the hand) and from the lower (hand-specific, FHAND) control level to the higher (total force, FTOT) level. This scheme has several non-trivial predictions related to the findings in our study. First, if all the back-coupling loops function, their effects are expected to lead to the synergic inequality, VUCM > VORT, for the task-specific variable. If no target for FTOT is presented, however, the task control level shifts to the lower level of the hierarchy, and pairs are specified for each hand separately. Then, the back-coupling loops to the level related to specification of FTOT stop functioning, and no synergy stabilizing FTOT is expected (VUCM ≈ VORT) even though FTOT variability can be low due to the target-related constraints on each FHAND. In contrast, if only the FTOT target is presented, VUCM ≈ VORT for each of the finger pairs is expected. The relatively high VORT leads to sufficient variability in the contributions of each of the finger pairs to FTOT, thus facilitating the emergence of FTOT-stabilizing synergies (cf. Gorniak et al. 2007).

When all three targets are presented, however, all three of the performance variables can be stabilized by the involved back-coupling loops, two FHAND variables, and FTOT. Given the inherent competition between synergies at different hierarchical levels (see the next section), the synergy indices for all three performance variables are expected to be lower compared to their values when visual targets for only FHAND or only FTOT are presented (see Fig. 4 in Results). Subtle manipulations of the feedback, however, can sway this competition in favor of FTOT or in favor of FHAND, as we observed in the comparison of the conditions with continuous and off-target feedback. In particular, under continuous visual feedback, the subjects were accurate in keeping the cursor close to the centers of the targets, which led to relatively small variance at the FHAND level, leaving little room for having large enough VUCM at the FTOT level. Indeed, much smaller VUCM values were seen under the continuous feedback compared to the off-target feedback condition, confirming this interpretation.

We observed differences in the synergy index between the left and right hands, which were under the significance level but were typically in the direction of higher ∆V values in the left (non-dominant) hand (Fig. 4 in Results). These differences are consistent with earlier observations reporting stronger force-stabilizing synergies during steady force production by the non-dominant hand (Park et al. 2012; de Freitas et al. 2019). They are also in line with the dynamical dominance hypothesis (Sainburg 2005) suggesting better performance of the non-dominant hand in steady-state tasks, such as holding a loaf of bread, and better performance of the dominant hand in movement tasks, such as moving the knife to slice a piece of bread.

The concept of hierarchical control of movements can be dated back at least to the classical studies of Hughlings Jackson (1889), who introduced the concept of multiple cortical representations of motor elements, from single muscles to the whole body. This concept is also central for the theory on the construction of movements by Bernstein (1947), who considered all actions as being built on at least two levels, the leading level and the background level(s). Within the aforementioned theory of control with spatial referent coordinates for effectors, the control at the task level is assumed to be relatively low-dimensional, representing two basic command vectors, reciprocal and coactivation (R and C), which are defined as functions of spatial referent coordinates for the agonist and antagonist muscle groups. The implementation of any action involves a sequence of few-to-many mappings leading to the emergence of higher-dimensional sets of the R- and C-commands at the levels of the involved effectors, such as limbs and joints, and, ultimately, to time profiles of high-dimensional sets of thresholds of the stretch reflex (λ, cf. Feldman 1986) for the involved muscles and motor units.

Potentially, the output at any effector level can be stabilized by co-varied adjustments of the respective pairs (Ambike et al. 2016; Nardon et al. 2022). The action of individual muscles can be stabilized by co-varied involvement of motor unit groups (MU-modes), likely based on spinal circuitry (Madarshahian et al. 2021; Latash et al. 2023). During actions performed by large effectors up to the whole body, task-specific performance variables can be stabilized by co-varied involvement of stable muscle groups addressed as factors, primitive, or modes (reviewed in Ivanenko et al. 2006; Giszter 2015; Overduin et al. 2015; Latash 2020). Such hierarchical control has also been considered at the levels of kinetic or kinematic variables produced by individual elements involved in a multi-element task. For example, during prehensile tasks, a hierarchy has been suggested (Arbib et al. 1985) with the task-related force and moment vectors applied to the hand-held object shared between the thumb and an opposing “virtual finger”, an imaginary digit with the mechanical action equivalent to that of the actual fingers combined. At the lower level of the hierarchy, the action of the virtual finger is shared among the actual fingers. During two-arm pointing tasks, the control has been considered at the level of joint rotations moving the endpoint of each of the arms as well as at the level of the vectorial or scalar distance between the endpoints (Domkin et al. 2002, 2005).

There is, however, a catch inherent to hierarchical control schemes: A high ∆V index requires relatively high VUCM magnitudes to satisfy VUCM > VORT, which requires relatively high variability of the contributing elemental variables. At the level of analysis of each of the elemental variables, this is expected to translate into high values of VORT, which makes it hard or impossible to satisfy the inequality VUCM > VORT, i.e., to have a high synergy index. Along similar lines, a performance variable stabilized at a lower level can serve as an elemental variable at a hierarchically higher level. If this elemental performance variable is highly stable, its variations are constrained, which does not allow it to show large enough variability that may be needed to satisfy the inequality VUCM > VORT at the higher level of analysis.

In our experiment, we observed several examples of the trade-off between force-stabilizing synergies at the FHAND and FTOT levels. The general pattern was similar for the synergy index, ∆V, computed for FHAND and FTOT: Large positive values for variables with visual feedback and low (close to zero) values for variables without visual feedback (Fig. 4 in Results). However, at the upper level of the hierarchy, the modulation of ∆V for FTOT with visual feedback was primarily due to the modulation of VUCM, whereas at the lower level of the hierarchy, the modulation of ∆V for FHAND was primarily due to the modulation of VORT (see Figs. 5 and 6). This pattern was particularly obvious under continuous visual feedback on the force variables.

Additional insights were provided by the analysis of total variance (VTOT). At the FHAND level, VTOT showed no significant effects of the factors reflecting visual feedback and was dominated by VUCM across all conditions, which also showed no significant effects of feedback manipulations (see Fig. 7). In contrast, the VORT magnitude was significantly smaller when FHAND feedback was available and smaller for the continuous feedback compared to the off-target feedback (see Fig. 5). As a result, changes in VORT were the main factor affecting ∆V across the feedback conditions. At the FTOT level, VTOT depended strongly on feedback manipulations, which affected both VUCM and VORT (Figs. 5, 6 and 7). In particular, both VTOT and VUCM were much smaller when FHAND feedback was available (even in combination with FTOT feedback!). This effect was particularly strong under the continuous feedback condition. The comparison of the effects suggests that, in agreement with the described trade-off, changes in VORT at the FHAND level with feedback manipulation were the dominant factor affecting, in particular, changes in VUCM at the hierarchically higher FTOT level (cf. Hypothesis-1 in the Introduction).

A number of earlier studies provided experimental support for the trade-off between the synergy index magnitudes computed at two levels of a hierarchy (Gorniak et al. 2007, 2009). The described interpretation, however, remained speculative. Our study is the first to demonstrate significant correlations between VUCM computed at the higher (FTOT) level and VORT computed at the lower (FHAND) level of the hierarchy across the participants (Fig. 8 in Results). In other words, subjects who facilitated relatively sloppy performance at the lower level were more likely to have higher VUCM and stronger synergies at the higher level. A number of studies have provided evidence that can be seen as specific illustrations of this general rule, i.e., facilitating higher variance at the level of elements to be able to assemble task-specific synergies. These involved studies of kinematic synergies during throwing the basketball into the basket (Hasanbarani and Latash 2020) and during walking with and without stepping targets (Rosenblatt et al. 2014), as well as studies of the effects of practice challenging performance stability (Wu et al. 2012, 2013).

We have to admit that manipulating the number of salient visual targets and of the variables reflected in the visual feedback could exert effects at higher levels of the control. These factors could lead to sharing attention between the targets. In addition, the subjects could change their understanding of the task goals between focusing on individual hand force production to combined FTOT production. These factors could, by themselves, have effects on the stability of performance as reflected in our main outcome variable, such as VUCM, VORT, and ∆V. At this moment, we cannot disambiguate such effects from the ones discussed in this section and related to the neural control within a hierarchical system. While there is qualitative similarity of the effects observed in our study and in earlier studies by Gorniak et al. (2007, 2009), which did not manipulate the number of targets, additional study may be needed to address the issues of sharing attention across effectors and targets and of switching task goals when visual feedback conditions are modified. These issues relate to the levels C and D within the hierarchical control scheme introduced by Bernstein (1947) and pertain more to the field of ecological psychology (cf. Gibson 1979; Turvey 2007).

Force production tasks are particularly sensitive to the availability and quality of visual feedback. In particular, when visual feedback becomes unavailable, the force magnitude drifts, typically to lower values, and the performer is unaware of the drift even when it reaches substantial magnitudes, up to 30–40% of the initial force level (Vaillancourt and Russell 2002; Ambike et al. 2015). These phenomena have been interpreted as reflecting the loss of stability of the control variables at the task level (Abolins and Latash 2022). Drifts in the C-command have been documented and interpreted as primary factors causing the force drifts (Reschechtko and Latash 2017; Cuadra et al. 2021). Force drifts can be seen as natural consequences of partial loss of stability of the force magnitude. This interpretation is corroborated by earlier studies exploring inter-sample variance during individual trials and showing that the motor output samples demonstrate the synergic signature over time, VUCM > VORT, but only under continuous visual feedback. This inequality disappeared (VUCM ≈ VORT) when visual feedback was unavailable (see also De et al. 2024).

Note that the crucial importance of visual information for the control of force has been documented primarily during accurate force production in isometric conditions. Prehensile tasks involving object manipulation present a more complex picture, suggesting an interplay between sensory information of visual, haptic, and proprioceptive modalities. In particular, visual information may be unable to ensure proper feed-forward control of the moment of force applied to an asymmetrical object (Zhang et al. 2010; Craje et al. 2013; Shibata and Santello 2017). Under such conditions, even when the subjects observed the placement of an additional load or a change in the material density that changed the loading symmetry of the object, they were unable to avoid object tilt during the fast lifting action, although the tilt magnitude quickly reduced over a few trials. In other words, visual information was unable to ensure adequate time profiles of the total moment of force applied by the digits to the object, although visual information has been shown to be important for digit placement and swift digit-based force control (Bland et al. 2023). We would like to emphasize that in most of the cited studies deviations of performance variables from their desired values were quantified, i.e., the accuracy of performance of salient performance variables such as the vertical orientation of the object. We focus on the stability of performance variables, as reflected in the relative magnitudes of two variance components, VUCM and VORT. Since VUCM, by definition, has no effects on the salient performance variable, comparisons between such studies should be done with caution. The nature of the studied tasks could also play a role in the role of visual information: In the current study, isometric force production was studied, while in a number of cited earlier studies, the tasks involved object manipulation by the hand. Differences in the control of movement tasks and isometric force production tasks have been discussed recently (De et al. 2025).

During constant force production tasks, changing the frequency of presentation of visual feedback has a major impact on the accuracy of task performance (Sosnoff and Newell 2005, 2006). These observations are particularly relevant to our comparison of the continuous and off-target feedback conditions. In the off-target condition, force drifts could be expected, similar to those mentioned earlier. The size of the target naturally limited the magnitude of those drifts, but it still allowed larger force deviations from the center of the target, resulting in larger VORT (as observed in our study). Deviations along the UCM could also take place, but these were unlikely to be corrected since, by definition, they had no effect on the salient performance variable. Presenting continuous feedback also allowed the subjects to show variable accuracy of performance: Some of the subjects could be happy simply to keep the cursor inside the target, while others could strive towards perfection and tried to keep the cursor as close to the center of the target as possible during the trials. This could be the reason for the larger across-subjects variability in VORT under the continuous feedback compared to the off-target feedback, although the average magnitude of VORT was larger in the latter condition.

The control of force under the off-target visual feedback can be seen as consisting of two qualitatively different phases. When the cursor was inside the target, the feedback loop was ineffective, and force drifts similar to those described earlier could be expected over variable time intervals that took the cursor to reach the border of the target. When the cursor exited the target zone, visual feedback-based corrections were expected to bring the cursor back into the target. This type of control can be compared to the concept of intermittent control suggested for a range of actions from balancing an inverted pendulum with the hand to the control of posture during quiet standing (Bottaro et al. 2005; Loram et al. 2006; Gawthorpe et al. 2011).

It is of interest that the differences between the continuous and off-target feedback conditions were seen in all the variance variables, including VTOT, at the higher level of the hierarchy, i.e., when computed with respect to FTOT as the sum of two FHAND variables (Figs. 5, 6, and 7). These differences in VTOT and VUCM disappeared when analysis was performed at the lower level, i.e., when these indices were computed with respect to each FHAND as the sum of the forces produced by the index and middle fingers of the corresponding hand. The effects were seen, however, for VORT reflecting the continuous vs. intermittent control. These findings emphasize the role of VORT modulation at the lower level as a factor defining the range of VUCM at the higher level, as confirmed by the statistically significant correlations between these variables found in Fig. 7.