Developmental dynamics for action differentiation
In this study, we developed a dynamical system model for explaining action differentiation depending on the relationship between the infant and environment in MCR. In addition to a pair of limb and mobile oscillators with positive feedback for reinforcement as introduced by the KF model (Kelso and Fuchs 2016), bifurcation dynamics were incorporated for selecting the enhancement or inhibition of self-movements in response to detecting contingencies between the limb and mobile movements based on self-referential processing using the efference copy. Whereas the monostable state led to an inability to differentiate actions, the bistable state made it possible to differentiate actions. The changes in the control parameter b induced bifurcation between the monostable (b = − 5) and bistable (b = 15) states; this was in good agreement with the behaviors of the 2- and 3-month-old infants in Watanabe's experimental study, respectively (Watanabe et al. 2011).
This study showed that the time evolutions of the variables in this model were qualitatively different for different values of the control parameter and under different experimental conditions. In the 2-month parameter regime, the variable u was increased in response to the onset of the mobile oscillation over the time scale determined by τ₁; correspondingly, the limb oscillation frequency was slightly increased in both of the interaction and stimulation conditions. In the 3-month parameter regime, the variables of the system evolved over three time scales. First, the time evolution of u over the time scale determined by τ₁ was similar to that in the 2-month regime. Then, the variable v(t) evolved over the second time scale determined by τ₂ towards a positive value in the interaction condition and a negative value in the stimulation condition. These changes in v further induced changes in u, leading to the enhancement or inhibition of the limb oscillations. Third, the phase relationship between the x and y oscillations changed from in-phase to anti-phase synchronization and further enhanced the limb oscillation only in the interaction condition. Taken together, the present model not only reproduced the specific results of previous experimental studies, but also provided a framework for a comprehensive understanding of the development of action differentiation under various environmental conditions in terms of a dynamical system.
The model can be used to provide clues for testing detailed mechanisms for the development of action differentiation in future studies. For instance, the time evolution of the limb movements over the first and second time scales in the interaction condition with 3-month-old infants was not evident in the infant-averaged curve for the baseline ratio in the experiment (Watanabe et al. 2011). To clarify this, a detailed analysis of this behavior is required on an individual basis. The emergence of the phase transition towards the further enhanced state over the third time scale in the interaction condition with 3-month-old infants has not been proven in experimental studies. Future studies are needed to analyze both the limb and mobile movements (Kelso and Fuchs 2016). In an intermediate regime of the control parameter b between 2 and 3 months of age, the model showed the presence of bistable states, but no phase transition to the further enhanced state. Future studies should test whether this is the case in infants aged between 2 and 3 months.
Internal state dynamics and memory
The dynamic changes in variables u and v in this model can be regarded as those of the internal state of the infant brain for producing actions over multiple time scales. Such dynamics were also detailed in previous modeling studies on the dynamical systems of infant behaviors, such as studies on habituation and dishabituation (Schöner and Thelen 2006) and the A-not-B error effect (Aerdker 2022). Thus, it is important to study the commonalities and differences in the internal state dynamics among the behaviors of infants in future studies.
The MCR paradigm was originally discussed in relation to infants’ long-term memories (Rovee and Sullivan 1980; Watanabe and Taga 2006; Sen and Gredebäck 2021). In our model, the variable v functions as a memory for the experimental conditions. For the simulation of 3-month-old infants, u declines immediately after the disconnection of the mobile, whereas v maintains the value of the experimental periods, i.e., a positive value in the interaction condition and negative value in the stimulation condition. Although these results demonstrate the mechanisms of the memory generation and maintenance, the model did not include a decay property for the memory. Thus, the model in the present study cannot account for amnesia in infants. Further extension of the model to incorporate long-term memory dynamics is crucial for future studies.
Putative neural mechanisms
In our model, the bifurcation and phase transitions were induced by increases in the parameter b. What is the neural substrate for the parameter b? Watanabe et al. (2011) argued that the change from 2-month-old to 3-month-old behavior in MCR could be explained based on changes from subcortical to cerebral cortex-based mechanisms. In addition, recent progress in studies of the subplate (Molnár et al. 2020) suggests that the subplates may be involved in developmental changes in behavior. The subplate is formed prior to the cortical plate in the early fetal period, and then plays an important role in establishing the cortical layer (Ohtaka-Maruyama et al. 2018), thalamocortical tract (Molnár et al. 2020), and cortico-cortical network (Kostović 2020) in later fetal periods. Around the term period, it degenerates owing to apoptosis, and the cortical layers become a major part of the cortex (Molnár et al. 2020). Thus, the putative neural mechanism for the behavioral changes in MCR is discussed in relation to the model herein.
Spontaneous movements appear early in the fetal period and are likely induced by the spinal cord (de Vries et al. 1982). As the subplate develops, the spontaneous activity of the subplate neurons becomes involved in modifying spontaneous movements (Milh et al. 2007). After birth, the spontaneous movements, such as general movements, are maintained as the major body movements (Prechtl 2001). The characteristics of general movements change at approximately 2 months after birth and gradually disappear after 3 months (Einspieler and Prechtl 2005). This process coincides with the timing at which the subplate neurons undergo degeneration and the cortical neurons play major roles in movement generation, suggesting that the subplates play an important role in the regulation of spontaneous movements until 2 months of age (Hadders-Algra 2007, 2018). In addition, the thalamocortical pathway for transmitting sensory information to the cortex is first formed in the subplate, and the subplate neurons respond to sensory stimuli (Molnár et al. 2020). Therefore, it is speculated that the basis for the reinforcement of spontaneous movements in response to sensory stimulation can already be in place in the later fetal period, and that the behavior of the mobile task in 2 month-old infants may be generated by a mechanism similar to that established during the fetal period.
At 3 months of age, the subplates are already degenerated, and the cerebral cortex is thought to exhibit mature function. At this age, general movements are replaced by goal-directed movements, in which a specific pattern of movements using a specific part of the body is selected, and unnecessary spontaneous movements are suppressed (Watanabe and Taga 2006; Hadders-Algra 2007; Watanabe et al. 2011). To generate such movements, one needs to have cortical mechanisms to create multiple stable states and make state transitions according to the situation and goal. In this model, the control parameter b causes bifurcation between the monostable and bistable states in the equation of the variable v representing the function of the cerebral cortex. The two equilibrium points posterior to the pitchfork bifurcation, with increases in the parameter b, have larger positive and negative values, amplifying the difference between the enhancement and inhibition of action, respectively. In addition, brain imaging studies have revealed that the cortical mechanism involved in audiovisual changes rapidly develops between 2–3 months, enabling the mature processing of stimulus features (Watanabe et al. 2008; Watanabe et al. 2010). These cortical mechanisms are thought to be essential for contingency detection in mobile tasks using the efferent copy signals (Sperry, 1950; von Holst and Mittelstaedt, 1950; Sommer and Wurtz, 2008) involved in the movement generation and sensory signals triggered by the mobile movements. This has been supported by experiments measuring the event-related potentials of the brains of 3 month-old infants in response to visual stimuli, in which the contingencies between self-generated movements and visual stimuli were manipulated (Zaadnoordijk et al 2020; Meyer and Hunnius 2021).
In summary, the control parameter b is an index that represents the degree of subplate degeneration and cortical maturation.
Developmental emergence of physical agency
Finally, we discuss how physical agency (Gergely 2002) emerges in early infancy. It has been suggested that experiments with young infants using the MCR paradigm can provide clues to understanding the manifestation of physical agency (Watanabe et al. 2011; Sen and Gredebäck 2021; Bednarski et al. 2022). Kelso and Fuchs (2016) constructed a dynamical system model including a mechanism of positive feedback, in which a mobile movement that accompanied a movement further enhanced it. In that model, increasing the control parameter caused a transition in the phase relationship between the limb oscillations and mobile oscillations, and stabilized the movements in the highly enhanced state. They further argued that this transition was the origin of agency.
In our model, it was revealed that increasing the value of the control parameter caused a similar phase transition from a state in which the mobile was passively pulled by the oscillatory movements of the limb to a state in which the mobile and limb oscillations mutually enhanced each other under the interaction condition. The latter state converged to a stable attractor as a whole system through rhythmic interactions of the brain, body, and environment; this phenomenon has been referred to as "global entrainment" (Taga et al. 1991; Taga 2021). This is consistent with Gibson’s view emphasizing the bidirectional coupling of action and perception (Gibson 1977), and is considered to represent an important requirement for adaptive behavior to occur in the environment. Furthermore, this study clarified that this phase transition did not occur under stimulation conditions. In other words, the transition occurred only when the limb oscillation and mobile oscillation had bidirectional interactions. This abrupt change cannot be accounted for by a simple reinforcement learning model (Zaadnoordijk et al 2018), and may represent an important property for the generation of behavior as a physical agency.
However, to act as a physical agency, one must change their behavior in the timing as they want, which further requires a meta-system to enable the choices of whether to act. In this sense, not only the enhancement of action, but also the inhibition of action according to the situation infers the mechanism for physical agency (Watanabe et al. 2011). This property cannot be reproduced using the KF model (Kelso and Fuchs 2016). Thus, in addition to the positive feedback mechanism of the KF model, the present model incorporated the dynamics of multiple internal states for changing behaviors according to the situation. The model also incorporated a mechanism for correlating the efference signal to move the limb and signals originated from mobile movements, so as to be sensitive to precise differences in contingencies between the infant's own actions and environmental changes. As a result, the model of this study showed the capability to inhibit the action and thereby break the action-perception coupling. This study further captured the developmental changes in action differentiation between 2-month-and 3-month-old infants as a bifurcation phenomenon. This provides a framework for understanding the mechanisms of the development of physical agency.