When interacting with infants, human adults modify their behaviours in an exaggerated manner. Previous studies have demonstrated that infant-directed modification affects the infant's behaviour. However, little is known about how infantdirected modification is elicited during infant-parent interaction. We investigated whether and how the infant's behaviour affects the mother's action during an interaction. We recorded three-dimensional information of cup movements while mothers demonstrated a cup-nesting task during interaction with their infants aged 11 to 13 months. Analyses revealed that spatial characteristics of the mother's task demonstration clearly changed depending on the infant's object manipulation. In particular, the variance in the distance that the cup was moved decreased after the infant's cup nesting and increased after the infant's task-irrelevant manipulation (e.g. cup banging). This pattern was not observed for mothers with 6-to 8-month-olds, who do not have the fine motor skill to perform the action. These results indicate that the infant's action skill dynamically affects the infant-directed action and suggest that the mother is sensitive to the infant's potential to learn a novel action. A video abstract of this article can be viewed at: https://www.youtube.com/watch?v=VNS2IHwLIhg&feature=youtu.be Research highlights• We examined how a mother's task demonstration changes depending on the infant's action skill during infant-mother interaction by recording the mother's object manipulation with a three-dimensional motion tracking system.• The variance in object movements made by the mother increased when the infant did not reproduce the task while it decreased when the infant did so.

This paper presents a computational approach to measuring information transfer in infant-caregiver interaction. It is supposed that both an infant and a caregiver mutually shape the interaction by sending various signals to each other, of which the dynamic structure changes according to the infant's age. We investigated such developmental change both in infants and caregivers by measuring transfer entropy within and between their body movements. Our analysis demonstrated that infants significantly improve their body coordination and social contingency between 6 to 13 months of age. Their gaze, for example, start responding to caregivers' gaze, which indicates the development of joint attention. The coordination between infants' two hands also drastically improves as they grow. Of particular interest is that such development in infants elicits caregivers' adaptation. Caregivers change their social responses and body coordination to a more sophisticated manner in order to further facilitate infant development. Our approach is the first study to quantitatively verify the "co-development" of infants and caregivers, which appears as increases in information transfer within and between their behaviors.

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