Experimental set-up and example of continuous variables.

a) Raw data sample, showing (from top) infant EEG over fronto-central electrodes, after pre-processing, infant gaze behaviour, infant vocalisations, caregiver EEG over fronto-central electrodes, caregiver gaze behaviour, caregiver vocalisations. b) Example camera angles for caregiver and infant (right and left), as well as zoomed-in images of caregiver and infant faces, used for coding. c) Topographical map showing electrode locations on the bio-semi 32-cap; fronto-central electrodes included in the theta activity analysis are highlighted in orange (AF3, AF4, FC1, FC2, F3, F4, Fz). d) Continuous behaviour and EEG variables extracted from the caregiver and infant time-series, showing (from top), caregiver looks to objects, the partner, and off-task looks, caregiver binary attention durations (for part 1), caregiver continuous attention durations (for part 2 and 3), caregiver vocalisation durations, rate of change in caregiver F0, infant looks to objects, their partner, and off-task looks, infant binary attention durations (for part 1), infant continuous look durations (for part 2 and 3), infant relative theta activity.

Testing for oscillatory patterns of attention behaviour in infants and caregivers.

a) Histogram of caregiver and infant attention episodes to objects, their partner and off-task episodes. Stacked bars show the number of episodes in each category for each 100ms bin for all episodes up to 10s in duration. b) PACF computed at different time lags for caregiver and infant gaze time series. Coloured lines show the PACF for infants (green) and caregivers (pink); shaded areas show the SEM. Dashed black lines show the PACF of shuffled attention duration data. c) Cross-correlation between caregiver and infant binary gaze variables. Black line shows the Spearman correlation coefficient at time-lags ranging from 0-10s; error bars indicate the SEM. Blue dashed line shows the permutation cross-correlation between two time series of poisson point process; one matching the average look rate of caregivers and the other, the average look rate of infants.

Relationship between infant attention durations and infant theta activity.

a) Cross-correlation between infant theta activity and infant attention durations. Black line shows the Pearson correlation at each time lag, coloured shaded areas indicate the SEM. Significant time lags identified by the cluster-based permutation analysis are indicated by black horizontal lines (*p <0.05). Cluster-based permutation analysis revealed a significant cluster of time points ranging from -2 to +6 seconds (p = 0.004). b) Linear mixed effects model, predicting infant object attention durations from infant theta activity. The model reveals a significant positive association between infant theta activity and attention durations (β=0.33; p<0.001). c) Infant theta activity split into 3 attention chunks across the duration of attention episodes, binned according to episode length. Wilcoxon signed ranks tests explored significant differences between attention chunks, for each duration bin (*p < 0.05).

Assessing forwards-predictive associations between caregiver attention durations, infant attention durations, and infant theta activity.

Black lines show the Pearson cross-correlation between two variables; coloured shaded areas indicate the SEM. Black horizontal lines show significant clusters of time lags (*p < 0.05). a) Infant and caregiver continuous attention durations. Cluster based permutation analysis revealed no significant clusters of time points, although one cluster verged on significance (p=0.10). b) Infant theta activity and caregiver continuous attention durations. Cluster-based permutation analysis indicated one significant cluster ranging from -1 to 5s (p=0.012).

Dynamic event-locked association between infant object attention and caregiver attention durations.

a) Event-related analysis showing change in caregiver attention durations around infant attention onsets to objects: black line shows average caregiver attention durations (log); coloured shaded areas indicate the SEM. Black horizontal line shows areas of significance revealed by the cluster-based permutation analysis (p < 0.05). Cluster-based permutation analysis reveals a significant cluster of time points 0 to 4 seconds after attention onset (p = 0.009). b) event-related analysis split by infant object attention-duration time bins. Black lines show average caregiver attention durations (log); coloured shaded areas indicate the SEM. Black horizontal lines shows areas of significance revealed by the cluster-based permutation analysis (p < 0.05). Permutation analysis again revealed a decrease in caregiver attention durations in the time after attention onset for looks 3-35s long. c) Modulation analysis: each bar shows the median caregiver attention duration, across participants, for each chunk, averaged across all infant object attention durations. Wilcoxon signed ranks tests investigated significant differences between chunks (*p < 0.05). d) same as c), for each infant object attention duration time bin. e) Scatter-plot showing the association between infant object attention durations and caregiver continuous attention durations. Coloured dots show each individual object attention duration; black line shows the linear line of best fit. Linear mixed effects modelling revealed a significant positive association between the two variables (β = 0.16, p < 0.001).

Assessing forwards-predictive associations between caregiver vocal behaviour, and infant attention, and infant theta activity.

Black lines show the Pearson cross-correlation between two variables; coloured shaded areas indicate the SEM. Black horizontal lines show significant clusters of time lags (*p<0.05). a) Rate of change in caregiver F0 and continuous infant attention durations. b) Rate of change in caregiver F0 and infant theta activity.

Reactive change in caregiver vocal behaviour relative to infant attention onsets.

a) Scatter plot of the association between infant attention durations and rate of change in caregiver F0. A linear mixed effects model revealed a significant positive association between the two variables (β=0.13; p< 0.001), b) Event related analysis examining reactive change in caregiver F0 in the time after the onset of an infant object look. Black line indicates the average across participants; coloured shaded area indicates SEM. c) Modulation analysis: each bar shows the median for each chunk across participants; errors bars show the SEM. Wilcoxon signed ranks tests explored significant differences between attention chunks (*p < 0.05), d) Same as c), binned by infant attention durations.

Event-related analysis for relative infant theta activity.

a) Event-related analysis showing change in infant theta activity around infant attention onsets to objects: black line shows average infant theta activity (log); coloured shaded areas indicate the SEM. Black horizontal line shows areas of significance revealed by the cluster-based permutation analysis (p < 0.05). Cluster-based permutation analysis revealed no significant clusters of time points (all p < 0.05). b) event-related analysis split by infant object attention-duration time bins. Black lines shows average infant theta activity (log); shaded areas indicate the SEM. Black horizontal lines shows areas of significance revealed by the cluster-based permutation analysis (p < 0.05). Permutation analysis again revealed no significant clusters of time points (all p < 0.05).

Assessing forwards-predictive associations between caregiver vocal behaviour, and infant attention, and endogenous oscillatory activity.

Black lines show the Pearson cross-correlation between two variables; shaded areas indicate the SEM. Black horizontal lines show significant clusters of time lags (*p<0.05). First column shows the association between caregiver vocal durations and a) infant attention durations, and b) infant theta activity. Second column shows the association between caregiver amplitude modulations and c) infant attention durations and d) infant theta activity.

Reactive change in caregiver vocal behaviour relative to infant attention onsets.

First row: scatter plots of the association between infant attention duration and a) caregiver vocal durations, d) caregiver amplitude modulations. Coloured dots show each infant object look; black line indicates linear line of best fit. Second row: event related analysis to all infant object looks for b) caregiver vocal durations, e) caregiver amplitude modulations. Black line indicates the average across participants; coloured shaded area indicates SEM. Third row: modulation analysis for each infant object look for c) caregiver vocal durations, g) caregiver amplitude modulations. Each bar shows the median for each chunk across participants; errors bars show the SEM. Wilcoxon signed ranks tests explored significant differences between attention chunks (*p < 0.05). Fourth row: same as third row, binned by infant attention durations, for d) caregiver vocal durations, h) rate of change in caregiver F0, l) caregiver amplitude modulations. Bottom row: event-related analysis showing change in caregiver vocal behaviour around infant attention onsets to objects: black line shows average across participants; coloured shaded areas indicate the SEM. Black horizontal lines shows areas of significance revealed by the cluster-based permutation analysis (p < 0.05). d) caregiver vocal durations, h) caregiver amplitude modulations.

Percentage of caregiver vocalisations that were co-vocalisations.

Box plot showing the percentage of caregiver vocalisations that were vocalisations across participants.

Percentage of clipped vocalisations.

The box plot shows the percentage of clipped vocalisations, across participants. The pink horizontal line indicates the threshold at which participants were excluded from analyses (30%).