Analysis of data from current study using cross correlation method

To demonstrate how the cross correlation works with data from the current study, I will continue with the example of gaze following. First, I will repeat the example shown above in Figure 4.1: when the subordinate gazes towards the bait, does the dominant gaze towards the bait? As shown below in Figure 4.5, after the subordinate gazed towards the bait, the dominant gazed towards the bait significantly more than expected from the within-trial shuffled control (collapsed data should be compared to the within-trial baseline). The correlogram on the left of each figure plots the cross correlation as well as the between- and within-trial shuffled controls. The Significance Values graph on the right of each figure plots the probability that the experimental data are different from the between- and within-trial shuffled controls.

FIGURE 4.5: Referent behaviour: subordinate gazing towards the bait. Target behaviour: dominant gazing towards the bait. After the subordinate gazed towards the bait, the dominant gazed towards the bait significantly more than expected from the within-trial shuffled control (peak at time= +4, r= 0.2897, n= 777; –log-likelihood= 23.6418, p<0.05)

When the reverse situation is analysed (i.e., whether the subordinate looks towards the bait after the dominant starts looking towards it), it appears that the subordinate had already been gazing towards the bait by the time the dominant started to gaze at time= 0. The data in Figure 4.6 below are the same as in Figure 4.5 above: the cross correlation with the referent and target swapped results in a graph that is reversed in time along the x-axis.

FIGURE 4.6: Referent behaviour: dominant gazing towards the bait. Target behaviour: subordinate gazing towards the bait. After the dominant gazed towards the bait at time= 0, the subordinate had already been gazing towards it significantly more than expected from the within-trial shuffled control.

The dominant followed the subordinate’s gaze towards the bait; but did she follow gaze away from the bait? This is difficult to answer, since ‘away’ can be any other direction except ‘towards,’ and while both chimpanzees may be looking away from the bait, they might not be gazing towards the same place. This is exactly why I need to use absolute data, in addition. Thus, I analysed gaze following towards the four absolute quadrants of the enclosure. Figures 4.7-4.10 cross-correlate the referent behaviour at time= 0 of the subordinate gazing towards Quadrant 1 with the target behaviour of the dominant gazing towards quadrants 1, 2, 3, and 4; each cross correlation is represented in its own graph.

Figure 4.7 shows the cross correlation of the subordinate and the dominant both gazing towards Quadrant 1: after the subordinate gazed towards Quadrant 1 (and after she did

not gaze), the dominant also gazed (and did not gaze), and this relationship is significantly different from the between-trial shuffled control (absolute data should be compared to the between-trial baseline). It appears that the dominant’s gaze direction is contingent on the subordinate’s direction of gaze.

FIGURE 4.7: Referent behaviour: subordinate gazing towards Quadrant 1. Target behaviour: dominant gazing towards Quadrant 1. After the subordinate gazed towards Quadrant 1, the dominant gazed towards Quadrant 1 significantly more than expected from the between-trial shuffled control (peak at time= +2, r= 0.1420, n= 843; –log-likelihood= 5.1116, p<0.05)

The graphs in Figures 4.8-4.10 below show the value of this method of analysis: when the subordinate was gazing towards Quadrant 1, the correlation coefficient of the dominant gazing towards Quadrant 2, 3, or 4 is low and not significantly different from the between- trial shuffled control.

FIGURE 4.8: Referent behaviour: subordinate gazing towards Quadrant 1. Target behaviour: dominant gazing towards Quadrant 2. After the subordinate gazed towards Quadrant 1, there is no relation of the dominant gazing towards Quadrant 2 compared to the between-trial shuffled control.

FIGURE 4.9: Referent behaviour: subordinate gazing towards Quadrant 1. Target behaviour: dominant gazing towards Quadrant 3. After the subordinate gazed towards Quadrant 1, there is no relation of the dominant gazing towards Quadrant 3 compared to the between-trial shuffled control.

FIGURE 4.10: Referent behaviour: subordinate gazing towards Quadrant 1. Target behaviour: dominant gazing towards Quadrant 4. After the subordinate gazed towards Quadrant 1, there is no relation of the dominant gazing towards Quadrant 4 compared to the between-trial shuffled control.

As expected, the between-trial shuffled controls on these graphs generally hover around zero: there is no relationship between points when the relative time-locked

relationships are disrupted. Additionally, there seems to be no relationship between the two subjects’ gaze behaviour towards incongruent quadrants. The graphs serve to demonstrate this intuitive lack of relationship, and the fact that there is a sustained correlation when both

subjects gazed towards Quadrant 1 emphasizes that both subjects were often gazing in the same direction. This pattern holds true for the subordinate gazing towards quadrants 2, 3, and 4: the dominant also gazed towards the same direction at a significantly high level, but not towards any other direction (see Chapter 6: Gaze Following). Therefore, the chimpanzees not only gaze towards the relative position of the bait at the same time, but in general after the subordinate starts to gaze towards a specific direction in the enclosure the dominant also gazes towards the same direction as the subordinate.