For over 200 years researchers have been developing graphical techniques that allow us to use our capacities for visual pattern recognition to see regularities in quantitative data that would otherwise be difficult to discern [12-14]. This paper provides an example of how we might use those same capacities with new graphical techniques such as music notation graphs to understand better social interaction in human and animal groups. I suggest that music notation graphs can be of particular help in a variety of fields interested in social interaction in humans, animals, and machines such as behavioural ecology, behavioural economics, social organization in animals, development of social networks in humans, human conversational analysis, and the coordination of actions in social robots.
In this paper, I have shown how the basic music notation concept can be used to display extensive, detailed records of interaction in an easily seen and understood format; to facilitate the comparison of processes of interaction in different groups of real animals and in real animals versus those generated by computer simulations; to discover the occurrence and context of small-scale sequences of interaction during the formation of groups; and to break down the interaction records of a larger group into simultaneous records of interaction in different subgroups. While I have illustrated these different possibilities using the example of hens forming dominance hierarchies, I have suggested that music notation could be used as a general method for visualizing many kinds of social interaction in groups of animals and humans. Let me raise several considerations that are important in doing this: limitations on the number of group members that can be displayed, showing different kinds of behavioral acts in the same music notation graph, indicating behaviours with durations, and layering other sorts of data with music notation displays, showing simultaneous interactions, and facilitating the use of music notation displays by colour-blind researchers.
First, concerning group size, music notation techniques are probably best suited for groups with relatively few members. I have experimented with hypothetical data on hierarchy formation, and here I would think that interactions among seven to ten individuals are the maximum that can be shown clearly with music notation graphs. With larger numbers of individuals it becomes increasingly difficult to pick colors that allow a user to clearly distinguish among the lines and arrows representing the individuals. However, choosing a color background for the graph, such as a medium or dark blue, rather than just using white as I have here, makes it easier to chose a larger set of distinct colors for individuals. Showing interaction among a larger number of individuals becomes especially difficult when the interaction is not well-ordered, for example, if there are many attacks and counter-attacks between individuals. But if the interactions are well-ordered or relatively infrequent, it might be possible to make good use of music notation graphs at the upper end of this range, or perhaps even extend it a bit.
Second, in displaying different kinds or intensities of behavioural acts, the colours of arrows and the shapes of both arrowheads and arrow shafts might be altered. For example, in order to show differing intensities of interaction, say, from threat displays to physical aggression in two-animals contests, a basic color could be chosen for each animal with lighter shades indicating threat behaviors and darker shades indicating escalating physical contacts. In the case of completely different kinds of behaviors, the heads or shafts of the arrows could be altered. For example, I could have used modified heads to distinguish different kinds of aggressive contacts in the chickens, say, a regular arrowhead (the kind shown in the graphs) for a peck; a small, closed circle for one chicken scratching another; and a small, open square for one chicken striking another with its foot. In other situations arrow shafts might be modified, for example, in small human groups, a dotted shaft might signify an interruption, a wavy shaft a question, and a standard shaft, like the one used here, a statement. In portraying, for example, two-person athletic contests, modified heads or shafts might be used to indicate different sorts of punches or thrusts in, say, boxing or fencing matches. Punches or thrusts that connected with the opponent could be signified by arrows that touched the opponent's line, while those that did not could stop short of this line. Using different colors and modified shafts and heads would impose greater cognitive loads on users of music notation graphs than the sorts of graphs shown here, and these loads would have to be considered and kept as small as possible in any modifications and extensions of music notation.
Third, in the case of behaviors having duration, as opposed to the more or less instantaneous ones considered here, arrows would not be satisfactory. For behaviours with duration, a possible modification might be to use line segments or bars in the color of the initiator, corresponding to the duration of the behaviour, and laid down on the line of the receiver. For example, such a modification could be used to show the length of time that two or more primates took in grooming each other.
Fourth, in the case of layering other types of behavioral information about individuals with music notation graphs, it might be very helpful to know such things as heart rate, blood pressure, respiration rate, vocalizations, etc. that occurred at specific times in bouts of interaction. For example, having a music notation graph of interaction combined with a record showing things of this type, on the same time scale, could help researchers pinpoint the particular behavioral contexts in which specific vocalizations were used in primates or birds, or what kinds of interactions led to increases or drops in heart or respiration rates.
Fifth, in small groups of individuals, such as those portrayed here, only one pair of animals usually interacts at a time. However, in larger groups, but still within the size limit appropriate to music notation, two or more pairs might interact simultaneously. To present these simultaneous interactions, the standard display for a group shown here could be modified to present two music graphs for the group for the same time interval – one over the other – as in the method for showing the graph of a group along with those of component subgroups (Figure 7). The top graph could present the bulk of the interaction in the group while the bottom graph could display those acts, probably few in number, which occurred simultaneously with certain of the acts shown in the upper graph. For example, if at some point, A attacked B at the same instant as C attacked D, the interaction between, say, A and B could be presented in the upper graph at the time it occurred (along with all the other non-simultaneous acts that occurred in the group), and the simultaneous interaction between C and D could be presented on the lower graph directly below the A-B interaction.
Sixth, in order to help facilitate the use of music notation by colour-blind researchers, I can think of two possible approaches. One would be to alter the colours for the individuals with a particular kind of colour-blindness. For example, for those with red-green colour-blindness, one or both of those colours could be avoided, and one or more other colours that could be distinguished could be substituted. A second approach would be to apportion the lines and arrows along a grey scale: this should work for all the various varieties of colour-blindness. Here the lines might go from very light grey, through mid-greys to black. However, the use of a grey scale would probably restrict the numbers of animals that could be displayed to less than those possible using colours, since it might be difficult to distinguish easily a large number of different grey tones.