A detailed account of the method is provided in Appendix 1. The basic idea is that pairs of participants played a cooperative referential communication game on computers. The game involved taking turns as Sender and Receiver in communicating a set of animal silhouettes (Figure 1). At the start of the game, four animal referents were visible on the left of the screen (later, more would be added). Every turn one of these animals would be marked for the sender as the referent that needed to be communicated that turn. Players could not see or hear each other and so the sender had to communicate via a non-linguistic medium. In particular, they could communicate by moving their finger around on a trackpad. Finger positions (which were recorded as xy coordinates) corresponded reliably to points on an underlying color space (Figure 2). Participants never saw the whole underlying colorspace; however, as the sender moved their finger around, different colors (which were recorded as RGB values) would appear on their screen. If they held their finger in place for 1 s the color would be sent to the receiver and would appear on their screen. (see Figure 15B in Appendix A for an example.) The sender could select and send as many colors as they wished within the available time of 20 s per round. Before the round was up the receiver could use arrow keys to select the referent they thought the sender was trying to communicate. Feedback was provided to both players at the end of the round. As pairs got better at communicating referents (specifically when every current referent had been communicated successfully on at least three of the previous four rounds where it had occurred) four new referents would be added up to a total of 12. (The full set of referents can be seen in Figure 15A in Appendix A)

Because we were interested in the role of a trade-off between the sender's ease in reliably and consistently selecting colors to send and the receiver's ease in distinguishing colors sent to them, we manipulated how well these pressures lined up. In the Outer-edge condition colors became more brighter and more distinct the further the sender's finger was from the center of the pad. This meant that the clearest colors for the receiver were also the easiest to locate consistently. In the Inner-edge condition colors initially became brighter and more distinct before abruptly getting darker and less distinct again. This meant that the best colors for the receiver were harder to locate consistently (Figure 2). The most convenient parts of the pad for the Sender to select reliably were still along the outer edge of the pad, but the easiest colors to distinguish for the Receiver were closer to the inner edge. The inner edge was in no way marked on the pad or screen; it became apparent to the Sender as they moved their finger around the pad and observed the effect.

Participants' behavior in the communication game created sets of signs. By sign we mean a pairing of a referent (i.e., one of the animal silhouettes) with a signal (a series of colors). Each signal consisted of two sets of coordinates, a set of xy coordinates corresponding to the sender's finger position on the trackpad and a set of RGB coordinates corresponding to the color that appeared on screen. Because the RGB coordinates for any given trial can be straightforwardly derived from the xy coordinates, and the patterns of results for the two spaces are thus the same for many dependent variables, Roberts and Clark's (2020) analysis focused primarily on the xy coordinates, which—being two- rather than three-dimensional—are simpler to deal with. We will do the same in this paper. The main exception concerns the mode brightness measure, described below. This will be presented separately.

Roberts and Clark (2020) identified inventories for each pair of players by pooling the colors used by each participant (across signals) and calculating Pillai scores to identify “color phonemes” (Hay et al., 2006; Hall-Lew, 2010; Nycz and Hall-Lew, 2013).¹ They then looked at a series of measures, including—most importantly—dispersion and success. Dispersion was measured in three different ways: mean pairwise distance (in terms of xy coordinates) between phonemes in an inventory; mean distance of xy coordinates from the center of the space; and mode brightness. Mode brightness meant the mean value of the brightest RGB component in each phoneme and was a perceptual analog of the distance-from-center measure.² These measures could then be compared with chance-level values, which were calculated by randomly generating 100,000 inventories (for which the mean value is indicated on Figure 4 by a red dotted line; see Roberts and Clark, 2020, p. 132–133, for more details.)

Success was measured by first counting, for every round of a given game, how many referents each player had established a signal for at that point (establishing a signal meant communicating it successfully in at least three of the last four rounds in which it had occurred). The success index was then calculated as (∑i=1nrs)/12nr, where n_r is the number of rounds and the numerator is a cumulative count of s, the number of successfully established words in a given round, with 12 being the maximum possible given the number of referents.³ We also measured the number of established signals at the end of the game, the mean word length, and the number of phonemes in players' inventories. The results of all these measures are presented in Figures 3, 4.

Overall the results indicated that dispersion qualitatively analogous to that seen in natural-language vowel systems had indeed emerged. This can be seen particularly well in Figure 5, which shows heat maps of final phoneme sets across pairs. A comparison of the two conditions suggested that the pattern of dispersion was driven primarily by perceptibility demands rather than by ease of production. As a result, participants found the Inner-edge condition, in which perceptual demands were misaligned with production demands, significantly more difficult. Success was related to dispersion, but this relationship was only apparent when both conditions were considered together, suggesting that the difference between conditions was driving this relationship.

But how did the patterns observed come about? This was not addressed by Roberts and Clark (2020) and will be discussed in the following sections of this paper.

Our first question concerns participants' first signals. How did senders initially approach the task of selecting a signal in an unfamiliar medium? There are several possibilities for how a participant might approach it. One would be to privilege audience design. That is, a sender might attempt to take into account the needs of the receiver and select a relatively distinct color, perhaps one that has some iconic relationship with the referent (e.g., brown for a bear), or which is simply a very salient “basic” color (such as bright red). A second possibility is that senders might be driven more by what is easier for themselves, whether by selecting colors at points that are especially comfortable to reach on the trackpad or by selecting colors that will be easy to find reliably in future rounds. The corners of the pad fulfill this last criterion particularly well and also lead to systems that are relatively well-dispersed. Given that the systems participants ended up with in the Outer-edge condition tended to exhibit greater dispersion than would be expected by chance, it could be that they in fact began the game by concentrating on the corners and the center of the trackpad. A third possibility is simply to select randomly. In the first round participants were not yet familiar with the medium and its affordances, so it was not trivial to make decisions that really took into account the needs of either sender or receiver. Selecting a signal randomly is also a good way to start learning about the medium and a reasonable way to start establishing an arbitrary communication system.

To investigate what participants actually did, we took the first signal that was sent by every player across both conditions and plotted these signals according to their x and y coordinates. This is shown in Figure 6A. As can be seen, participants do not seem to have been starting with locations that were likely to help maximize later dispersion (e.g., the corners and center of the pad). In fact the most obvious pattern is that the x and y coordinates seem positively correlated. To confirm this we performed a mixed model predicting the y from the x coordinate, with random intercepts for referents, and indeed found evidence of a relationship: β = 0.37, SE = 0.12, t(26.58) = 3.01, p = 0.006. As can be seen in Figure 6, the relationship was stronger for the Outer-edge condition, for which the observed pattern also held true when taken alone, β = 0.397, SE = 0.16, t(11.87) = 2.45, p = 0.03. However, a model of all the data including condition as an interaction term found neither an interaction nor an effect of condition (ps>0.1). Overall, while participants were not selecting uniformly random points on the pad, it seems that they might have been selecting random points within an area of the pad stretching from the bottom left side (though not as far as the bottom left corner) to the top right corner. It is tempting to connect this with known human biases to interpret data in terms of positive linear relationships (cf. Kalish et al., 2007). However, what almost certainly matters more here is that this area of the pad is the most physically comfortable area for a right-handed person who is resting the bottom of their palm near the bottom right of the pad. Given this arrangement, the central area of the pad is rather easy to reach. This extends to the top of the pad, but not the bottom. In fact, the whole of the bottom quarter of the pad is hard to reach comfortably with the index finger without moving one's palm. Within the top three quarters of the pad, there is also an asymmetry between the leftmost and rightmost quarters. First, the top-right corner is easier to reach (assuming, as above, a right handed person resting their palm at the bottom right of the pad) than the top-left corner. Below that, however, the index finger has a slightly larger area available to it on the left than on the right. This is because reaching the leftmost area of the pad just below the central horizontal axis merely involves extending one's finger. Reaching the same area on the right (assuming the physical arrangement described above) involves moving one's palm or bending one's finger under the top of the palm. This likely accounts for the space participants drew their first signals from. As for how they selected signals within this space: The particular points selected within this space look rather random. Signals selected in the Inner-edge condition appeared to have a lower mean distance from the center of the pad than those in the Outer-edge condition (0.21 vs. 0.31) but there was no significant difference, t(25) = −1.71, p = 0.099. In other words, participants seem to have been driven primarily by physical ease.

This pattern seems to be a feature of initial exploration in particular. We conducted a linear mixed effects analysis as before on (instead of only the very first signal for each player) the first signal for all four of the initial set of referents. The relationship held across conditions, though it was weaker: β = 0.21, SE = 0.097, t(84.63) = 2.18, p = 0.032 Furthermore, the effect disappears if condition is included as in interaction term (ps>0.4). But there was no effect for successful signals (i.e., the first signal in each pair for which the receiver selected the correct referent; Figure 6B): β = −0.01, SE = 0.05, t(327.49) = −0.35, p = 0.73. In other words, the account given above seems to work as an account of basic starting strategy only. As participants started to get more used to the game and to actually establish a communication system, they seem to have explored more of the space (perhaps beginning to more readily move their palms). To investigate whether this was part of a general trend to use more of the space over time, we conducted a model with distance from center as dependent variable, turn number and condition as fixed effects, condition as an interaction term, and random intercepts for pair and referent. There was an effect of both turn number, β = 2.11 × 10⁻⁴, SE = 1.91 × 10⁻⁵, t(1.25 × 10⁴) = 11.03, p < 0.001, and of condition, β = −0.102, SE = 1.224 × 10⁻², t(40.4) = 11.03, p < 0.001, and an interaction with condition: β = −1.127 × 10⁻⁴, SE = 2.361 × 10⁻⁵, t(1.25 × 10⁴) = −4.78, p < 0.001. In other words, participants did indeed use more space over time, but more in the Outer-edge condition—where colors got reliably less dark toward the outer edges of the pad—than in the Inner-edge condition.

As can be seen in Figure 6B, however, participants' first successful signals still do not appear to have been established with an eventually well-dispersed system in mind; there is no evidence, for instance, that participants were preferentially establishing signals on the edges or corners of the space.

In summary then, the apparent picture is as follows. Participants seem to have begun by exploring the most accessible area of the pad and selecting relatively distinct colors from within that space. As they became more familiar with the game, they explored a larger area of the pad. But there is little evidence that they implemented any more coordinated plan to maximize overall dispersion in their emerging system. This is consistent, in other words, with accounts of phonological structure as an emergent, self-organizing phenomenon (Lindblom et al., 1983; Wedel, 2003). In terms of Keller's (2005) account of language change we should think of dispersion as a phenomenon of the third kind: an epiphenomenal, large-scale consequence of deliberate smaller-scale behaviors, as opposed to being a directly intended consequence of human decisions or a “natural” phenomenon not caused by human actions.

In the next section we discuss in more detail what this looked like.

In general, as can be seen in Figure 4, pairs in the Outer-edge condition tended to end up with more dispersed systems than would be expected by chance. The general pattern can be seen rather clearly in Figure 5A, which shows a heatmap of final successful signals across pairs in this condition. A comparison with the underlying color spaces in Figure 2 indicates that, while perceptual distinctiveness seems to have driven a great deal of participants' behavior, participants were not simply selecting points in the space that afforded particularly bright colors. If that were so, the center of the space would not be as favored as it apparently was. Rather, signals seem to be distributed across the space in a way that increases dispersion, with a slight bias for the top over the bottom of the pad. (see Section 3.1 for a discussion of how this bias might arise from the location of participants' hands.) The pattern for the Inner-edge condition, shown in Figure 5B, suggests that—while systems in this condition were not more dispersed than we would expect by chance—this may be an artifact of participants avoiding the corners of the space, which in this condition were dark (Figure 2). The fact that participants in this condition made much less use of the center than participants in the Outer-edge condition is notable and seems likely driven by a bias for maintaining distance between signals.

However, as discussed in Section 3.1, there is little evidence that participants in any condition were directly targeting a high mean distance or that they planned from the beginning to create well-dispersed systems. Rather, system-wide dispersion seems to be a feature that emerged over the course of the experiment, most likely as a result of participants simply trying to keep new signals distinct from already established ones. Figures 7, 8 are of interest in this respect. They show mean dispersion (operationalized as the mean distance between all successful signals) over time in the Outer-edge and Inner-edge conditions, respectively. The pattern for most pairs is of an initial increase in dispersion levels over (roughly) the first 75 turns and then a plateau. For some pairs, however, dispersion decreased—in part as a result of having to accommodate new referents. In fact, it is rather interesting that there seems to have been a broadly optimal level of dispersion that pairs converged on. For the Outer-edge condition overall mean dispersion for the whole game was 0.65. Given that the maximum possible distance for two signals (i.e., the distance between coordinates 0,0 and 1,1) is 1.41, this means that the typical situation in the Outer-edge condition was to settle for most of the game on a level of dispersion that was close to half that, which is a rather high level of dispersion for larger sets.⁴ The other notable feature is that levels of dispersion began as very variable, but variability reduced over time. This happens to a great extent in the Outer-edge condition. It also happened in the Inner-edge condition, but to a much smaller degree.

In Section 10 above we reported that auto-distance (i.e., the distance between successive signals for the same referent by the same participant) tended to go down over time. The same is true for partner distance, by which we mean the distance between a given signal and the last signal for the same referent produced by the other member of the pair. We conducted a linear mixed model with partner distance as the dependent variable, turn number and condition as fixed effects, condition as an interaction term, random intercepts for pair and referent, and a random slope for condition by referent. We found an effect of turn number, β = −2.48 × 10⁻⁴, SE = 2.5 × 10⁻⁵, t(1.12 × 10⁴) = −9.91, p < 0.001 and an interaction with condition: β = −1.26 × 10⁻⁴, t(1.16 × 10⁴) = −4.03, SE = 3.14 × 10⁻⁵, p < 0.001, suggesting that the relationship between turn number and partner distance was stronger in the Outer-edge condition. More interestingly, mean auto-distance and mean partner distance were very well-correlated across pairs: r(28) = 0.75, p < 0.001 (Figure 13), suggesting that more consistent participants were also more likely to do a good job of aligning with their partners. There was also a negative relationship between partner distance and success. We performed a linear mixed effects model with pair distance as dependent variable, success index and condition as fixed effects, condition as an interaction term, random intercepts for pair and referent, and a random slope for condition by referent. There was an effect of success, β = −0.43, SE = 0.13, t(26.05) = −3.23, p = 0.003, but no effect of, or interaction with, condition. This supports the intuition that consistency and alignment were beneficial to performance in the game, regardless of condition.

One other thing to consider is that the relationship between pair-distance and auto-distance might itself be of importance. A player who was highly consistent with themselves but who never followed the lead of their partner might drag down success in spite of their low auto-distance. However, a comparison of the ratio between partner distance and auto-distance with success index did not yield evidence of a relationship. This is not too surprising given the close relationship between partner distance and auto-distance discussed above. As can be seen in Figure 13, there are in fact very few points under the regression line (indicating higher than average auto-distance relative to partner distance); nor were they especially unsuccessful. There is also no particularly clear success pattern to be seen among the participants with high partner distance relative to auto-distance.

How did pairs converge? Part of the story is that players paid attention to success. In general partner distance was smaller if the last signal for the same referent was successful (Figure 14). A mixed model with partner distance as dependent variable, last outcome and turn number as fixed effects, their interactions with condition, pair and referent as random intercepts, and random slopes for last outcome by referent, found an effect of the last outcome being correct, β = −6.82 × 10⁻², SE = 2.83 × 10⁻², t(16.6) = −2.41, p = 0.028, an effect of turn number, β = −1.66 × 10⁻⁴, SE = 2.37 × 10⁻⁵, t(9.42 × 10³) = −6.99, p < 0.001, an interaction between last outcome (correct) and condition, β = −0.15, SE = 4.09 × 10⁻², t(2.48 × 10³) = −3.63, p < 0.001, and an interaction between turn number and condition, β = −1.43 × 10⁻⁴, SE = 2.93 × 10⁻⁵, t(1.18 × 10⁴) = −4.88, p < 0.001. For auto-distance, we also found an effect of last outcome (correct), β = −0.11, SE = 1.57 × 10⁻², t(1.19 × 10⁴) = −6.73, p < 0.001, and of turn number, β = −2.24 × 10⁻⁴, SE = 1.77 × 10⁻⁵, t(1.17 × 10⁴) = −12.62, p < 0.001, but no effect of condition and no interactions. In other words, when pairs had signaled successfully, they generally tried to stay close to what had worked; when they were unsuccessful they tried something new.

As might be expected, the introduction of new referents complicated things. The distance between successive signals for the same referent tended to be highest just after a new referent had been introduced. That is, introducing a new referent seems to have destabilized existing systems. To investigate this we used a linear mixed-effects model with auto-distance (distance between the current signal and the last signal for the same referent) as a dependent variable; as fixed effects we had turn number since the last new referent was introduced, condition, and overall turn number, as well as their interactions. We included random intercepts for referent, pair, and sender. There was an effect of turn since last referent, β = −5.83 × 10⁻⁴, SE = 1.02 × 10⁻⁴, t(1.18 × 10⁴) = −5.75, p < 0.001, and an effect of overall turn number, β = −3.25 × 10⁻⁴, SE = 3.27 × 10⁻⁵, t(1.17 × 10⁴) = −9.94, p < 0.001, but no effect of condition. There was, however, an interaction between the three fixed effects, β = −6.87 × 10⁻⁷, SE = 3.18 × 10⁻⁷, t(1.18 × 10⁴) = −2.16, p = 0.03. This suggests that, while turn number (and experience) had an effect on the distance between successive signals, the introduction of new referents was having an effect of its own, distinct from how far into the game participants were.