The influence of the few: a stable ‘oligarchy’ controls information flow in house-hunting ants

Animals that live together in groups often face difficult choices, such as which food resource to exploit, or which direction to flee in response to a predator. When there are costs associated with deadlock or group fragmentation, it is essential that the group achieves a consensus decision. Here, we study consensus formation in emigrating ant colonies faced with a binary choice between two identical nest-sites. By individually tagging each ant with a unique radio-frequency identification microchip, and then recording all ant-to-ant ‘tandem runs’—stereotyped physical interactions that communicate information about potential nest-sites—we assembled the networks that trace the spread of consensus throughout the colony. Through repeated emigrations, we show that both the order in which these networks are assembled and the position of each individual within them are consistent from emigration to emigration. We demonstrate that the formation of the consensus is delegated to an influential but exclusive minority of highly active individuals—an ‘oligarchy’—which is further divided into two subgroups, each specialized upon a different tandem running role. Finally, we show that communication primarily occurs between subgroups not within them, and further, that such between-group communication is more efficient than within-group communication.

: Defining tandem run quality from the net distance travelled. (a) Temnothorax albipennis worker with a RFID tag glued to the thorax (photo courtesy of N.R. Franks c ). (b) Illustration of the calculation of the net distance tracelled for a single tandem run that departed the initial nest (at top), but which broke up before reaching either left or right target nests. The distances d and d respectively represent the initial and final beeline distance to the target. The, net distance travelled towards the target, is then d − d .
(c) Spatial distribution of tandem run break-up locations within the arena for (forwards) tandem runs that departed from the original nest. Point colours indicate the identity of the target nest (red; left, blue; right). (d) Break-up locations for (reverse) tandem runs. (e) Distribution of the net distance travelled towards the target, which is used to calculate tandem quality. Although most tandems reached the target nest, a large proportion broke up before doing so.

Negative degree assortativity
In the main paper we showed that tandem recruitment networks exhibit a negative degree assortativity, that is a negative correlation between the out-degree centrality of an ant and that of its immediate neighbours.
We here calculate the same correlation using weighted degree centrality, which is the summed quality of the tandem runs each ant led or followed. We find that individuals that played a major role in the emigration by transmitted a large amount of information by leading tandem runs (high summed out degree quality), tended to be connected to neighbours that transmitted only a little information (Fig. S2a). Conversely, the immediate neighbours of individuals that received a large amount of information (high summed in degree), had neighbours that received little information (Fig. S2b). Hence, as for the regular degree, the weighted degree also exhibits negative degree assortativity: neighbours of ants that were particularly active tandem leaders tended to be particularly inactive leaders, whereas the neighbours of particularly active followers tended to be particularly inactive followers.  The summed quality of all tandems an follows is negatively correlated with the summed quality of the tandems followed by its nearest neighbours.

Practice predicts performance
In this section we present barplots to confirm the results of the mixed effects models presented in Table 1 in the main paper. The quality of the tandem runs that an ant led showed a positive dependence upon its leading reliability but a negative dependence upon its following reliability, whereas the quality of tandems it followed showed a positive dependece upon its following reliability and no dependence upon its leading reliability The quality of the tandem runs that an ant led showed a positive dependence upon its leading reliability but a negative dependence upon its following reliability (Fig. S3 a,c). Similarly, the quality of tandems an ant followed showed a positive dependece upon its following reliability and no dependence upon its leading reliability (Fig. S3  b,d). Therefore, there is a positive association between the amount of practice within a given role, and the performance in the same role. Furthermore, the negative association between following reliability and the mean quality of tandems led indicates that specialization in one role may inhibit performance in other roles, even when the roles are as closely related as leading and following in tandem runs.  Figure S3: Individual performance as a leader or follower depends upon practice within the same role. Evidence that specialization in one role may inhibit performance within the same role: The greater the reliability of an ant in the leading role, the greater the quality of the tandems it led (a), and the greater the reliability of an ant in the following role, the greater the quality of the tandems in which it was a follower (d).
(b) Evidence that specialization in one role may inhibit performance in other roles: the greater the reliability of an ant in the following role, the lower the quality of the tandems it led. (c) There was no association between leading reliability and the quality of the tandem runs an individual followed. The fits are given by the linear mixed model presented in Table 1 in the main text.

Testing for assortative matching between leaders and followers
In the main paper, the distribution of leader-follower role reliability differences f tand Obs (∆R leading , ∆R following ), was seen to be biased towards positive values. Whilst this demonstrates that tandem runs tend to be composed of a leader that was a more reliable leader than the follower, and a follower that was a more reliable follower than the leader, it does not by itself demonstrate the presence of assortative mathcing. Therefore, we investigate the statistical significance of this bias. To that end, we compare the observed distribution, f tand Obs (∆R leading , ∆R following ), with the equivalent distribution expected in the absence of any association between role reliability and role performance, namely f tand Exp (∆R leading , ∆R following ) (Fig. S4a). This expected distribution was generated by constructing randomly-matched tandem runs by repeatedly sampling leaders and followers from the joint role reliability distribution, f ant (R leading , R following ), which is shown in Figure 5a in the main paper.
Plotting the difference between these two distributions, that is, f tand O−E (∆R leading , ∆R following ), confirmed that the observed bias towards positive values of ∆R leading and ∆R following , is real (Fig. S4b), and hence consistent with assortative matching between leaders and followers within tandem pairs.  Figure S4: Differences between the observed and expected leader-follower reliability differences. (a) Reliability differences expected when R leading and R following are independent, f tand Exp (∆R leading , ∆R following ). (b) Signed difference between the observed and expected joint distributions, f tand O−E (∆R leading , ∆R following ). This distribution is skewed towards the upper right quadrat were the tandem leader is a more reliable leader than the tandem follower, and where the follower is a more reliable follower than the leader.