Information Certainty Determines Social and Private Information Use in Ants

Decision-making in uncertain environments requires animals to evaluate, contrast and integrate various information sources to choose appropriate actions. In consensus-making groups, quorum responses are commonly used to combine private and social information, leading to both robust and flexible decisions. Here we show that in house-hunting ant colonies, individuals fine-tune the parameters of their quorum responses depending on their private knowledge: informed ants evaluating a familiar new nest rely relatively more on social than private information when the certainty of their private information is low, and vice versa. This indicates that the ants follow a highly sophisticated ‘copy-when-uncertain’ social learning strategy similar to that observed in a few vertebrate species. Using simulations, we further show that this strategy improves colony performance during emigrations and confers well-informed individuals more weight in the decision process, thus representing a novel mechanism for the emergence of leadership in collective decision-making.


The role of direct contacts
Nest population should grow faster in familiar than unfamiliar nests because (i) there are already some workers in the familiar nest at the onset of emigration and (ii) the discovery rate of the familiar nest is greater, giving it a head start in the recruitment process 1,2 . The faster assessment of familiar nests could thus be a direct consequence of these nests attaining the quorum threshold earlier than unfamiliar nests. If this mechanism alone accounts for expedited familiar nest evaluation, then we expect that (i) decisions to switch to transport should occur at similar nest populations for all nests, and (ii) delaying nest population growth, for example by clearing the familiar nest of workers at the onset of emigration, should delay decisions to switch to transport. Experiments QT1 and QT2 aimed at testing these predictions (Table 1). For each experiment, sources of information that were available ('yes') and non-available ('no') during emigration are listed. Direct contacts in the new nest depended on whether there were workers inside the new nest at the onset of emigration ('Workers in'), and whether we allowed all workers free access to the new nest or whether we limited access to the new nest to specific workers. Informed workers that were removed from familiar nests at the onset of emigration were returned to their old nest.

Treatment
In experiment QT1, colonies moving to a familiar nest that was cleared of workers at the onset of emigration were significantly faster than colonies moving to an unfamiliar nest ( Figure S1 A). This was at least in part due to evaluation of familiar nests being expedited compared to unfamiliar nests: assessment time was significantly shorter, fewer tandem runs were led, and workers made fewer and shorter visits to familiar than unfamiliar nests before transport started ( Table 2). As predicted, nest population increased faster in familiar than in unfamiliar nests, which could contribute to familiar nests attaining the quorum threshold earlier. However, contrary to our expectation, scouts switched to transport at significantly lower nest populations for familiar than unfamiliar nests, that is, they used significantly lower quorum thresholds for familiar than unfamiliar nests ( Figure S1A; Table2 In experiment QT2, contrary to our expectation, clearing familiar nests of workers at the onset of emigration (test) did not slow down nest assessment or nest emigration relative to familiar nests that were not cleared of workers (control). There were no differences between treatments in the number of visits to the new nest before transport started, in tandem running behaviour, or in the time to attain the quorum threshold. Importantly, carrying was initiated at significantly lower nest populations in test than in control colonies, probably due to the initial depletion of workers inside the new nest in the test ( Figure S1B; Table 2).
Overall, these two experiments do not support the hypothesis that faster nest population growth alone accounts for the faster assessment of familiar nest sites. Indeed quorum threshold values differed for familiar and unfamiliar nests, and also differed for identical familiar nests depending on initial population conditions. Nest assessment time therefore did not solely reflect the time necessary for the nest population to attain a given, fixed quorum threshold. Other factors, such as chemical marking of the familiar nest or use of existing private information by informed workers, may also underlie the faster evaluation of familiar nests.

The role of chemical communication
Experiments P1 and P2 aimed at investigating the effect of chemical cues on familiar nest evaluation by informed (experiment P1) and naïve colonies (experiment P2; see Table 1).
Colonies moving to familiar nests that were cleared of workers at the onset of emigration showed no differences in overall emigration time whether chemical marking of the nest had been left intact (control) or removed (test; experiment P1). Decisions to start carrying were made after a similar number of visits and at similar quorum thresholds in test and control conditions, and workers did not change the duration of their visits to the new nest in reaction to the absence of chemical cues.
However, workers led more tandem runs to the unmarked than to the marked nest. In addition, nest populations increased more slowly when chemical marking was removed from the familiar nest, presumably because workers engaged in the slow recruitment method of tandem running spent more time outside the nest. Accordingly, the quorum threshold was attained more slowly. However, the duration of the assessment phase tended to be longer when chemical marks had been removed, although this trend was not statistically significant ( Figure S1C; Table 2).
Naïve half-colonies moving to unfamiliar nests that had been previously visited by sister halfcolonies emigrated significantly faster than naïve half-colonies moving to fresh, previously unvisited unfamiliar nests (experiment P2). Although test and control colonies did not differ in the number of tandem runs they produced, or in the number or duration of visits to the new nest before transport started, colonies that had access to chemical cues (test) initiated tandem running earlier and showed a faster increase in nest population. Since decisions to start carrying were made for similar quorum thresholds in the control and in the test, this resulted in the assessment phase tending to be shorter in test than in control conditions, although this trend was not statistically significant ( Figure S1D; Table   2).
These two experiments suggest that chemical marking of the familiar nest by nestmates influences nest evaluation by both informed (P1) and naïve (P2) colonies in emergency emigrations, though this effect is limited and did not result in significantly faster nest evaluation.

General experimental design
Throughout experiments, colonies were housed in artificial nests consisting of a cardboard perimeter sandwiched between two glass slides (50×76 mm), with an internal cavity of 35×50 mm, a ceiling height of 1.8 mm and an entrance tunnel of 2×8 mm. All nests were covered with an opaque cardboard sheet to make the interior dark. Previous work showed that T. albipennis colonies consider such nests as high-quality housing sites 1-3 .
All experiments were carried out in experimental arenas consisting of five interconnected Petri dishes with Fluon-coated walls, similar to those used in previous studies (Fig 1A; 1,2 ). Colonies housed in high-quality nests ('old nest', ON in Fig 1A) were positioned in the middle of the central dish and left to explore the arena for one week. The old nest was then destroyed and colonies had to move to a single high-quality new nest (NN in Fig 1A), identical to their old nest, positioned at one end of the arena.
During emigrations, we recorded the emigration time (time interval between the destruction of the ON and the last brood item being carried into the NN) and its three components: discovery time From this we determined an approximate quorum threshold for each emigration (maximum population attained in the new nest before the first transport). Despite fluctuations, the population in the new nest progressively increased over time between discovery and first transport, thus repeatedly reaching new, previously unattained maximal values. We recorded the times at which these successive new maxima were attained to evaluate the rate of nest population increase prior to transport.
In all experiments, every colony experienced both control and test conditions (detailed below) in a pseudo-random order: half the colonies experienced control conditions first, and the other half experienced test conditions first. After experiencing one treatment, colonies were left undisturbed for at least one week before being tested in the second treatment to minimise the effects of previous experience 4 . Colonies which had not discovered the familiar nest and colonies which had prematurely moved to the familiar nest during the exploration period were not included in the experiment. Table 1 shows the final sample sizes for each experiment.

The role of direct contacts: experiments QT1 and QT2
Experiment QT1 In control conditions, colonies had no available nest to visit during exploration. They then emigrated to an unfamiliar new nest. In the test, colonies were allowed to familiarise themselves with the new nest during exploration. The familiar nest was then opened by lifting the top glass slide, and all workers present inside the nest were gently removed with soft tweezers and released near the old nest.
The familiar nest was then closed back and emigration was induced immediately thereafter (Table 1).

Experiment QT2
In both control and test conditions, colonies were allowed to familiarise themselves with the new nest during exploration. In the test, the familiar nest was then opened and all workers inside were removed and released near the old nest. In the control, the familiar nest was also opened by lifting the top glass slide to induce similar disturbance, but workers were left inside the nest. In both treatments, the familiar nest was then closed back and emigration was induced immediately thereafter ( Table 1).

The role of chemical communication: experiments P1 and P2
Experiment P1 In both control and test conditions, colonies were allowed to familiarise themselves with the new nest during exploration. The familiar nest was then opened, and all workers inside were removed and released near the old nest. In the control, the familiar nest was then closed (chemical cues present), whereas in the test, it was replaced with an identical, novel nest (chemical cues absent). Emigration was induced immediately thereafter (Table 1).

Experiment P2
Twenty-two colonies were each split into two equal halves. During exploration, 'informed' halfcolonies were allowed to familiarise themselves with the new nest whereas 'naïve' half-colonies had no available nest to visit. In the control, naïve half-colonies were then induced to emigrate to an unfamiliar new nest. In the test, familiar nests from informed half-colonies were opened and all workers inside were removed. The nests were then closed and transferred to the arena of naïve halfcolonies. Naïve half-colonies were then immediately induced to emigrate to the transferred new nest (Table 1). To avoid any confounding effects of nestmate recognition 5 , transfers were always done between half-colonies from the same mother colony, as they usually maintain the same colony odour for several weeks in Temnothorax sp. 6 .

Supplementary File 2 Effect of model parameters on simulation outcome
The following three figures present the average simulation outcome for different values of parameters: -n i . number of informed workers ( Figure S2) p low , proportion of informed workers with low probability of independent acceptance ( Figure S3) -, commitment bias:  We also investigated the effect of recruitment on our simulation results. We defined d nest the probability of workers discovering the focal nest (nest 1 if worker is uninformed; familiar nest if worker is informed) as follows:  The following figure (Figure S5) presents the effect of parameter r on simulation outcome (note that r=0 corresponds to the situation where there is no recruitment, as in the main manuscript).

I. Graded 'copy-when-uncertain' vs. fixed quorum rule
In order to facilitate data interpretation, we plotted the relative performance of colonies using the graded 'copy-when-uncertain' strategy compared to informed colonies using a fixed quorum rule (a i =a u and w d 1; Figure S6).
We used GLMM to test whether the accuracy, cohesion and emigration time of colonies using the graded 'copy-when-uncertain' strategy differed from the average performance of informed colonies using a fixed quorum rule. We found that overall, colonies using the 'graded copy-when-uncertain' strategies were faster (F 1,1997 =754.69, p<1.10 -15 ), showed stronger preference for the majority nest (F 1,1997 =50.71, p< 1.10 -11 ), but were less cohesive (F 1,1997 =24.94, p<1.10 -6 ) than informed colonies using a fixed quorum rule.
When repeating the same analyses for each value of p 1 separately, we found the same results for  . For example, in the cohesion rows, all parameters values for which the plotted values are greater than 1 correspond to parameter values where colonies using the 'copy-when-uncertain' strategy were more cohesive than informed colonies using a fixed quorum rule.

II. Graded 'copy-when-uncertain' vs. naïve colonies
In order to facilitate data interpretation, we plotted the relative performance of colonies using the graded 'copy-when-uncertain' strategy compared to naïve colonies (p i =0; Figure S7).

III. Graded 'copy-when-uncertain' vs. homogeneous informed behaviour
We repeated all simulations with parameter values p low =0 and =1 ( Figure S8; all other parameter values as in main manuscript). This corresponds to the case where all uninformed workers have a low probability of independent acceptance a u , and all informed workers have the same probability of independently accepting the familiar nest a i a u , regardless of the certainty of their private information. This differs from the graded 'copy-when-uncertain' strategy, where informed workers have varying probabilities of independently accepting the familiar nest depending on the certainty of their private information, with an overall average a i . Figure S9 shows a point-by-point comparison of both strategies.
We used Wilcoxon matched-pairs tests to compare the simulation outcomes of both strategies for each {p 1 , a i ,w d } triplet. We found that colonies using the 'copy-when-uncertain' strategies were slower (V = 1793500, p<1.10 -15 ), more cohesive (V = 1733500, p<1.10 -15 ) and showed stronger preference for the majority nest (V = 1018900, p<1.10 -15 ) than colonies using the alternative strategy.

Model simulations
The following analysis aimed at investigating the relative influence of different categories of workers (uninformed workers and informed workers with high, intermediate and low probability of independent acceptance) on the collective decision. For each combination of parameter values (see main manuscript), we performed 1,000 additional simulations where we recorded the order in which workers committed to each nest. The first few workers committing to each nest are those who influence the collective decision the most, because they increase the probability of their nestmates also committing to the nest: once the number of committed workers reaches the quorum threshold, all subsequent workers have a higher than 50% chance of themselves committing to the nest. We therefore calculated the proportion of workers of each category among the first workers committing to each nest until the quorum threshold was reached, or 'pre-quorum workers'. This was compared to the proportion expected under the null hypothesis of random commitment order, i.e. to the proportion of each category of workers among all workers modelled. Figure S10 shows the results obtained for the majority nest, N1, for the parameter values used in the main manuscript (n i =24; p low =0.5; σ=4; r =0; w d ranging from 1 to 9 and a i ranging from 0.1 to 0.31).
Relative to random expectations, informed workers were overrepresented among pre-quorum workers (except informed workers with low a for ai > 0.1). This overrepresentation increased with their probability of independent acceptance a (Figure S10 A). Informed workers with high a thus have the highest individual influence on the collective decision.
In addition, informed workers with high a were more numerous than any other worker category among pre-quorum workers at the majority nest provided a i >0.05 (Figure S10 B). Informed workers with high a thus also have the highest influence as a group on the collective decision.

Experimental data
We evaluated the relative contribution of the different categories of recruiters to the decision process in the experimental dataset from Stroeymeyt et al. 2011 1 . We counted the number of workers recruited to either nest by each category of recruiters (informed worker groups 1-4 and uninformed workers) during the early phase of the emigration, i.e. until the total number of recruits reached the quorum threshold. We used a chi-square test to compare these observed numbers to the expected numbers of recruits given the proportion of each category among all recruiters. Following Sharpe 2 , we then evaluated which category of recruiters significantly deviated from null expectations by comparing the absolute value of the adjusted standardised residuals to a critical value z=2.58 (corresponding to a significance level of =0.05/5 to account for multiple comparisons).
In agreement with the model prediction, we found the contribution of the 5 categories of recruiters to worker recruitment during the early deliberation process diverged significantly from random expectations (Chi-square test, 2=60.55, df=4, p<1.10-11). Residual analysis 2 showed that this was due to informed workers from groups 1 and 2 recruiting significantly more workers than expected and uninformed workers recruiting significantly fewer workers than expected (group1: adjusted standardised residuals 1=4.26, group 2: 2=5.01; group 3: 3=0.18; group 4: 4=-0.27; uninformed: u=-6.63; critical z-value for significance after adjustment for multiple comparisons: z=2.58 2 ; 73% of all recruitments directed towards the familiar nest). This confirms that informed workers with a non-zero probability of independent acceptance have a significantly higher influence on the deliberation process and the collective choice of the familiar nest than other workers.