Study site and subject attributes

We conducted our study from 2 October to 15 November 2011 in a lowland dry-forest study site on the central west coast of Grand Terre island, New Caledonia (Gouaro-Déva, 21°33′40′′S, 165°19′00′′E; Fig. 1c). The resident crow population had been undisturbed by research activity4,18,39 for ca. 2 years before the current study. From 2 to 21 October, 42 crows were trapped using meat-baited whoosh nets40, deployed at four different locations (Fig. 1c). At two sites, capture rates diminished over the course of trapping, while the other two sites produced only one crow each (Supplementary Fig. 5). We estimate that these 42 birds constitute over 80% of the local crow population during our study period. We note that these crows are likely to be a nonrandom sample, as neophobic individuals that were wary of approaching trapsites (and may also have avoided our experimental manipulations) are less likely to have been included. All trapped crows were blood-sampled (for molecular sexing41), allocated to age categories (according to gape colouration, which changes as individuals mature20,42), weighed, measured and tagged, with the exception of an adult male, which had an injured wing and was released immediately. We genotyped individuals at 12 polymorphic loci36 and used Kinship to generate a binarized matrix G of first-order relatedness43,44. Following best-practice guidelines for biologging studies45, backpack-mounted tags (including braided nylon weak-link harnesses; Sirtrack, NZ) totalled less than 5% of the recipient’s body mass in all cases13. For summary information on subjects and their tags, see Supplementary Table 1.

System overview

‘Encounternet’ is a fully digital animal-tracking system that uses advanced WSN technology; a detailed description of hardware components and basic functionality has been provided elsewhere13,14. Briefly, in this first full-scale deployment of a proximity-enabled Encounternet system, crow-mounted transceiver tags were programmed to emit regular ID-coded radio pulses (see ‘Software settings’), while recording pulses from all other tags within reception range. Tag-to-tag encounters were written to ‘logs’, which were stored in the on-board memory of each participating tag. Logs included the identities of the sending and receiving tags, time data from on-board clocks and a ‘received signal strength indicator’ (RSSI) summary of received radio pulses, which allowed post hoc inference about the proximity of associating birds (see ‘Estimating bird-to-bird distance from signal strength’). When a tag containing stored logs came within communication range of a fixed receiver (‘basestation’), 45 of which were arrayed across our study site (Fig. 1c), all logs were transferred wirelessly from tag to basestation, and automatically cleared from tag memory following successful upload. Basestations also directly recorded the time and sender-ID of all radio pulses from tags within reception range, providing useful spatial context for the association dataset (Fig. 1c). Finally, hand-held transceivers (‘masternodes’) were used by fieldworkers to wirelessly download logs from tags and basestations, and to perform software adjustments, such as routine synchronization of the on-board clocks of all tags.

Basestation array and tag detection

We deployed a higher density of basestations in areas of preferred crow habitat, in order to maximize data retrieval from roaming tags (Fig. 1c). At night (see ‘Experimental schedule’) we visited each basestation in turn, using masternodes to download the encounter logs accumulated during the preceding daylight period. Basestations in areas of high crow density typically recorded thousands of logs over a 24 h period, while units positioned at the far north and south of the main study valley acquired few (if any) data, suggesting that the array was appropriately widespread to monitor our study population13. The maximum number of encounter logs recorded on any crow-borne tag was 885, while the maximum number recorded on any basestation was 58,645, substantially below the memory capacity of tags and basestations respectively, implying that our system was never memory-limited. Every night before programmed tag-shutdown at 20:00 (starting no earlier than 18:45; see ‘Software settings’), we remotely contacted tags on roosting birds using masternodes, to ensure clock synchronization. Of our 41 deployed tags, four apparently failed to transmit, as they were never detected by other tags, basestations or masternodes, even during regular, wide-ranging searches outside the core study area. A further four tags either ceased transmitting, or developed irremediable on-board clock issues during the study (on average 8.0±1.6 days after data collection had commenced), and were excluded from all analyses. Of the remaining 33 tags, 26 delivered immediately useable data, while the on-board clocks of the other seven had drifted, or spontaneously reset at least once during deployment, which necessitated post hoc adjustment of logged times (see ‘Data processing’).

Experimental schedule

From the time that traps were permanently removed from the study area (21 October 2011) until data collection ceased, fieldworkers only entered the study site during the crows’ inactive roosting period (range: 18:45–05:00) to ensure that the social network under investigation was minimally disturbed. Tags switched on synchronously at 04:00 on 27 October 2011 (see ‘Software settings’), after a 5-day standby period during which the birds could habituate to their tags, and the population could recover from our trapping activities. After initial switch-on, tags operated on a 16/8 h on–off duty cycle (see ‘Software settings’ below). Data were collected over 19 consecutive days, divided into four experimental time periods: a 7-day perturbation-free ‘baseline’ control period (‘B’); a 3-day experimental period with a simulated tree fall in the centre of the main study valley, approximately midway between the two crow communities (‘E1’); a 4-day experimental period with a simulated tree fall close to the geographical centre of each crow community (‘E2’); and a 5-day post-experimental reversal period (‘R’), replicating baseline conditions. Each tree-fall simulation (E1, 1 site; E2, 2 sites; Fig. 1c) consisted of ca. 150 kg of decaying candlenut timber transported to the experimental sites and collected into a pile as though an infested tree had freshly fallen46 (Supplementary Fig. 1). This timber was ‘salted’ each night with longhorn beetle larvae, which were collected elsewhere and placed carefully into existing beetle burrows and crevices19. For logistical reasons, the E1 stimulus was covered with a tarpaulin at the end of the E1 period, while both E2 stimuli were physically removed from the study site at the end of the E2 period. As with all data collection and system maintenance, experimental stimuli were positioned and removed at night, to avoid crow disturbance.

Software settings

We programmed tags to optimize system performance within the constraints imposed by their memory and battery capacity. Following the initial standby period (see above), tags operated on a 16/8 h on–off duty cycle, starting at 04:00 each morning (68.4±0.7 min before sunrise) and shutting down every evening at 20:00 (112.1±0.7 min after sunset). Tags were programmed to emit a single radio pulse (433 MHz) every 20 s. Since on-board memory may have been insufficient to record every single received radio pulse individually, tags were programmed to dynamically calculate the mean received signal strength (RSSImean) for pulse sequences during sustained encounters, and to record this value in a log, together with the identities of transmitting and receiving tags, the start- and stop-time of the pulse sequence (Tstart and Tstop), and the power of the weakest (RSSImin) and strongest (RSSImax) received radio pulses. The receiving tag closed the log when either (i) no pulse was received from the transmitting tag for six consecutive pulse intervals (in our study, 6 × 20 s=120 s); or (ii) the encounter reached a threshold of 15 received pulses (in either case, Tstop would equal the time of the last received pulse). For encounters that exceeded 15 pulses, fresh logs were initiated sequentially for as long as the encounter continued (for example, a 12-min encounter would generate a series of three separate logs, of 5, 5 and 2 min, respectively). Condition (i) above was designed to allow for accidentally missed pulses, occurring (for example) because of temporary obstructions between transmitting and receiving tags. Condition (ii) was implemented to reduce information loss through averaging over the course of protracted encounters and caused logs to record a maximum duration (Tstop minus Tstart) of 300 s in the case that 15 consecutive 20-s pulses were received. As condition (i) effectively allowed six consecutive missed pulses during the course of an encounter, however, it was possible for encounter logs to last for longer than 300 s14.

Estimating bird-to-bird distance from signal strength

‘Proximity loggers’, including our Encounternet transceiver tags, record the strength of received radio signals (RSSI; see above), from which the distance between tags (and hence animals) is later estimated. Such inference is possible because radio signals attenuate predictably with distance from their source. Before deploying our system, we experimentally explored the effects of distance and several nuisance variables (habitat structure; height of tags above ground; relative alignment of transmitting and receiving tag antennae) on RSSI (reported in full elsewhere14). The resulting statistical model allowed us—given some assumptions about the movement of crows (for example, that relative antenna angles were sampled randomly) and their habitat preferences and activity profiles (as characterized in previous years with crow-mounted, miniature video cameras47)—to establish an RSSI threshold value, with which we could identify relatively close encounters, during which crows may have observed each other. While RSSImax (see above) provides a convenient tool for preliminary analyses13, high values may be generated by fleeting passes of birds, rather than by protracted social encounters. To address this problem, we filtered our raw dataset using RSSImean values instead, which are computed by averaging RSSI across series of consecutively received pulses (see above) and therefore contain considerably more information. This averaging process has two noteworthy consequences. First, the RSSImean of many encounters (in particular, very short ones) will be reduced by weaker pulses during the approach and separation periods of associating individuals; therefore, we will have discarded a number of encounter segments in which crow pairs came within close proximity at least part of the time. Second, because animals are unlikely to be stationary throughout an encounter, their distance of closest approach will generally be much lower than the recorded RSSImean suggests. To obtain a dataset for our network and diffusion analyses comprising predominantly of close encounters, during which social learning through close observation could have taken place, we applied a filtering threshold of RSSImean≥15. Our calibration analyses suggest that a single-pulse RSSI of 15 will correspond to an inter-crow distance of ≤4.7 m in 50% of cases, and ≤11.3 m in 95% of cases14. These distance estimates are likely to be highly conservative: of all logs with RSSImean≥15, we found that the median RSSImax value was 37, indicating that dyads generally spent part of their encounter in much closer proximity than the RSSImean value suggests.

Data processing

Before analysis, we conducted a quality-control exercise48, in which: (i) incomplete, corrupt or duplicate logs were removed; (ii) data from tags that failed temporarily or wholly during the 19-day deployment period were discarded; (iii) the timing of encounter logs was compared visually between each tag in a given dyad, to identify offsets that might indicate clock-drift issues; and (iv) post hoc time adjustments were made to logs of seven tags with faulty clocks. Step (iii) was omitted for one tag (ID no. 35), which was actively transmitting throughout the deployment, but which failed to upload any logs to basestations, so that its encounters were recorded only by its social partners’ tags rather than by both participating tags. Time adjustments in step (iv) were based on tag clock readings, which we had recorded from each tag at known times using the masternode on an approximately nightly basis (see above). These adjustments were also facilitated by the basestation array, which recorded the activity schedule of the affected tags, as well as by unaffected tags, which reliably logged the time of encounters with affected tags. For social-network analyses and graphs, we subsampled tag-to-tag logs according to their RSSImean values in order to include only encounter segments where crows remained within a given distance of each other on average (see above; Supplementary Fig. 6a,b). Because each encounter between tagged birds is effectively recorded twice (once by each participating tag), it is necessary to reconcile between-tag discrepancies in RSSI and start- and stop times. Such discrepancies can arise from phase offsets in pulse patterns between tags, from minor clock asynchronies, and from between-tag power differences likely associated with small variations in power cells, amplifier circuits and antennae14,49; we reconciled such log pairs by accepting the earliest start time and the latest stop time. Finally, because protracted encounters generated a series of ca. 5-min long logs (see above), we considered logs that started within 23 s of each other (marginally over a single-pulse interval; see above) to be contiguous and amalgamated them to form a single encounter record50 (Supplementary Fig. 6c).

Network analyses

Node layout for network graphs was the same in all figures and was achieved by spring-embedding, with minor manual adjustments to improve legibility. ‘Close’ associations are indicated by edges coloured according to the summed duration of associations with an RSSImean≥15 (see above) logged during the period of interest (Fig. 1d, 7 days; Fig. 2a, 3-day subsamples to allow comparison). More distant spatial associations (RSSImean≥0) are indicated by grey edges. To produce time-series plots (Fig. 2b–d), we used daily aggregated associations, stored in a matrix D of the total (daily) duration of pairwise encounters with RSSImean≥15 (see above). We computed each metric (k, d and f, see below) on each of the 19 consecutive study days, first for all 33 crows, and then separately for the northern and southern communities (here each community was treated as an ‘isolated’ group with its own duration matrix D). The degree of a crow on a given day is the number of other tagged crows it encountered (at the specified RSSImean level); for crow j, it is simply the count of non-zero elements in row j of matrix D. This number, averaged over all crows (n=33, 20 or 13), gives the mean daily degree (k). The mean duration of encounters (d) is the average, over all possible crow dyads, of the daily duration of encounters, computed as the average of the off-diagonal elements of D. Encounter durations among crows in the southern community were substantially longer than in the northern one on average; therefore, for the purposes of visualization (Fig. 2c), the mean duration was scaled by the average value in the first seven baseline days (1.07 min for all crows, 0.55 min for the northern and 5.79 min for the southern community). Molecular analysis of crows’ blood samples (see ‘Study site and subject attributes’) generated a binarized matrix G of first-order relatedness36. We used two approaches to explore the role of relatedness in shaping daily association networks. The first was to correlate the association matrix for all crows for each day of the baseline period (days 1–7) with matrix G. We used standard Mantel matrix correlation tests for this, with the Pearson correlation coefficient as the test statistic. To test the hypothesis that the correlation coefficient was greater than expected by chance, we used a stratified node permutation test in which node labels of crows from the northern community (and from the southern community) were shuffled only among themselves51. The second approach (shown in Fig. 2d) examined changes in the fraction of daily encounter durations that occurred between pairs of first-order related crows (f). If all non-zero entries in matrix D align with non-zero entries in G, f=1.

Information-flow simulations

The potential flow of social information across networks was investigated through a series of daily simulations (Fig. 2e–g; for details, see main text). In each simulation, a single crow was seeded with a hypothetical piece of information at the start of the day. The information could pass from ‘informed’ to ‘naive’ crows during encounters between them, simulating the spread of information through the population. Within the time window of each encounter, the transmission process was modelled to be stochastic, with a constant probability per unit time, characterized by the mean time for information transfer (λ). We set λ at 5 min, reflecting the modal duration of empirically observed encounters. Each crow in turn was chosen as the information seed. Our measure of information flow is the size of the ‘indomain’; for crow j, this is the number of seed crows from which crow j could have received the hypothetical piece of information by day’s end. We ran 1,000 simulations per starting crow per day and plotted the daily indomain size averaged over the 1,000 simulations and over all crows, those in the northern community, and those in the southern one (i; Fig. 2e). Varying λ by±3 min caused the average all-crow indomain (i) to vary in size by less than one crow. For more detailed analyses of indomain effects (Fig. 2f,g), we plotted matrices that summarize data from the same contiguous 3-day blocks (B, E1, E2 and R) that had been used to construct network graphs (Fig. 2a). Each cell in the matrix panels was coloured according to the probability of simulated information passing from the starting crow (arranged along the y axis) to another crow (x axis), averaged over all runs on all days used in the relevant 3-day period (the only difference between panels f and g is the ordering of the crows; for details, see figure caption). Wilcoxon rank-sum tests were used to compare values of daily network metrics between experimental time periods; to illustrate effects, the medians are presented, together with the full data range, and the estimated effect size (the median of the difference between a sample from the first group and a sample from the second) with its 95% confidence interval. Finally, because the maximum distance at which individuals are considered to be ‘in association’ will influence the results of social-network analyses, we generated descriptive metrics for each experimental period using a range of RSSImean threshold values (RSSImean≥13, 14, 16 and 17), demonstrating that the described results remained qualitatively unchanged (Supplementary Fig. 7).