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Species used in the experimentsMilnesium inceptum32 (Fig. 1A, a picture taken using Olympus BX41 Phase Contrast light Microscope associated with Olympus SC50 digital camera) is an obligatory predatory species with the body length ranging from 326 to 848 μm. It feeds on rotifers, nematodes and other tardigrades and lays smooth eggs in exuviae. To stay active, M. inceptum needs a thin water film around its body14. The species inhabits places exposed to shorter and longer periods of drying i.e. frequently drying mosses growing on cement walls32. Till now it was reported in Poland, Germany, Japan, Switzerland and Bulgaria32. At the same time, it is a perfect organism for our research because (1) it is large and easy to observe, (2) it tolerates frequent periods of entering and leaving anhydrobiosis, (3) it easily creates a tun stage. Milnesium inceptum for experimental purposes were acquired from a moss sample from a cement wall in Poznań, Poland (52°24′15″N, 16°53′18″E). The extraction of tardigrades was conducted under stereomicroscope (Olympus SZ51) using standard methods33. Then specimens, further used in our experiments, have been cultured based on protocol proposed by Roszkowska et al.34. Only fully active, adult specimens were selected for the experiments.Figure 1Model animals used in experiments: (A) Milnesium inceptum; insert shows tardigrade in the tun state; (B) Cepaea nemoralis in its natural environment; (C) a tardigrade that appeared on moss surface during in vivo observation of rehydrated moss cushion (red arrow). Figures were assembled in Corel Photo-Paint 2017 (http://www.corel.com).Full size imageCepaea nemoralis35 (Fig. 1B, a picture taken using Motorola g(9), Camera version 7.3.63.53-whitney) is a stylommatophoran European land snail species, which is widespread and common throughout the continent36. The average maximum shell diameter is 20 to 22 mm37. It feeds on plant materials available, yet has a strong preference for dead and senescent herbs38. C. nemoralis occurs in variable habitats (frequently in synanthropic ones) such as forests, meadows, gardens, near shrubs or dunes36.The period of its activity falls on the growing season; it usually comes out of the shell and crawls when the air humidity reaches 70% or more, independently from solar radiation and air temperature28. The species is a good model for our study due to its: (1) large size compared to tardigrades, and (2) co-occurrence with M. inceptum in natural environments. Individuals of C. nemoralis were harvested from anthropogenic environment: gardens adjacent to detached houses (52°25′28″N, 16°46′52″E). Snails were collected from plants, cement walls and ground surfaces. After collection, all C. nemoralis specimens were washed-up and placed in 30 L (480 × 360 × 252 mm) transparent plastic box with mesh covering for ventilation. Soil and rocks were placed in the box allowing to maintain a moist shelter for snails, and a sepia was used as a source of a calcium. Animals were fed with lettuce, cabbage and nettle twice a week and sprinkled with water to stimulate their activity. Box containing snails was kept in a rearing room, at 17 °C in 12:12 photoperiod. Snails were kept in the box for 1.5 months prior to the experiments. For the experiments we used only adult animals. The snails were checked under Olympus SZX7 stereomicroscope prior to the experiment to ensure they were free of tardigrades.Pilot studiesDoes the tardigrades’ distribution within a moss cushion enable tardigrade-snail contact?To check whether tardigrades may come into a close encounter with the snail in the natural environment (which would be impossible if the tardigrades were only present in the lower layers of the moss), we investigated the distribution of water bears within moss cushions. The observations were performed for 6 samples of dried moss cushions (ca. 1 cm high and 3 cm in diameter). The moss containing M. inceptum specimens, was collected from a concrete wall in Poznań, Poland (52°24′15″N, 16°53′18″E), the same from which tardigrades were initially collected for the culturing purposes. Three moss cushions were rehydrated, and left for 3 h followed by further observation to check whether tardigrades may actively move across the moss cushion. On the remaining three moss samples, a horizontal cut was made through the center of the moss cushion to check in which layer tardigrade tuns are present while the moss remains dry. The extraction of tardigrades from separated layers was conducted under stereomicroscope (Olympus SZ51) using standard methods33.Within the dry moss cushions tardigrades were present in both the upper and lower moss layers. We did not observe any difference in the number of individuals of M. inceptum that would be dependent on the moss layer. A total of 353 tardigrades were extracted from one moss cushion (dry weight of moss = 0.332 g), what gives the density of tardigrades per 1 g of dry moss sample equal to 1063 specimens. The observation of rehydrated moss cushions conducted in vivo using Olympus SZX16 stereomicroscope associated with Olympus DP74 digital camera and cellSens software revealed that single active tardigrades may also appear on the moss surface (Fig. 1C, red arrow). Therefore, observed in the pilot studies tardigrades distribution within the moss cushion enables tardigrade-snail contact.Is it possible for a tardigrade to take a snail ride?The initial observations were carried out for snails and tardigrades to check whenever a tardigrade may be transferred by a snail. In total, 10 snails and 20 active tardigrades were used. Two variants of Petri dishes (ø 90 mm) were prepared: (1) with smooth and (2) scratched bottom, to avoid and allow tardigrade attachment to the bottom of the dish, respectively. We repeated the observation five times per option. For each single observation we used one snail and two tardigrades.Snails and tardigrades were split equally between the pilot’s experimental options (in total 5 snails and 10 tardigrades per option). We checked whether tardigrades may be transferred by snails by putting tardigrades in the drop of water in the center of a Petri dish and releasing an active snail to crawl through the drop. In total, in the case of the smooth-bottom option, three tardigrades glued to the snail’s body within which two were moved to a distance up to a few centimeters. The third one fixed to a snail’s leg and had a potential to be transferred to a greater distance. In the case of the dishes with the scratched bottom, we did not notice any transfer. Tardigrades were attached tightly to the dishes’ bottom and remained unmoved after the snail had passed through them. Therefore, the observation in the pilot study confirmed that tardigrades may stick to snails’ body and be transferred by a gastropod at least when the substratum (bottom of the dish) is smooth.Experimental design
Experiment 1. Do snails have a significant effect on tardigrade dispersion that depends on the substrate type?As the laboratory environment offers limited possibilities to reflect natural conditions, we aimed to create an environment similar to the natural one by eliminating as many artificial elements as possible and, at the same time, enabling observation and data collection. To imitate a natural microhabitat of water bears we used a piece of moss as a substrate. Moss is a natural shelter and a hunting space for these animals, and a gripping surface that prevents them from being easily carried away by a stream of water or wind. The moss Vesicularia dubyana39 used in the experiment was purchased in an aquarium shop and was derived from an in vitro culture. It was checked under Olympus SZX7 stereomicroscope prior to the experiment to ensure it was free of tardigrades. For experimental purposes we used plastic ventilated boxes with dimensions 950 mm × 950 mm × 600 mm, tightly closed with a plastic lid. The bottom of each box was scratched with sandpaper in order to (1) imitate a rough surface of a concrete wall to which mosses are attached in the natural environment; (2) allow tardigrade locomotion. At the same time, moss and (unfortunately) plastic elements are quite common surroundings of C. nemoralis frequently found in anthropogenic habitats36.Using transparent, non-toxic aquarium silicone, a square with a side length of 3 cm and a height of 0.5 cm was mounted on the bottom of the box. Before starting the experiment, the tightness of the square silicone barrier was checked by pouring 2.5 ml of water inside and leaving the boxes for observation for 24 h. After this time, all silicone squares turned out to be impermeable to water.Boxes for each of the experimental option, namely: (A) control (further in the text referred as C), (B) tardigrades + snail (referred as TS), and (C) tardigrades + snail + moss (referred as TSM, see Fig. 2), were prepared in a following way: 2.5 ml of water was added to the scratched bottom of the box inside the silicone square and 7.5 ml to the area outside of the silicone square to enable survival and active locomotion of tardigrades on both sides of the silicone barrier. Then, 10 active individuals of M. inceptum taken from the culture were transferred to the center of the silicone square. It was repeated for 90 boxes (30 boxes per each C, TS and TSM option). Therefore we used 300 tardigrades per each experimental option which gives 900 tardigrades in total for all experimental options. In case of 30 boxes with TSM option, a piece of moss (ca. 2.5 cm in diameter) was added. It was situated in the center of the silicone square, just after the tardigrades were placed at the boxes in order to isolate tardigrades from the snail during the experiment.Figure 2Graphical representation of three designed experimental options of the experiment 1. (A) 10 tardigrades in the silicone square (control (C)); (B) 10 tardigrades in the silicone square and one snail placed in the box (tardigrades + snail (TS)); (C) 10 tardigrades in the silicone square, one snail placed in the box and additional piece of the moss added as a barrier between tardigrades and snail (tardigrades + snail + moss (TSM)). Figures were assembled in Corel Photo-Paint 2017 (http://www.corel.com).Full size imageFinally, in the boxes targeted for TS and TSM experimental options, one adult and active individual of C. nemoralis snail was placed in each box outside the silicone square. In total, 60 snails were used (30 individuals per experimental option).The boxes were then placed in the rearing room (17 °C, 80% of humidity, photoperiod 12:12) for 72 h. After this time, the number of tardigrades inside and outside the silicone square was counted (both: live and dead) separately for each box, using Olympus SZX7 stereomicroscope.Experiment 2. Effect of the snail’s mucus on tardigrade recovery to active life after anhydrobiosis
Milnesium inceptum anhydrobiosis protocolOnly fully active, adult specimens of medium body length were selected for the experiment. The animals were transferred to ø 3.5 cm vented Petri-dishes with bottom scratched by sandpaper to allow tardigrade locomotion. Five tardigrade individuals were placed to each Petri dish together with 450 µl of water and then dehydrated. In total, 16 Petri dishes with 5 tardigrades on each were prepared. Dehydration process lasted 72 h and was performed in the Q-Cell incubator (40–50% RH, 20 °C, darkness). After that time tardigrade tuns were kept under the abovementioned conditions for 7 days.Impact of the snail’s mucus on tardigrade tunsAfter 7 days of anhydrobiosis, one individual of C. nemoralis was transferred to each dish with tardigrade tuns and was left there for 1 min allowing the snail to actively crawl over the tuns. 30 min after the snail was removed from the dish, tardigrade tuns were observed under the Olympus SZX7 stereomicroscope for any animal movements. Then, all covered and vented dishes were left in the Q-Cell incubator overnight. After 24 h, the dried tuns were rehydrated by adding 3 ml of water to each Petri dish to check whether snail’s mucus affected mortality rates of tardigrades. After 3 and 24 h following rehydration tardigrade tuns were observed for any animal movements. Pictures of tuns were taken using Olympus SZ61 stereomicroscope associated with Olympus UC30 camera (Fig. 3). As reference data on the rehydration of the M. inceptum tuns free of the snail’s mucus, we used the data from Roszkowska et al.20 who tested anhydrobiosis survivability of above-mentioned species. Individuals used for the tuns preparation in the control option were collected from the same laboratory breeding stock, and prepared at the same laboratory conditions as those used in our experiments20.Figure 3Milnesium inceptum tuns: (A,B) before contact with snail mucus; (C,D) coated with wet snail mucus; (E,F) coated with dry snail mucus. Figures were assembled in Corel Photo-Paint 2017 (http://www.corel.com).Full size imageStatistical analysesThe number of tardigrades relocated in each experimental option (C, TS and TSM) was compared with a one-way ANOVA randomized version using RundomPro 3.14 software40. We used non-parametric methods because of the lack of normality. Differences were considered significant at p  More

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Experimental setupThis research was approved by the Carnegie Mellon University Committee of the Use of Human Subjects. All methods were performed in accordance with the relevant guidelines and regulations. Informed consent was obtained from all participants. Our data includes no identifying information of human participants. We conducted experiments from February to August 2021 (except for the preliminary sessions of random information; we ran the condition from June to November 2020). We preregistered the main experiment settings using AsPredicted (https://aspredicted.org/sm4k5.pdf).A total of 2786 subjects participated in our incentivized decision-making game experiments. We recruited subjects using Amazon Mechanical Turk (MTurk)52,53. Supplementary Table 1 shows the subject demographics. Our participants interacted anonymously over the Internet using customized software playable in a browser window (available at http://breadboard.yale.edu). All participants provided explicit consent and passed a series of human verification checks and a screening test of understanding game rules and payoffs before playing the game (see SI). We prohibited subjects from participating in more than one session of the experiment by using unique identifications for each subject on MTurk.In each session, subjects were paid a $2.00 show-up fee and a bonus depending on whether they took the appropriate disaster decision in four rounds. Furthermore, subjects earned $1.00 when they completed all four rounds. In each round, when a disaster stroke before they evacuated, the subjects earned no bonus. Otherwise, they earned a bonus of $1.00 without disaster or $0.50 with disaster by spending $0.50 for evacuation, plus $0.05 per other players who took the correct action accordingly (Supplementary Table 2). We have confirmed with prior work that the amount of evacuation cost, if any, makes no significant difference in the game’s performance23.At the start, subjects were required to pass a series of human verification checks. They needed to pass Google’s reCAPTCHA using the “I’m not a robot” checkbox. They were also requested to answer whether they were human players. The exact question asked was: “Please select an applicable answer about you.” The options were: “I am not a bot. I am a real person.” “I am not a real person. I am a bot.” “I am anything but a human.” and “I am a computer program working for a person.” The option’s order was randomized. Only the participants who selected “I am not a bot. I am a real person.” moved to the step of informed consent.When subjects provided explicit consent, they were asked to take a tutorial before the actual game would begin. In the tutorial, each subject separately interacted with three dummy players in two rounds of a 45-s practice game. In the actual game, some subjects would be informed in advance whether a disaster would indeed strike or not. In the practice game, while all subjects were not informed of such information in the first round, they were informed of the information in the second round. Thus, they practiced both conditions in terms of prior information on the disaster (see SI).After the practice game, subjects were assessed for their comprehension of the game rules and payment structure using four multiple-choice questions with three options. If they failed to select the correct answer in one of the questions, they could reselect it only once through the entire test. If they failed to select the correct answer more than once, they were unable to join the actual game.At 720 s after the tutorial beginning, a “Ready” button became visible simultaneously to all the subjects who completed the tutorial and passed the comprehension tests. The actual games started 30 s after the “Ready” button showed up. If subjects did not click the button before the game started, they were dropped. The game required a certain number of subjects. When the subjects who successfully clicked the button were more than 16, surplus subjects, randomly selected, were dropped from the game. When the number of qualified subjects was less than 12, the game did not start. As a result, subjects started the game in a group with an average size of 15.5 (s.d. = 1.1).At the start of the actual game, we selected one subject (the “informant”) at random who was informed in advance whether a disaster would indeed strike or not. The other subjects were informed that some players had accurate information about the disaster, but they were not informed who the informant was. The exact sentence that the informants received in their game screen was “A disaster is going to strike!” when a disaster would strike or “There is no disaster.” when a disaster would not strike. The one that the other uninformed subjects received was “A disaster may or may not strike.” Then, the group had the same informant across the four rounds except for a supplement condition of random informants. In the random informant condition, an informant was randomly selected every round.To prevent an end-of-game effect, we randomly set the game time with a normal distribution of a mean of 75 s and a standard deviation of 10 s. Prior work has confirmed that the game time is sufficient for players to communicate and make an evacuation decision23. As a result, each round ended at 75.0 s on average (s.d. = 9.5) without prior notice. In half of the sessions, a disaster struck at the end of the game. We did not inform any subjects, including the informants, when their sessions would end, the global network structure they were embedded in, or how many informants were in the game. After making their evacuation choice, subjects were informed of their success and failure along with overall results in their group. Then, subjects played another round of the evacuation game until they completed four total rounds. They had the same local network environment across four rounds except for the dynamic network condition.Network structure and tie rewiringIn the network sessions, subjects played the game in a directed network with a random graph configuration. A certain number of ties were present at the game’s onset as the initial density was set to 0.25.In the dynamic network conditions, subjects also could change their neighbors by making or breaking ties between rounds. In the tie-rewiring step, 40% of all the possible subject pairs were chosen at random. Thus, subjects could choose every other player at least once throughout the entire session (i.e., a set of four rounds) with a probability of about 80%. When the chosen pairs were connected, the pairs (the ties) were dissolved if the predecessor subject of the directed ties chose to break the tie. When the chosen pairs were not connected, the pairs (the ties) were newly created when the predecessor of the potential tie chose to create the tie. Subjects were not informed of the rewiring rate.To equalize the game time, we made subjects in the independent and static network conditions wait for additional 10 s after each game round ended. Despite the adjustment, the game time was significantly longer in the dynamic network sessions than in the independent and static network sessions. The average game time is 429.5 s (s.d. = 20.2) for the independent condition; 428.8 s (s.d. = 19.0) for the static network condition; and 564.7 s (s.d. = 36.3) for the dynamic network condition.To clarify mechanisms for dynamic networks to facilitate collective intelligence, we added one supplementary condition. In the supplementary condition, subjects were assigned to one of the 40 isomorphic networks that other subjects had developed with tie-rewiring options through the three rounds in the dynamic network condition (567 subjects in 40 groups). Network structure and other game settings (i.e., whether a disaster stroke, how long the game was, and which node was the informant) were identical to where the others played the game at the final round. However, players were different, and they had no prior experience in the game. They played the game in a network with a topology created by others ostensibly to optimize the accurate flow of information. In contrast to other conditions, subjects played only one round in the isomorphic network condition.Signal buttonsDuring the game of network sessions, subjects were allowed to share information about the possibly impending “disaster” by using “Safe” and “Danger” buttons that indicated their assessment (see SI). The default node color was grey. Then, when they clicked the Safe button, their node turned blue and, after 5 s, automatically returned to grey. Likewise, the Danger button turned their node to red for 5 s. Subjects could see only the colors of neighbors to whom they were directly connected. Since the signal exchange occurred through directed connections, an individual could send, but not receive, information from another subject (and vice versa). Once subjects chose to evacuate, they could no longer send signals, and their node showed grey (the default color) for the rest of the game. The neighbors of evacuated subjects were not informed of their evacuation. We have confirmed with prior work that collective performance does not vary with the communication continuity and the evacuation visibility23. Subjects could use the Safe and Danger buttons any time unless they evacuated, or they did not have to.Players dropping during the gameAfter each game round, when a player was inactive for 10 s, they were warned about being dropped. When they remained inactive after 10 s, they were dropped. When the selected informant was dropped, the session stopped at the round, and we did not use the data. Furthermore, as too many dropped players could affect the network structure and the behavioral dynamics of remaining players, we did not use the sessions where more than 25% of initial players were dropped during the game. Overall, 4 players dropped in 15 sessions; 3 players dropped in 22 sessions; 2 players dropped in 41 sessions; 1 player dropped in 44 sessions; and no player dropped in 58 sessions. The dropped players were prohibited from joining another session of this experiment.As noted above, players took the additional tie-rewiring step every round in the dynamic network sessions. Thus, the total game time was longer in the dynamic network sessions than in the independent and static network sessions even with the adjustment. As a result, more players were dropped in the dynamic network sessions than in the independent and static network sessions. The average number of dropped players across the four rounds is 0.40 (s.d. = 0.60) for the independent condition; 1.15 (s.d. = 0.86) for the static network condition; 1.75 (s.d. = 1.19) for the dynamic network condition. Although group size could affect collective performance, we found the differences in group size small enough for our study. We have confirmed the dynamic network’s performance improvement with a comprehensive analysis controlling the effect of group size (Supplementary Table 3). Also, there was no statistically significant difference in the dropped players’ performance of the dynamic network condition, compared with the other two conditions. The rate of correct actions of dropped players is 0.456 (s.d. = 0.322) for the independent condition, 0.594 (s.d. = 0.387) for the static network condition, and 0.558 (s.d. = 0.411) for the dynamic network condition; P = 0.106 between the independent condition and the dynamic network condition; P = 0.599 between the static network condition and the dynamic network condition (Welch two-sample t test).Analysis of signal diffusionsTo examine the change in signal diffusion, we analyzed “diffusion chains” for each signal type in the network sessions. We first identified the subjects who sent a signal when their neighbors had never sent one as spontaneous “diffusion sources.” When a subject sent a signal after at least one neighbor had sent the same type of signal, we regarded the subject’s signaling (and evacuation with danger signals) as occurring in a chain of signal diffusion and the total number of the responded subjects (including the diffusion source) as the diffusion size.We analyzed the distribution of signal diffusion chains with complementary cumulative distribution functions, measuring the fraction of diffusion chains that exhibit a given number of diffusion sizes. We found that the number of diffusions of both signals did not change across rounds. Safe-signal diffusions were more likely to occur than danger-signal diffusions regardless of whether a “disaster” would strike and how many rounds subjects played. On the other hand, the diffusion size varied greatly across rounds in disaster situations. With “disaster,” false safe signals spread further than true danger signals at the first round, but after that, warnings outperformed safe signals in terms of diffusion size. Figure 2B and Supplementary Fig. 3 scrutinize the changes in diffusion chains with their distributions.Analysis of individual responsivenessWe analyzed how individual evacuation behavior varies with exposure to signals from neighbors54. Let$${a}_{i}^{evacuate},, (t)=left{begin{array}{ll}1&quad text{if subject } i text{ evacuates at time } t\ 0&quad text{otherwise}end{array}right.$$$${a}_{i}^{show, safe},, (t)=left{begin{array}{ll}1&quad text{if subject } i mathrm{ shows a safe signal at time } t\ 0&quad text{otherwise}end{array}right.$$$${a}_{i}^{show , danger} ,, (t)=left{begin{array}{ll}1&quad text{if subject } i text{ shows a danger signal at time } t\ 0&quad text{otherwise}end{array}right.$$The hazard function, or instantaneous rate of occurrence of subject (i)’s evacuation at time t, is defined as:$${lambda }_{i},, (t)=underset{mathit{dt}to 0}{{mathrm{lim}}}frac{{mathrm{Pr}}({a}_{i}^{evacuate}=1;,, tt)}{dt}$$To model the time to evacuation, We used a Cox proportional hazards model with time-varying covariates for the number of signals, incorporating an individual actor-specific random effect55:$${lambda }_{i} ,, left{t|{{P}_{i}, X}_{i}(t), {G}_{i},{Y}_{i}(t)right}={lambda }_{0}(t)mathrm{exp}left{{{beta }_{P}^{{prime}}{P}_{i}+beta }_{X}^{{prime}}{X}_{i}(t)+{beta }_{G}^{{prime}}{G}_{i}+{beta }_{Y}^{{prime}}{Y}_{i}(t)+{gamma }_{i}right}$$where λ0(t) is a baseline hazard at time t.In the model, the hazard λi(t) depends on the covariates Pi, Xi(t), Gi, and Yi(t). The covariate Pi is the vector of subject i’s experiences before the sessions; that is, the number of rounds, the number of disasters that she has experienced, and the number of disasters that she has been struck by.The covariate Xi(t) is the vector of the number of safe signals ({x}_{i}^{safe} (t)), the number of danger signals ({x}_{i}^{danger} (t)). When subject j is a neighbor of subject i (i.e., (jin {N}_{i})), subject i is exposed to the signal of subject j, so that:$${x}_{i}^{safe},, (t)=sum_{jin {N}_{i}}{a}_{j}^{show, safe}(t)$$$${x}_{i}^{danger},, (t)=sum_{jin {N}_{i}}{a}_{j}^{show, danger}(t)$$The covariate Gi is the vector of the properties of the network in which subject i is embedded, out-degree, in-degree, and a network plasticity indicator. The covariate Yi(t) is the vector of the number of the subject i’s actions of sending safe and danger signals before time t. The coefficients β are the fixed effects and γi is the random effect for individual i. We assumed that waiting times to evacuation in different actors are conditionally independent given the sequence of signals they receive from network neighbors. This model shows how the hazard of an individual’s evacuation depends on the signaling actions of others, their network position, and experience (Supplementary Table 4). We applied the same model to the first signaling behavior. More