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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

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Deterministic logistic modelThe following population dynamics model was applied to reconstruct the initial dugong population size in 1894 from fishery statistics between 1894 and 1914:$$N_{t + 1} = N_{t} left( {1 , + r{-}r , N_{t} /K} right) – C_{t} ,$$where r is the intrinsic rate of population increase, Nt is the population size in year t, K is the carrying capacity, and Ct is the number of individuals removed from the waters near the Ryukyu Islands in year t. The carrying capacity (K) in 1893 was sufficient to sustain the initial population of dugongs at that time (N1894). The intrinsic rate of population increase (r) was given between 1 and 5% within a range of natural one.Approximate Bayesian calculationWe conducted approximate Bayesian calculation (ABC)32 to estimate the number of individuals in 1979 based on bycatch data between 1979 and 2019, and the constraints of the numbers of individuals were 11 in 1997, three in 2007, and almost extinct in 2019. We denoted fecundity as f, the survival rate until 1 year old as s0, the annual survival rate after 1 year old as s, the age at maturity as am, and the physiological longevity as A. We assumed that the sex ratio at birth was 1:1 on average; the age at maturity am was eight years of age33, and the physiological longevity A was 73 years6. We ignored environmental stochasticity because no mass deaths caused by infectious diseases or changes in survival or mortality rates due to environmental fluctuations have not been recorded during this period. We also ignored density effects because the carrying capacity of the location was sufficiently greater than the initial population size, and our goal was to investigate the possibility of population recovery after a decrease in population using a population dynamics model and estimate the natural growth rate during this period. The detailed extinction risk depends on age structure.According to the life history parameters, except the physiological longevity compiled by (ref.33), the annual survival probability of an a year-old individual is s for a = 1, 2, …, 72; s0 for a = 0, and 0 for a = 73; the reproductive probability of an adult female  > 8 years old is 2f. As the number of years for a population to become extinct or recover depends on age composition, age-specific survival, and reproductive rates, we obtain the population growth rate by the maximum eigenvalue of the following Leslie matrix, L = {Lij} (i = 1,…73, j = 1,…,73) as:$$L_{i1} = s_{0} f/2quad {text{for}}quad i ge a_{m} ,L_{i+ 1,i} = squad {text{for}}quad i = 1, ldots ,72,quad {text{and}}quad L_{ij} = 0,{text{otherwise}}{.}$$We used the population growth rate λ, defined by the maximum eigenvalue of L, as an indicator of the population growth rate.We assumed that the sex of each individual in 1979 was randomly sampled by the 1:1 sex ratio, and its age was randomly sampled by the stable age structure that is given by the eigenvector of the Leslie matrix with the maximum eigenvalue. We assumed that the number of individuals at age 1 year in year t + 1, denoted by N1,t+1, is determined by the binomial distribution:$$Prleft[ {N_{1,t + 1} = x} right] = left( {begin{array}{*{20}c} {N_{f} } \ x \ end{array} } right)left( {s_{0} f} right)^{x} left[ {1 – left( {s_{0} f} right)} right]^{{N_{f} – x}} ,$$where Nf represents the number of adult females in year t. We assumed that no twins were born. We assumed that the probability that an individual with age x survived in the next year is s if x = 1 or s0 if x = 0. We also assumed that Ct individuals who died by bycatch were randomly chosen from any sex and age because the age of individuals caught by bycatch is rarely known. We do not know the sex of some individuals.We assumed the following prior distributions for N1997, f, and s: N1979 (in) U(11, 80), f (in) U(1/14, 1/6) if at least one adult male existed in the population, s0 (in) U(0.1, 0.85); and s (in) U(0.8, 0.97), where U(a, b) is the uniform random variable between a and b. These probabilities were constant for each simulation trial from 1997 to 2019. We selected the set of parameters with the population growth rate (λ) obtained when the maximum eigenvalue of the Leslie matrix was between 0.96 and 1.01.We rejected trials that did not satisfy the following summary statistics: N1997 ≥ 11 (intensive survey in 1997), Nt ≥ 3 during 2004–2017 (monitoring), and N2019 ≤ 1 (“local extinction”). We obtained the prior distributions of N1997, f, s0, s, and N2004, and of the  > 130,000 trials in the prior distribution with natural population growth rates λ of 96.1–98.8%, 99.3% were rejected. For 95% of the 1000 adopted trials, N1979 ranged from 14 to 58. If λ  > 98%, N1997 was ≤ 45 for the adopted trials (Extended Data Fig. 7. Even if all the stranding deaths were due to anthropogenic factors, such as the release of dugongs after bycatch or boat strike, the range of N1997 changed to  98%, with only a slight upward shift, but positive natural growth rate (or λ  > 1) was again very unlikely (0.3%) among the adopted trials.Population viability analysis to assess the impact of bycatch on the extinction riskWe re-evaluated the extinction risk with and without bycatch using the 1000 parameter sets of N1979, f, s0, and s that satisfied the summary statistics in the ABC and stochastic individual-based model, beginning from N1979 for the corresponding parameters. For each parameter set, 100 trials were conducted for each scenario to compare the extinction risks. More

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