Individual and collective encoding of risk in animal groups

Matthew M. G. Sosnaa,1, Colin R. Twomeyb, Joseph Bak-Colemana, Winnie Poelc,d, Bryan C. Danielse, Pawel Romanczukc,d, and Iain D. Couzinf,g,h,1

aDepartment of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544; bDepartment of Biology, University of Pennsylvania, Philadelphia, PA 19104; cInstitute for Theoretical Biology, Department of Biology, Humboldt Universitat¨ zu Berlin, D-10099 Berlin, Germany; dBernstein Center for Computational Neuroscience Berlin, Humboldt Universitat¨ zu Berlin, D-10115 Berlin, Germany; eArizona State University-Santa Fe Institute (ASU–SFI) Center for Biosocial Complex Systems, Arizona State University, Tempe, AZ 85287; fDepartment of Collective Behaviour, Max Planck Institute of Animal Behavior, D-78547 Konstanz, Germany; gDepartment of Biology, University of Konstanz, D-78547 Konstanz, Germany; and hCentre for the Advanced Study of Collective Behaviour, University of Konstanz, D-78547 Konstanz, Germany

Edited by Gene E. Robinson, University of Illinois at Urbana–Champaign, Urbana, IL, and approved August 28, 2019 (received for review April 1, 2019)

The need to make fast decisions under risky and uncertain condi- For example, if we consider an individual in isolation, it must tions is a widespread problem in the natural world. While there base its decisions on sensory inputs and previous experience, has been extensive work on how individual organisms dynami- which may also be modulated by physiological state. However, cally modify their behavior to respond appropriately to changing it is clearly the individual that is “responsible” for the decision. environmental conditions (and how this is encoded in the brain), If we consider instead individuals embedded in a social net- we know remarkably little about the corresponding aspects of work, another possibility is introduced: As in other information- collective information processing in animal groups. For example, processing networks, such as neural circuits, computation may many groups appear to show increased “sensitivity” in the pres- be affected by changes in the individual components themselves ence of perceived threat, as evidenced by the increased frequency (network “nodes”) and/or by changes in the structural connec- and magnitude of repeated cascading waves of behavioral change tivity (topology) among the components (network “edges”). In often observed in fish schools and bird flocks under such cir- animal groups, individuals often exhibit a highly dynamic group cumstances. How such context-dependent changes in collective structure, with individuals’ spatial positions, orientations, and sensitivity are mediated, however, is unknown. Here we address sensory neighborhoods changing rapidly (5, 7–9). Yet nonethe- this question using schooling fish as a model system, focusing on less, individuals exhibit the capacity to change, consistently and 2 nonexclusive hypotheses: 1) that changes in collective respon- repeatedly, the topology of their social connectivity by switch- siveness result from changes in how individuals respond to social ing between what is often a relatively small number of group cues (i.e., changes to the properties of the “nodes” in the social structural states (e.g., ref. 9). This presents an additional nuance network), and 2) that they result from changes made to the struc- to understanding collective cognition (10–12), as while individu- tural connectivity of the network itself (i.e., the computation is als may be influenced by the topology of their network, they are encoded in the “edges” of the network). We find that despite the also able to modify this topology through their movements and fact that perceived risk increases the probability for individuals to perception of the environment. initiate an alarm, the context-dependent change in collective sen- sitivity predominantly results not from changes in how individuals Significance respond to social cues, but instead from how individuals modify the spatial structure, and correspondingly the topology of the net- work of interactions, within the group. Risk is thus encoded as a Many biological systems exhibit an emergent ability to pro- collective property, emphasizing that in group-living species indi- cess information about their environment. This collective cog- vidual fitness can depend strongly on coupling between scales of nition emerges as a result of both the behavior of system com- behavioral organization. ponents and their interactions, yet the relative importance of the two is often hard to disentangle. Here, we combined experiments and modeling to examine how fish schools col- group structure | antipredator behavior | social contagion lectively encode information about the external environment. We demonstrate that risk is predominantly encoded in the key challenge faced by animals is to appropriately adjust physical structure of groups, which individuals modulate in Atheir behavioral responses to changing environmental con- a way that augments or dampens behavioral cascades. We texts (1). To do so, organisms must make probabilistic decisions show that this modulation is necessary for behavioral cas- based on often imperfect or conflicting sensory information. cades to spread and that it allows collective systems to be Longer-term states such as fear or hunger can be considered as responsive to their environments even without changes in a persistent (but updatable) memory stored by the animal that individual computation. modulates the mapping from sensory input to behavioral change. The mechanisms by which individual organisms achieve effec- Author contributions: M.M.G.S., J.B.-C., and I.D.C. designed research; M.M.G.S. per- tive context-dependent behavior have been well studied (2–4), formed research; C.R.T., W.P., B.C.D., and P.R. contributed new reagents/analytic tools; M.M.G.S. and W.P. analyzed data; M.M.G.S., C.R.T., J.B.-C., W.P., B.C.D., P.R., and I.D.C. but what has been comparatively rarely explored is how such wrote the paper; and C.R.T., J.B.-C., W.P., B.C.D., and P.R. developed the mathematical behavioral plasticity is encoded by organisms that live in groups. model and performed and analyzed numerical simulations.y In highly coordinated animal groups, such as many species of The authors declare no conflict of interest.y schooling fish, flocking birds, or herding ungulates, individual This article is a PNAS Direct Submission.y reproductive success is often intimately linked with the func- This open access article is distributed under Creative Commons Attribution-NonCommercial- tional complexity of collective behavior (5, 6). This introduces a NoDerivatives License 4.0 (CC BY-NC-ND).y coupling between individual (“microscopic”) properties and col- 1 To whom correspondence may be addressed. Email: [email protected] or lective (“macroscopic”) behavior, and it is reasonable to expect [email protected] that this coupling will impact how evolution has shaped the This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. mechanisms by which individuals sense and respond to changing 1073/pnas.1905585116/-/DCSupplemental.y environmental conditions. First published September 23, 2019.

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ECOLOGY Changes to Cascade Frequencies and Sizes. Because golden shiners comparable to the water control (SI Appendix, section 4.2, t.s. = frequently startle even in the absence of any apparent external −0.117 individuals, P = 0.221). stimulus (28), we can discern between 2 forms of individual-level responses to predation risk: changes in intrinsic alarming (the Predictors of Startle Response. The increase in cascade sizes under onset of an alarm cascade) and changes in alarm propagation the first exposure to Schreckstoff can occur by 2 nonexclu- (participation in an alarm cascade). We chose not to manually sive mechanisms: a change in internal rules or probabilities trigger startles, as a global stimulus makes it impossible to dis- of response to neighboring alarms (individual responsiveness) tinguish between the social (response to neighbors) and asocial and/or a change in group structure that enhances alarm prop- (response to stimulus) progression of a cascade, and locally trig- agation (spatial positioning). To tease apart these mechanisms, gering individuals is experimentally challenging. In addition, our we set out to determine 1) the top predictors of response to a previous work has shown that startles triggered by an aversive neighboring startle before and after Schreckstoff, 2) whether the stimulus are indistinguishable from, and propagate in the same sensitivity to these predictors changes with Schreckstoff, and 3) way as, spontaneous startles (28). We developed a way of cate- whether including information on when startles occurred (before gorizing startles based on the product of speed and acceleration, or after Schreckstoff) improves our ability to predict whether a which corresponds to the change in kinetic energy (work rate) fish will respond. of the startling individual (SI Appendix, section 3), allowing us To examine what is predictive of response to a neighboring to reliably identify startling fish by thresholding (SI Appendix, startle, as in ref. 28, we focused on the first responder to an ini- Fig. S3). tiator in cascades featuring at least 1 responder (baseline, n = 46 As suggested by previous studies (34, 40, 47), Schreckstoff events; alarmed, n = 108 events), since here we have the clear- increased the intrinsic frequency of startling (Fig. 2A). The num- est causal relationship between alarm initiation and response. ber of cascades significantly increased on both the first and third (Because startles are relatively rare, we combined prestimulus exposures to Schreckstoff (1-way Wilcoxon signed-rank test on data from first-exposure Schreckstoff and water trials, i.e., prior groups’ difference in number of cascades: first exposure, V = to either treatment being given.) We then used L1-penalized 28, P = 0.011; third exposure, V = 15, P = 0.029). Exposure logistic regression (48, 49) to determine the features that are to water did not increase the frequency of alarms (V = 11, most predictive of response to an initiator. We included a set P = 0.219). of features that can be broadly categorized into the measurable In addition to cascades being initiated more frequently under properties about the stimulus itself (e.g., distance, relative spatial the first exposure to Schreckstoff, the average cascade size also orientation) and associated visual information. (Full details are increased (Fig. 2B; permutation test, t.s. = 0.954 individuals, in SI Appendix, section 5.1.) P < 0.0001). On the third exposure, however, despite cascades In agreement with previous work on this species (28), the fea- occurring more frequently, the average number of participants tures best predictive of response to an initiating startle were did not increase (t.s. = 0.060 individuals, P = 0.313) and was the logarithm of the metric distance to, and the ranked angu- lar area subtended by, visible neighbors (Fig. 3). These features emerged as the most predictive under both baseline and alarmed conditions. Similar features were found for predicting startle A B responses upon third exposure to Schreckstoff (SI Appendix, sec- tion 5.1). Our data also do not provide evidence of a change in the functional form for responding to a neighbor given these top 1.5 30 2 predictors after first exposure to Schreckstoff (see SI Appendix, 20 1.0 Tables S3 and S4 for logistic regression model coefficients

10 0.5 and 95% confidence intervals for before and after Schreckstoff model fits). 0 0.0 We then took 2 approaches to determine whether including 0.5 information on when startles occurred (before vs. after st rd st rd

Increase in N cascades 1 3 1 3 Water Increase in cascade size Water Schreckstoff) improved our ability to predict whether a fish will exposure exposure exposure exposure respond. First, we fitted a mixed-effects generalized linear model with a logistic link function on all startles in the first exposure C D to Schreckstoff (SI Appendix, section 5.2). We included log met- ric distance and ranked angular area as fixed effects, as well as their interactions with time (before vs. after Schreckstoff). Cas- cade ID nested within group ID was included as a random effect. We did not find support for statistical significance for time or its interactions with log metric distance and ranked angular area (SI Appendix, Table S5). Then, we performed a likelihood-ratio test comparing this model to an identical model that did not include time or its interactions. Model fit did not significantly improve when including information on when startles occurred (χ2 = 3.925, P = 0.270). Fig. 2. Perceived predation risk changes alarm propagation. (A) Taken together, these results suggest that individuals follow Schreckstoff increases the intrinsic frequency of alarms: The number of the same rules for responding to neighbors, the sensitivity to startle cascades increased upon first and third exposure. Raw data are these rules does not change with Schreckstoff, and information plotted alongside the mean ± 1 SE. (B) Schreckstoff increases average on when startles occurred does not improve our ability to predict cascade size following first exposure, but not upon third exposure. Expo- responses. While this indicates that changes in individual respon- sure to water does not increase frequency of alarms or average cascade siveness with Schreckstoff are either negligible or small, these size. (C) Distribution of cascade sizes before and after the first exposure to Schreckstoff. Lines represent contagion model fits to data, with shaded results alone are insufficient to conclude that changes in respon- regions representing 95% confidence intervals. Model is described in main siveness do not contribute to changes in collective sensitivity. text. (D) Cascade size distributions before and after the third exposure to Below we employ a behavioral contagion model that builds on Schreckstoff. these results and explicitly compares the relative contributions

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ECOLOGY translating sensory input into alarms), their spatial positioning may become activated due to inputs received from active neighbors. After a (the physical spacing and sensory network of group members), or fixed activation time τact , activated individuals transition into the recovered some combination of them. In solitary animals, the only option state. The activation time is set to τact = 0.5 s, matching the experimentally for responding to changing environmental conditions is to mod- observed average startle duration. For simplicity, we consider the recov- ify responsiveness. For social animals such as golden shiners, ered state as an absorbing state with no outward transitions, which restricts the model dynamics to single, nonrecurrent cascades. A simulation run is either option (or a combination) is possible. Our approach allows terminated when no active individuals remain. us to separate the relative contributions of spatial positioning As an initial condition we set all individuals as susceptible, and at time and individual responsiveness, and we find that any changes in t = 0 a single individual is activated (spontaneous startle). A susceptible collective responsiveness are predominantly encoded in spatial individual i receives from an active neighbor j stochastic doses of activat- positioning. ing signal of size da at a rate rij = ρmaxwij, with ρmax being the maximal Using a combination of experiments and modeling, we demon- rate of sending activation doses for wij = 1. The maximal activation rate is strate that individual-level changes in responsiveness do not con- bounded by limits on response times due to physiological constraints and tribute meaningfully to the augmented spread of startle cascades neuronal processing of sensory cues which trigger a startling response in fish (59). The fastest startling responses to artificial stimuli were reported to under perceived risk. Risk did not change the sensory features 3 −1 be of the order of few milliseconds. Therefore, we assume ρmax = 10 s , predictive of responding to neighboring alarms or the sensitiv- which allows in our model for fastest response times of the order of 1 ms ity to these features. Information on whether a startle occurred (for wij ≈ 1). To be able to resolve this timescale, we choose the numerical under baseline or alarmed conditions did not improve the ability time step accordingly to ∆t = 1 ms (ρmax = 1/∆t). to predict startle responses. In our behavioral contagion sim- Thus, with small ∆t, the activation signal received from individual j is a ulations where we explicitly vary individual responsiveness, we stochastic time series dij(t) with 2 possible values, da and 0, whereby the found that changes in responsiveness are not necessary to gen- probability of receiving an activation dose per simulation time step ∆t is erate the observed changes in cascade sizes. Finally, when simu- pa = rij∆t. Each agent integrates all inputs over a finite memory τm = 2 s. lating cascades under solely changes in responsiveness, changes The agent becomes activated if the cumulative dose

in spatial positioning, or both, we find that average cascades did Z t 1 X 0 0 not change with changes in responsiveness but did with changes Di(t) = dij(t ) dt [1] K in spatial positioning. i j t−τm In contrast to typical conceptualizations of collective cog- received by a susceptible agent i within its memory time exceeds its internal nition, in which individuals interact on a relatively fixed net- threshold θi. Here, Ki is the in degree of the focal individual, such that the work structure (51, 52), the fish schools in our experiment can doses received by the focal individual are rescaled by the number of its net- change their group structure on the same timescale as rel- work neighbors, a form supported by prior work in a similar system (28). The evant changes in the environment. The fact that this group individual thresholds are drawn from a uniform distribution with minimum structure encodes relevant environmental features suggests that 0 and maximum 2θ¯, producing an average threshold of θ¯. This accounts for the fish could actively control and make adaptive use of their stochasticity due to inaccessible internal states of individuals at the time of emergent group features, a concept with growing theoretical sup- initial startle. port (53–57). The work we have presented here indicates the The expected value of the cumulative activation dose received by agent potential for self-organized animal groups to reveal additional i due to the activation of a single neighbor j (Ki = 1) over the activation time τact is thus hDii = daρmaxwijτact . We choose the weights wij to be equal insights into how dynamical networks may play an important to the probability that i responds and is the first responder to an initial role in collective intelligence emerging from simple interacting startle of j, inferred using the logistic regression model depicted in Fig. 3. components. The linear relationship between the cumulative dose hDii and the weights wij, along with the uniform distribution of thresholds across fish, guaran- Materials and Methods tees that the complex contagion process produces the correct relative initial Experiments. Groups of 40 golden shiners were filmed freely swimming in a response probabilities in the limit of small ∆t and wij (SI Appendix). With- 1.06 × 1.98-m tank filled to 4.0 cm depth. One hour after being transferred out loss of generality, we can set daρmax = 1. Thus, based on the maximal 3 −1 −3 to the tank, an automated sprayer released either Schreckstoff or water rate ρmax = 10 s , we set the activation dose da = 10 . This leaves us into the tank. The group was then filmed for an additional 0.5 h. No experi- with a single free parameter, the average dose threshold θ¯, which we fit menter was present in the room for the duration of the trial. Details on data via maximum likelihood. A total of 104 independent runs were performed extraction, processing, and analysis are available in SI Appendix, section 1. for each threshold value to estimate corresponding cascade size probability All experiments were conducted in accordance with Princeton University’s distributions. Institutional Animal Care and Use Committee. ACKNOWLEDGMENTS. We thank the Couzin Laboratory for helpful dis- Behavioral Contagion Model. Our model is based on a generalized model of cussions. This work was funded by an NSF Graduate Research Fellow- contagion proposed by Dodds and Watts (50, 58). Here, we have reformu- ship (to M.M.G.S.). C.R.T. was supported by a MindCORE (Center for lated the original model in terms of activation rates to describe behavioral Outreach, Research, and Education) Postdoctoral Fellowship. P.R. and W.P. contagion dynamics in continuous time. This allows us to more easily were funded by the Deutsche Forschungsgemeinschaft (DFG) (German constrain parameters based on experimentally determined timescales and Research Foundation), Grant RO47766/2-1. P.R. acknowledges funding by networks of influence, derived from the logistic regression’s predictions for the DFG under Germany’s Excellence Strategy–EXC 2002/1 “Science of response probabilities given fish positions at the time of the initial startle. Intelligence”–Project 390523135. I.D.C. acknowledges support from the NSF (IOS-1355061), the Office of Naval Research (N00014-09-1-1074 and N00014- We then simulate the model using a standard Euler discretization. 14-1-0635), the Army Research Office (W911NG-11-1-0385 and W911NF14- Individual fish, as nodes in a network, are connected by weighted 1-0431), the Struktur- und Innovationsfunds fur¨ die Forschung of the State directed edges wij ∈ [0, 1] that define the rate of signaling doses received of Baden-Wurttemberg,¨ the Max Planck Society, and the DFG Center of by individual i when individual j startles. Each individual i can be in 1 of 3 Excellence 2117 “Center for the Advanced Study of Collective Behavior” (ID: states si that we call susceptible, active, and recovered. Susceptible nodes 422037984).

1. S. Lima, L. Dill, Behavioral decisions made under the risk of predation: A review and 5. T. Pitcher, J. Parrish, “Functions of shoaling behaviour in Teleosts” in Behaviour of prospectus. Can. J. Zool. 68, 619–640 (1990). Teleost Fishes, T. Pitcher, Ed. (Chapman and Hall, London, ed. 2, 1993), pp. 363–439. 2. A. Sih, Optimal behavior: Can foragers balance two conflicting demands? Science 210, 6. J. Krause, G. Ruxton, Living in Groups (Oxford University Press, Oxford, UK, 2002). 1041–1043 (1980). 7. I. Couzin, J. Krause, Self-organization and collective behavior in vertebrates. Adv. 3. M. Milinski, “Predation risk and feeding behaviour” in Behaviour of Teleost Stud. Behav. 32, 1–75 (2003). Fishes, T. Pitcher, Ed. (Chapman and Hall, London, ed. 2, 1993), pp. 285– 8. M. Ballerini et al., Empirical investigation of starling flocks: A benchmark study in 305. collective animal behaviour. Anim. Behav. 76, 201–215 (2008). 4. S. Lima, P. Bednekoff, Temporal variation in danger drives antipredator behavior: The 9. K. Tunstrøm et al., Collective states, multistability and transitional behavior in predation risk allocation hypothesis. Am. Nat. 153, 649–659 (1999). schooling fish. PLoS Comput. Biol. 9, e1002915 (2013).

20560 | www.pnas.org/cgi/doi/10.1073/pnas.1905585116 Sosna et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 1 .Bral .Tre,C ono,J ai,I ozn mretsnigo complex of sensing Emergent Couzin, I. Faria, J. Ioannou, C. Torney, C. Berdahl, A. minds. 11. Collective Couzin, I. 10. 2 .Buh .Kaae,J lc,Cnit fitrs mrv olciecmuainof computation collective improve interest of Conflicts Flack, J. Krakauer, D. Brush, E. 12. 4 .Fx .Gen .Hge,G itn atn sa nirdtrrsos of and response deer white-tailed antipredator in an patterns as grouping and Rafting strategies Hilton, Anti-predator G. Lingle, Hughes, S. predator. a B. 15. of Green, presence A. the Fox, in flocking A. Avian 14. Pulliam, H. Martindale, S. Caraco, T. 13. 3 .Pgir,D odn .Load euaino avse n oaiga closed- a as foraging ant harvester of Regulation Leonard, N. Gordon, D. Pagliara, R. com- and 23. processing Information colony: fish “Bacterial from Castro, de herd L. selfish Omar, the N. in Xavier, effect R. dilution 22. the for and Evidence individual Treherne, J. on Foster, herd. cues selfish W. external the for 21. of Geometry Hamilton, effects W. The 20. Ward, A. Dillingham, P. Schaerf, T. 19. vigilance, size, group on temporal risk predation and of spatial Effects Christianson, fine-scale D. to Schuette, P. size Creel, herd S. elk 18. of Responses Jr, fish. Winnie in W. choice Creel, size group S. Context-dependent Krause, 17. J. Godin, J. Couzin, I. Hoare, D. 16. 3 .Grleu .Vln,J epeo,Ptnildsdatgso sn socially using of disadvantages Potential Mathuru semipalmated Templeton, A. of J. 34. flocks Valone, staging T. in Giraldeau, of alarms L. utility false 33. of adaptive Determinants the Beauchamp, and G. 32. Reliability Daniel, J. Verneyre, of avoidance L. the governing Blumstein, rule a D. for Evidence 30. Ruxton, G. net- Hilton, hidden G. the Cresswell, W. Revealing Couzin, 29. I. Wu, H. Hartnett, A. Twomey, C. Rosenthal, S. 28. ( shiner Golden Post, J. Stewart, T. predation. McQueen, aerial D. of Johannes, threat M. the 26. to fish shoaling of Response fish. Litvak, of M. behaviour 25. schooling the of aspects Some Keenleyside, M. 24. 1 .Khet atr fetn saebhvori oliggelggeese greylag moulting in behaviour escape affecting Factors Kahlert, J. 31. swimming. fast-start fish of performance and kinematics The Blake, R. Domenici, P. 27. on tal. et Sosna niomnsb oieaia groups. animal mobile by environments dpiesca structures. social adaptive uedeer. mule duck white-headed wintering Nature opectbesystem. excitable loop (NaBIC) Computing in behavior” putational insect. marine a on predation fish. shoaling of behavior collective community. ungulate African an (2014). in behavior foraging and wolves. by predation of risk in variation Behav. Anim. fish. information. acquired sandpipers. answer callers. alarm among discrimination flights. escape superfluous behavioral complex of prediction allows groups contagion. animal mobile in interaction of works Biol. Exp. predators. and Sci. food with Correlations abundance: population cas) Fish. (1955). 247 1–1 (1989). 810–817 46, ur Biol. Curr. 8–9 (1993). 183–192 36, . 0–0 (1980). 400–401 285, .Ornithol. J. 1517 (1997). 1165–1178 200, rc al cd c.U.S.A. Sci. Acad. Natl. Proc. Ethology ea.Ecol. Behav. hnrii rget r drnsta rge erbhvo in behavior fear trigger that odorants are fragments Chondroitin al., et 5–6 (2004). 155–164 67, 3–4 (2012). 538–544 22, IE,2011). (IEEE, 6–7 (2006). 569–577 147, 9–1 (2001). 295–314 107, hls rn.R o.Bo.Sci. Biol. Soc. R. Trans. Philos. LSCmu.Biol. Comput. PLoS 8–8 (2010). 584–587 21, hr ol ogeso aueadBooial Inspired Biologically and Nature on Congress World Third c.Adv. Sci. rc .Sc B Soc. R. Proc. Nature Nature xualeucocephala. Oxyura 1 (2007). 715 445, 1031(2018). e1603311 4, c.Adv. Sci. rc .Sc B Soc. R. Proc. 6–6 (1981). 466–467 293, 6049 (2015). 4690–4695 112, Science nm Behav. Anim. 3–3 (2000). 733–737 267, 1020(2018). e1006200 14, .Ter Biol. Theor. J. 1021(2017). e1603201 3, 7–7 (2013). 574–576 339, 8115 (2004). 1851–1857 271, 5916 (2002). 1559–1566 357, Wildfowl 1118 (2005). 1181–1189 69, 9–1 (1971). 295–311 31, ea.Ecol. Behav. oeiou crysoleu- Notemigonus 3–4 (1994). 232–241 45, a.J ih Aquat. Fish. J. Can. Behaviour nio.Biol. Environ. 773–784 25, 183– 8, Anser J. 8 .Dds .Wts eeaie oe fsca n ilgclcontagion. biological and social of model generalized A Watts, D. Dodds, P. small-scale 58. a in behaviour critical Pruitt finite J. of Control 57. Flack, J. Krakauer, D. Daniels, B. 56. Hein A. criticality? 55. at poised systems biological Are groups. Bialek, animal W. moving Mora, in T. transfer Information 54. Couzin, I. Biro, D. Buhl, J. Sumpter, D. 53. of Effects Shaw, E. minnows Burgess, fathead Evidence movement: J. flock of crab 45. fiddler responses of analysis Quantitative Behavioural Wethey, D. Viscido, Shih, S. M. 44. Jr, Adrian J. Brown, G. 43. fishes. in groupings social on to Studies fish Breder, prey C. of responses 42. The Brown, G. A Chivers, D. minnow: Jackson, the C. of Elvidge, behaviour C. shoaling Ferrari, M. the on 41. ‘schreckstoff’ of effect The Krause, J. fish. of 40. species different between reaction shiner fright common of the Transmission Krause, in J. schooling on 39. substance alarm of Effects fishes. Seghers, B. in Heczko, cells fishes. E. in substance signals 38. alarm Alarm Smith, and R. reaction 37. fright of distribution The Pfeiffer, fish. W. of reaction fright 36. The Pfeiffer, W. 35. 9 .Kr,D ae,TeMuhe elhl etr ae:Anuoilgclmodel neurobiological A later: century a half cell Mauthner The Faber, D. Korn, H. 59. in principles criticality self-organized Dynamical causing synapses Abarbanel, Dynamical Geisel, T. H. Herrmann, J. Levina, Selverston, A. A. 52. Varona, contagion. of P. model Rabinovich, generalized a M. in 51. behavior Universal Watts, D. Dodds, P. 50. B P. Meier, L. models. Schelldorfer, J. linear generalized 49. for algorithm path L1-regularization Hastie, T. Park, minnows, M. fathead solitary 48. of response Behavioral Smith, R. Lawrence, B. 47. Strandburg-Peshkin A. 46. 0822(2018). 20181282 system. social populations. animal (2011). 302 Biosci. Theor. behaviour. herd’ ‘selfish for concentrations. varying (2001). at hypoxanthine-3-n-oxide to (1959). assessment? risk or habituation Sensory Ecol. risk: predation in variation temporal theory. herd selfish Hamilton’s of test (1993). 37–48 127, cyprinidae). cornutus, (Notropis Copeia o decision-making? for Biol. networks. neural in neuroscience. Lett. Rev. l (2014). using 460–477 models mixed linear generalized B Soc. Stat. R. substance. alarm to promelas, groups. animal in transfer analysis. matrix (1981). nearest-neighbor A fish: schooling 8–0 (2005). 587–604 232, 3–3 (2010). 532–536 21, 5–6 (1977). 653–665 1977, tal. et oiltpigpit naia societies. animal in points tipping Social al., et 171(2004). 218701 92, 7–8 (2008). 177–186 127, a.Commun. Nat. h vlto fdsrbtdsnigadcletv optto in computation collective and sensing distributed of evolution The , 5–7 (2007). 659–677 69, e.Md Phys. Mod. Rev. a.Phys. Nat. PNAS eLife Neuron iulsnoyntok n fetv information effective and networks sensory Visual al., et 195(2015). e10955 4, ur Biol. Curr. hmn,Gmlso nagrtmfrhigh-dimensional for algorithm An Glmmlasso: uhlmann, ¨ nm Behav. Anim. | 40 (2017). 14301 8, 32 (2005). 13–28 47, 2316 (2006). 1213–1266 78, 5–6 (2007). 857–860 3, .Ce.Ecol. Chem. J. coe ,2019 8, October nio.Bo.Fish. Biol. Environ. e.Fs il Fish. Biol. Fish Rev. Acoustico-Lateralis 79R1 (2013). R709–R711 23, nm Behav. Anim. il Rev. Biol. 1 3–4 (2002). 735–741 63, -penalization. 0–1 (1989). 209–219 15, ul m u.Nt Hist. Nat. Mus. Am. Bull. 9–1 (1962). 495–511 37, | 52 (1981). 25–29 6, 0912 (1993). 1019–1024 45, (1992). 33–63 2, ea.Nua.Biol. Neural. Behav. o.116 vol. eevto nafacultative a in denervation .Fs Biol. Fish J. .Cmu.Gah Stat. Graph. Comput. J. rc .Sc il Sci. Biol. Soc. R. Proc. .Sa.Phys. Stat. J. | o 41 no. 1465–1470 58, 393–482 117, 488–497 33, Pimephales Behaviour 268– 144, | .Theor. J. Behav. 20561 Phys. 285, 23, J.

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