Downloaded by guest on September 27, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1905585116 the shaped has changing evolution to respond how conditions. and environmental sense impact individuals which will expect by mechanisms to coupling reasonable this is it that and behavior, col- a (“macroscopic”) func- and introduces lective properties the This (“microscopic”) 6). individual with (5, between linked behavior coupling collective individual intimately of ungulates, of complexity often tional herding species is many or success as birds, reproductive such flocking such groups, fish, groups. animal how schooling in coordinated is live that highly explored organisms In by rarely encoded comparatively is (2–4), plasticity been studied behavioral has well effec- what been achieve have but organisms behavior individual context-dependent which tive that by change. animal mechanisms behavioral the to The input by sensory as from stored considered mapping memory information. the be modulates updatable) can sensory hunger (but or persistent conflicting fear a or as such imperfect states decisions Longer-term probabilistic often make must on organisms based so, do To (1). texts A structure group of scales between coupling organization. on behavioral strongly a depend indi- as can species encoded fitness group-living thus vidual in is that Risk emphasizing group. property, the collective within net- interactions, modify the of individuals of topology work how the correspondingly from and instead structure, spatial but the cues, social individuals to how in respond changes sen- from not collective results in predominantly change sitivity context-dependent to the individuals alarm, for the probability an despite the initiate that is increases find risk computation We perceived network). the that the fact (i.e., of “edges” itself the network struc- social in the encoded the the to in made of changes “nodes” connectivity from the result tural they of that properties 2) and the social network), to to changes respond individuals respon- (i.e., how collective cues in in changes changes from on result that focusing siveness 1) system, model hypotheses: a nonexclusive as cir- address 2 fish we such schooling Here using under unknown. question collective this is flocks however, in mediated, bird changes are and context-dependent sensitivity such schools How fish cumstances. in observed change behavioral of often waves frequency cascading increased repeated pres- the of the by magnitude and evidenced in as “sensitivity” threat, perceived increased of show ence example, of to For appear aspects groups. groups corresponding animal many in the processing about information brain), little collective the in remarkably encoded know is we this changing how to dynami- (and appropriately conditions organisms respond environmental to individual there behavior how While their world. on modify natural cally work the 2019) extensive 1, in condi- been April problem uncertain review has for and widespread (received risky a 2019 under 28, is decisions August tions fast approved and make IL, to Urbana, need Urbana–Champaign, The at Illinois of University Robinson, E. Gene Germany by Konstanz, Edited D-78547 Konstanz, of University Behaviour, Collective 85287; of AZ Study Tempe, Advanced University, Germany; State Konstanz, Arizona D-78547 Behavior, Systems, Animal Complex Biosocial for Universit Center Humboldt (ASU–SFI) Berlin, Neuroscience Computational for Center 19104; PA Philadelphia, a Romanczuk Pawel Sosna G. M. Matthew in groups risk animal of encoding collective and Individual eateto clg n vltoayBooy rneo nvriy rneo,N 08544; NJ Princeton, University, Princeton Biology, Evolutionary and Ecology of Department hi eairlrsosst hnigevrnetlcon- environmental changing to responses behavioral their e hleg ae yaiasi oaporaeyadjust appropriately to is animals by faced challenge key | nirdtrbehavior antipredator c,d c nttt o hoeia ilg,Dprmn fBooy ubltUniversit Humboldt Biology, of Department Biology, Theoretical for Institute n anD Couzin D. Iain and , a,1 oi .Twomey R. Colin , | oilcontagion social g eateto ilg,Uiest fKntn,D757Kntn,Gray and Germany; Konstanz, D-78547 Konstanz, of University Biology, of Department f,g,h,1 b oehBak-Coleman Joseph , tz eln -01 eln Germany; Berlin, D-10115 Berlin, zu at ¨ 1073/pnas.1905585116/-/DCSupplemental. y at online information supporting contains article This 1 and movements their are through environment. they the topology network, of this perception their modify of to topology able the also by group influenced individu- be while of may as nuance number als (10–12), additional cognition small an collective presents relatively understanding This to 9). a switch- ref. often by (e.g., states connectivity is structural social what their between and of consistently ing topology change, to the capacity nonethe- repeatedly, the Yet exhibit 7–9). and individuals (5, orientations, less, rapidly positions, changing neighborhoods spatial group sensory dynamic individuals’ highly with a In exhibit structure, “edges”). often (network connec- individuals components groups, structural animal the the among in (topology) changes themselves tivity by components and/or individual may “nodes”) the computation (network in net- changes circuits, by social neural affected as a be information- such other in in networks, As embedded processing introduced: decision. individuals is the possibility instead for another “responsible” work, consider is However, we that state. experience, individual If physiological the previous by clearly and modulated is inputs it be also sensory may on which decisions its base oeiaie ies . C BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This interest.y of conflict mathematical no the declare authors developed The P.R. simulations.y I.D.C. and numerical and analyzed B.C.D., P.R., W.P., and performed J.B.-C., B.C.D., and W.P., C.R.T., model J.B.-C., and per- C.R.T., tools; paper; reagents/analytic M.M.G.S., the M.M.G.S. new data; wrote research; contributed analyzed W.P. P.R. designed and and I.D.C. M.M.G.S. B.C.D., W.P., and C.R.T., research; J.B.-C., formed M.M.G.S., contributions: Author owo orsodnemyb drse.Eal atgssagalcmor [email protected] Email: addressed. be may [email protected]. correspondence whom To epniet hi niomnsee ihu hne in be changes to without systems even collective computation. environments allows cas- individual it their behavioral that to for and responsive We necessary spread cascades. is to behavioral modulation cades dampens this in or that modulate augments show the individuals that in which way encoded groups, a predominantly of is structure risk physical that col- demonstrate environment. schools external combined We the fish we about how Here, information encode examine disentangle. lectively to to importance modeling hard relative and often experiments the is two yet the interactions, of com- system their of behavior and the both ponents of result a pro- cog- as collective to emerges This nition ability environment. their emergent about an information cess exhibit systems biological Many Significance o xml,i ecnie nidvda nioain tmust it isolation, in individual an consider we if example, For a inePoel Winnie , f eateto olcieBhvor a lnkIsiueof Institute Planck Max Behaviour, Collective of Department b eateto ilg,Uiest fPennsylvania, of University Biology, of Department y tz eln -09 eln Germany; Berlin, D-10099 Berlin, zu at c,d ¨ ra .Daniels C. Bryan , e rzn tt nvriySnaF Institute Fe University-Santa State Arizona . y raieCmosAttribution-NonCommercial- Commons Creative www.pnas.org/lookup/suppl/doi:10. e NSLts Articles Latest PNAS , h etefrthe for Centre d Bernstein | f6 of 1

ECOLOGY Here we explore the possibility that information process- AB ing may be facilitated not only by individuals changing their internal behavioral rules/states, as is typically considered in animal behavior, but that, by forming a networked system, indi- viduals can facilitate collective computation by changing the structural topology of the network (their social connectivity), without necessarily adjusting the way they respond to sensory information. We refer to changes in individual behavioral rules 5 cm and states as individuals changing their responsiveness and to changes in group structure as individuals changing their spatial positioning. C Across many animal taxa, group structure is known to be highly 8 sensitive to group members’ perceptions of risk and resources (13–19). These changes have generally been attributed to sim- 7 ple game theoretic considerations (20, 21), where structure is merely a byproduct of individuals acting to maximize their sur- 6 vival (5). But overlooked is the possibility that group structure, as an emergent encoding of the external environment, could itself 5 be an important mechanism by which organisms effectively pro- NND (cm) cess information in a changing world. In this way, the group’s 4 structure could act as a collective memory that modifies future Schreckstoff: 1st exposure decisions, similar to how an individual’s memory guides its own Schreckstoff: 3rd exposure 3 Water behavior (22, 23). To test the relative contributions of group members’ respon- 0 102030405060 siveness vs. spatial positioning to collective information process- Time (min) ing, here we present results from experiments with schooling fish (golden shiners, Notemigonus crysoleucas), known to have highly DE dynamic and self-regulating group structure (9, 16, 19), and use these data to investigate context-dependent changes in individ- 40 1 ual and collective responses to perceived risk. Like many fish 30 0.8 species (3, 24, 25), predation is a source of extremely high mor- 0.6 tality in the wild (26) and juveniles form coordinated schools in 20 0.4 response to this risk. Shiners also exhibit startle responses as an 10 escape behavior (27) that is socially contagious (28). Startles in 0.2 this species occur even in the absence of an external stimulus, 0 0 N visible neighbors N visible 1st 3rd 1st 3rd and these spontaneous false alarms propagate through the group of vision Proportion in the same manner as triggered true alarms (28). In nature, exposure exposure exposure exposure false alarms account for a high proportion of overall alarms (29– Fig. 1. Effect of perceived predation risk on group structure. (A) A subset 32), very likely because there are such considerable costs to not of the school prior to Schreckstoff. Rays (purple) represent a visualization of responding to true threats relative to false alarms (33). the field of view of the focal individual (colored white). (B) The entire school In our experiments, we manipulate the magnitude of perceived after receiving Schreckstoff. (C) Median nearest-neighbor distance upon risk (individuals’ priors that an immediate threat is present) by exposure to Schreckstoff or water (dashed lines). Shaded regions indicate introducing, remotely, the natural alarm substance Schreckstoff. mean of the group medians ± 1 SE. (D) Distributions of number of visible Schreckstoff is a family of chondroitins released from fish skin neighbors before (black) or after (red and orange) exposure to Schreckstoff. Left and right pairs of violin plots correspond to first and third exposures to when punctured or torn, such as in the vicinity of a success- Schreckstoff, respectively. Dashed lines demonstrate difference in medians. ful predation event (34–37), that induces a “fear response” in (E) Distributions of the proportion of individuals’ visual field occupied by fish, increasing group cohesion and startling behavior (37–39). other fish. However, while response to Schreckstoff is innate (37), fish will habituate to Schreckstoff if repeatedly exposed with no paired stimulus (39–41). As will be shown, these changes in group dropped when individuals were first administered Schreckstoff structure and collective responsiveness (the increased spread of (permutation test, test statistic [t.s.] = −2.04 cm, P < 0.0001, alarms) allow us to ask whether this context-dependent change n = 7 groups; Fig. 1 A–C; similar results for density, SI Appendix, in collective behavior results from individuals modulating their Fig. S1). In contrast, individuals did not move closer to one responsiveness to neighbors and/or whether risk is encoded by another upon third exposure to Schreckstoff (t.s.=0.073 cm, changes in the groups’ internal spatial structure. Our analyses, P = 0.14, n = 6 groups), in agreement with previous observations involving automated tracking, computational visual field recon- of groups of habituated fish (39–41). struction, and determination of the functional mapping between Such dramatic changes in the spacing among individuals are socially generated sensory input and individual and collective associated with corresponding changes to the visual fields of the response, allow us to not only distinguish between these alterna- fish. Because golden shiners rely primarily on vision for school- tive mechanisms, but also demonstrate the relative importance ing (28, 45, 46), we set out to quantify the visual properties of of each. the group structure. Upon first exposure, group members on average saw fewer neighbors (Fig. 1D; permutation test, t.s. = Results and Discussion −4.47 neighbors, P < 0.0001) and more of their vision was taken Group-Level Changes under Perceived Risk. Schreckstoff changed up by neighbors (Fig. 1E; t.s. = 15.59%, P < 0.0001). On the group structure upon first exposure, but not upon third exposure third exposure to Schreckstoff, however, there were no signifi- (Fig. 1). In agreement with theoretical predictions on investment cant changes in the average number of visible neighbors (t.s. = in antipredator behavior (4, 5), as well as previous empirical −0.04 neighbors, P = 0.37) or proportion of visual field occupied results (19, 35, 42–44), average nearest-neighbor distance sharply by other fish (t.s. = 0.00%, P = 0.30).

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1905585116 Sosna et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 i o nrae(..=000individuals, 0.060 = participants (t.s. of increase number not average did the frequently, more occurring emtto et ..=094individuals, 0.954 = t.s. test, also size permutation P cascade 2B; average the (Fig. Schreckstoff, increased (V to exposure alarms first of the frequency the increase not P did exposure, water first to cascades: of on number 28, test in signed-rank difference third Wilcoxon and groups’ (1-way first Schreckstoff the both to on exposures increased num- significantly The 2A). cascades (Fig. of startling ber of frequency intrinsic the increased acd iedsrbtosbfr n fe h hr xoueto exposure third the after and before main distributions in Schreckstoff. size described shaded Cascade is with (D) Model data, intervals. text. to cascade confidence fits 95% average model representing or contagion regions represent alarms Lines of Schreckstoff. Expo- frequency to exposure. increase third not (C are upon does size. not data water but Raw to exposure, sure exposure. first of following third size mean number and cascade the The first alarms: alongside upon of plotted increased frequency cascades intrinsic startle the increases Schreckstoff 2. Fig. Appendix, (SI thresholding us by allowing fish 3 ), S3 startling Fig. section rate) identify Appendix, (work reliably (SI energy to individual kinetic startling in the change of acceleration, the cate- and to of speed of corresponds way product a which the developed on We based same startles (28). aversive the gorizing startles in an spontaneous propagate by as, and triggered way from, startles indistinguishable that are shown stimulus has our addition, work In trig- previous challenging. locally experimentally and is cascade, asocial individuals a dis- gering and of to progression neighbors) stimulus) impossible to to it (response (response makes social manually the stimulus to between global not propagation tinguish a chose alarm as We in startles, cascade). changes trigger alarm (the and an alarming cascade) in intrinsic alarm (participation in an changes of risk: onset individual-level external predation of forms apparent to 2 any between responses of discern can absence we the (28), stimulus in even startle Sizes. frequently and Frequencies Cascade to Changes on tal. et Sosna C A 0.219). = < Increase in N cascades under frequently more initiated being cascades to addition In Schreckstoff 47), 40, (34, studies previous by suggested As 10 20 30 P 0 .01.O h hr xoue oee,dsiecascades despite however, exposure, third the On 0.0001). .1;tidexposure, third 0.011; = itiuino acd ie eoeadatrtefis exposure first the after and before sizes cascade of Distribution ) ). exposure ecie rdto ikcagsaampoaain (A) propagation. alarm changes risk predation Perceived 1 st exposure 3 rd Water ± crcsoficessaverage increases Schreckstoff (B) SE. 1 D B Increase in cascade size V 15, = 0.5 0.0 0.5 1.0 1.5 exposure eas odnshiners golden Because P 1 P st .2) Exposure 0.029). = .1)adwas and 0.313) = exposure 3 rd Water 11, = V = ..= t.s. 4.2, section Appendix, individuals, (SI −0.117 control water the to comparable retto)adascae iulifrain Fl eal are details (Full information. in visual associated set spatial measurable relative and a the distance, orientation) (e.g., into included itself categorized stimulus We are the broadly about initiator. be that properties can an features that to the features response of determine used of to then predictive 49) We most (48, given.) regression being prior logistic treatment i.e., trials, prestimulus either water combined and to Schreckstoff we response. first-exposure rare, from and relatively data initiation are alarm startles between (Because relationship ini- causal an est to (baseline, responder responder first alarmed, 1 the least events; on at featuring focused cascades we in 28, tiator ref. in as startle, a whether predict to respond. ability will our fish improves Schreckstoff) (before after 3) occurred or and startles a when Schreckstoff, on to with information response including changes whether of predictors the predictors these whether 2) to top Schreckstoff, sensitivity the after and 1) before determine startle prop- mechanisms, neighboring to these alarm out apart enhances set tease that we To probabilities structure positioning). group nonexclu- or (spatial responsiveness) in agation (individual 2 rules change alarms internal by a neighboring and/or in occur to change can response of a Schreckstoff mechanisms: to sive exposure first the Response. Startle of Predictors hs eut n xlctycmae h eaiecontributions relative on the builds compares that sensitivity. explicitly model collective and contagion in results behavioral these changes a employ to we contribute respon- Below these in not changes small, do that conclude or siveness to negligible insufficient are either alone are results Schreckstoff respon- with individual in predict siveness changes to that ability indicates to our this information improve While sensitivity and not responses. does the Schreckstoff, occurred with startles neighbors, when change on to not does responding rules for these rules same the (χ occurred startles improve when significantly not on 3.925, did information fit include including Model not when did interactions. that its model or identical time an test to likelihood-ratio model a this performed comparing we (SI Then, its area S5). angular or Table ranked time Appendix, and for distance significance metric statistical log effect. with for random interactions support a find as not included as did was Cas- ID We well Schreckstoff). group as after within nested effects, vs. ID (before fixed cade time as exposure with area interactions first met- angular their log the ranked included in and We distance startles 5.2 ). after ric section all Appendix, on (SI vs. function Schreckstoff to link (before logistic model will linear a generalized fish with occurred mixed-effects a a whether fitted we predict startles First, to respond. ability our when improved Schreckstoff) on information Schreckstoff after and before fits). for model intervals confidence S4 95% and and S3 (see in Schreckstoff top change to Tables these a exposure given first neighbor of after a evidence predictors to 2 provide responding not for form do functional also the startle data sec- Our predicting Appendix, 5.1). (SI for Schreckstoff tion to found exposure third were upon responses features alarmed and angu- Similar baseline features both ranked These under conditions. 3). predictive the were most (Fig. and the neighbors startle as to, visible emerged initiating by, distance subtended an metric area to the lar of response logarithm of the predictive best tures oeaiewa speitv frsos oaneighboring a to response of predictive is what examine To ae oehr hs eut ugs htidvdasfollow individuals that suggest results these together, Taken including whether determine to approaches 2 took then We fea- the (28), species this on work previous with agreement In eto 5.1.) section Appendix, SI P 0.270). = n 0 vns,snehr ehv h clear- the have we here since events), 108 = P o oitcrgeso oe coefficients model regression logistic for 0.221). = h nraei acd ie under sizes cascade in increase The NSLts Articles Latest PNAS L IAppendix, SI 1 -penalized n | 46 = f6 of 3 2 =

ECOLOGY 0.13 0.5 tial positioning, however, are sufficient to explain this increase. 0 0 Moreover, the lack of a change in spatial positioning in the third 1.000 1.000 1.00 Baseline exposure case, resulting in no difference in average cascade size 0.500 0.50 0.500 Alarmed pre- and post-Schreckstoff, indicates that a change in spatial 0.20 0.10 positioning is also necessary to account for a change in average

) 0.100 0.100 j 0.05 cascade size. 0.050 0.050 0.02 Finally, we quantified the relative contributions of respon- | s

i 0.01 siveness and spatial positioning to average cascade size with 0.010 12345 0.010

P(s 0.005 0.005 a full factorial design (SI Appendix, section 6.3). We trained a regression model that allows weights of the contagion net- 0.001 0.001 work to depend both on the presence of Schreckstoff (capturing 0.04 0.06 changes due to individual responsiveness) and on distances and 0 0 orientation (capturing changes due to spatial positioning). In 0 1020304050 010203040the resulting behavioral contagion model, the increase in the average size of cascades post-Schreckstoff (Fig. 4D) could not Metric distance (cm) Angular area rank be accounted for by changes to individual responsiveness alone. Instead, the increase in cascade sizes required the observed Fig. 3. Probability of an individual startling in response to an initiator as change in spatial positioning. Thus we find that changes to spatial a function of the top 2 predictors, log metric distance (Left) and ranked positioning are essential for the increase of group responsiveness angular area (Right), holding the other predictor constant at its mean value. post-Schreckstoff. Gray corresponds to the first-exposure data prior to receiving Schreckstoff; red corresponds to after receiving Schreckstoff. Solid lines are the fit of the Conclusions model with the top 2 predictors to the first-responder data; shaded regions represent 95% confidence intervals. Top and Bottom histograms correspond The central question of our paper is whether collective sensitivity to first responders and nonresponders, respectively. is modulated by changes in individuals’ responsiveness (rules for

of individual responsiveness and spatial positioning on a com- A mon scale.

Changes to Cascade Size Distribution. Are changes in the spatial positioning of group members sufficient to account for larger cas- cades? Or are there changes in individual responsiveness that do not play a role at the onset of cascades but still contribute to their spread? Answering these questions requires that we con- sider the entire behavioral contagion process, as the decision of whether or not to startle likely depends on the decisions of all of an individual’s observable neighbors (28). Thus, to understand the origin of the change in average B C 1st 3rd cascade size, we investigated a generic model of behavioral con- exposure exposure tagion that incorporates 2 key components: the sensitivity of individuals to available social cues and the structure of the inter- action network. The latter is given by a network of weighted edges wij that represent the probability of individual i to be a first responder given that individual j initially startled. The

interaction network for each trial is parameterized directly by before after before after fish positions and orientations via a logistic regression on sen- sory features detailed in the previous section (SI Appendix, Eq. D Baseline S3). In this way, the interaction network captures the relevant Modulation of Responsiveness differences in pre- and postexposure sensory features caused by Modulation of Spatial Positioning changes to spatial positioning (Fig. 1). Once the interaction net- Both Modulations work is fixed, the complex contagion model contains a single free parameter that specifies the social sensitivity of individuals. average cascade size This sensitivity parameter (“dose threshold”) (50) determines how much perceived risk an individual tolerates before startling. Fig. 4. SIR-type behavioral contagion model explains alarm propagation and indicates that changes in spatial positioning are necessary to explain A An internal state (the “cumulative dose,” Fig. 4 ) tracks an increased cascade sizes. (A) Model schematic. The focal individual in the sus- individual’s perceived risk based on the time course of startle ceptible state (S, white) receives doses from active individuals (I, “infected,” responses of its network neighbors, causing a startle once reach- magenta) that it integrates over timescale τm. When the cumulative dose ing the threshold. See Materials and Methods and SI Appendix, reaches the individual’s threshold, it startles and remains in the active state section 6 for a complete description of the model. We fit this for time τact , after which it enters the recovered state (R, gray). (B) The individual-level sensitivity parameter to the observed cascade model is simulated starting with the observed initial startler and dose rates size distributions in 4 cases: before and after Schreckstoff in both that correspond to the first-responder probability functions for first and the first and third exposure treatments (Fig. 4 B and C). third exposure to Schreckstoff. The relative log-likelihood of the model For both experimental treatments (first and third exposure), producing the observed cascade sizes is plotted as a function of the sin- gle free parameter that modulates individual responsiveness, the average the 95% credible intervals of the maximum-likelihood estimated dose threshold θ¯.(C) Best-fit parameter values controlling responsiveness dose thresholds before and after Schreckstoff overlap (Fig. 4C), are similar pre- and postexposure, with overlapping 95% credible intervals. indicating that a change in individual responsiveness to the star- (D) Comparing average cascade sizes after modulating responsiveness and tles of neighbors is not required to explain the observed increase spatial positioning separately reveals that a change in spatial positioning is in average cascade size under perceived risk. Changes in spa- essential for the increase of group responsiveness post-Schreckstoff.

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1905585116 Sosna et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 states edges directed discretization. startle. Euler initial standard the a of using time model the easily the simulate at then more positions for We predictions fish to regression’s given logistic probabilities us the and response from timescales allows derived determined influence, This of experimentally networks on time. behavioral based describe continuous parameters to constrain rates reformu- in activation have of dynamics we terms Here, in contagion 58). model (50, original Watts the and lated Dodds by proposed contagion Model. Contagion Behavioral University’s Committee. Princeton Use with and accordance Care Animal in Institutional conducted in were data on available experiments Details are trial. All the experi- analysis of No and duration water h. the processing, 0.5 for or additional extraction, room an Schreckstoff the for in filmed either present then was released was menter group sprayer The tank. automated the an into tank, the to 1.06 Experiments. Methods and Materials important interacting simple an from play emerging may components. intelligence networks collective additional the in dynamical reveal indicates role how to here into groups presented animal insights have self-organized their we for of work potential use The adaptive sup- (53–57). theoretical group make growing port with and this concept a rel- control features, that group actively emergent as fact could that timescale The fish suggests features the same environment. environmental relevant the the encodes can structure on in experiment net- our structure changes fixed in evant group schools relatively fish their a the on change 52), interact (51, structure individuals work which in nition, changes with did but did positioning. responsiveness spatial cascades in in average changes that with find change we not both, changes or responsiveness, positioning, in spatial simu- changes in when solely gen- Finally, under sizes. to cascades cascade necessary lating in not changes are observed we the responsiveness sim- responsiveness, erate in contagion individual changes vary behavioral that explicitly found our we In where responses. ulations ability startle the improve occurred predict not startle did to a conditions whether alarmed sensitiv- or on the baseline Information under or features. features alarms these sensory neighboring to the ity to change responding not of did predictive Risk cascades risk. startle perceived of spread under augmented the con- to not do meaningfully responsiveness tribute in changes individual-level that strate spatial in in changes encoded any positioning. predominantly positioning that are spatial find responsiveness we of collective and contributions responsiveness, relative individual shiners, the and golden separate allows approach as to Our possible. us such is combination) animals a (or social option mod- either For to option is responsiveness. only conditions the environmental ify changing animals, to solitary responding In for them. or of members), positioning group combination of spatial some network sensory their and spacing alarms), physical into (the input sensory translating on tal. et Sosna individual by .M iisi Peainrs n edn eaiu”in behaviour” feeding and risk “Predation Milinski, M. 3. demands? conflicting and two review balance foragers A Can predation: behavior: Optimal of Sih, risk A. the under 2. made decisions Behavioral Dill, L. Lima, S. 1. .S ia .Bdeof eprlvraini agrdie nirdtrbhvo:The behavior: antipredator drives danger in variation Temporal Bednekoff, P. Lima, S. 4. niiulfih sndsi ewr,aecnetdb weighted by connected are network, a in nodes as fish, Individual cog- collective of conceptualizations typical to contrast In demon- we modeling, and experiments of combination a Using 0114 (1980). 1041–1043 prospectus. .Pthr d CamnadHl,Lno,e.2 93,p.285– pp. 1993), 2, ed. London, hypothesis. Hall, allocation risk predation and (Chapman Ed. Pitcher, 305. T. Fishes, × s .8mtn le o40c et.Oehu fe en transferred being after hour One depth. cm 4.0 to filled tank 1.98-m i htw alssetbe cie n eoee.Ssetbenodes Susceptible recovered. and active, susceptible, call we that a.J Zool. J. Can. ruso 0gle hnr eefimdfel wmigi a in swimming freely filmed were shiners golden 40 of Groups i hnindividual when w ij ∈ ,1] [0, 1–4 (1990). 619–640 68, htdfietert fsgaigdssreceived doses signaling of rate the define that u oe sbsdo eeaie oe of model generalized a on based is model Our j trls ahindividual Each startles. m Nat. Am. 4–5 (1999). 649–659 153, eto 1. section Appendix, SI eaiu fTeleost of Behaviour i a ei f3 of 1 in be can Science 210, xelne21 Cne o h dacdSuyo olcieBhvo”(ID: Behavior” Collective of Study Advanced 422037984). the for “Center 2117 Excellence Baden-W f W911NF14- Innovationsfunds of and und (W911NG-11-1-0385 Struktur- of the Office 1-0431), Research “Science N00014- Army and the (N00014-09-1-1074 2002/1 Research 14-1-0635), Naval Strategy–EXC NSF of the Office the from Excellence (IOS-1355061), support (German acknowledges Germany’s by for I.D.C. (DFG) funding 390523135. under (Center Intelligence”–Project acknowledges Forschungsgemeinschaft P.R. DFG MindCORE RO47766/2-1. Deutsche Fellow- the a Grant the Research W.P. Foundation), by and Graduate by Research P.R. supported Fellowship. NSF funded Postdoctoral was an were Education) C.R.T. and by Research, M.M.G.S.). funded Outreach, (to was work ship This cussions. ACKNOWLEDGMENTS. probability size cascade corresponding estimate distributions. to value 10 threshold threshold of each dose total for average A likelihood. the maximum parameter, via free single a with time i of time the at individuals of startle. states initial internal inaccessible to due minimum stochasticity with 2 distribution maximum The uniform and (28). a 0 system from similar net- drawn a its in are of work thresholds number prior individual the by supported by form rescaled a are neighbors, individual work focal the by received doses threshold agent susceptible a by received u oso eeaiy ecnset can we rate generality, of loss out dose cumulative the w between relationship linear The of that startle probability the to step time simulation per dose activation p an receiving of probability series time stochastic ms 1 of order the of times response fastest for assume model we (for Therefore, our milliseconds. in few allows to in of reported which response were order stimuli startling the artificial of a to responses be and trigger startling constraints which fastest The physiological cues (59). to fish sensory due of times processing response neuronal on limits for by doses bounded activation sending of size rate of signal ing individual is t run simulation A remain. cascades. individuals active nonrecurrent no single, recov- when restricts terminated which to the transitions, dynamics outward consider no model with we the state simplicity, absorbing an For as state duration. ered startle to average set observed is time activation The a state. After neighbors. active time from activation received fixed inputs to due activated become may epnepoaiiisi h ii fsmall of limit initial relative the correct in the probabilities produces process response contagion complex the that tees dose cumulative the if activated becomes agent The to accordingly step time .I ozn .Kas,Sl-raiainadcletv eairi vertebrates. in behavior collective and Self-organization Krause, J. of Couzin, Behaviour I. in Ruxton, 7. Teleosts” G. in Krause, J. behaviour shoaling 6. of “Functions Parrish, J. Pitcher, T. 5. .K Tunstrøm K. 9. Ballerini M. 8. a = u oteatvto fasnl neighbor single a of activation the to due ij = hs ihsmall with Thus, h xetdvleo h uuaieatvto oercie yagent by received dose activation cumulative the of value expected The sa nta odto estalidvdasa ucpil,ada time at and susceptible, as individuals all set we condition initial an As ln ihteuiomdsrbto ftrsod cosfih guaran- fish, across thresholds of distribution uniform the with along , .Pthr d CamnadHl,Lno,e.2 93,p.363–439. pp. 1993), 2, ed. London, Hall, and (Chapman Ed. Pitcher, T. Fishes, Teleost coln fish. schooling Behav. Stud. olcieaia behaviour. animal collective igeidvda satvtd(pnaeu trl) susceptible A startle). (spontaneous activated is individual single a 0 w ρ r τ ij ij act max ∆t ≈ sthus is = ahaetitgae l nusoe nt memory finite a over inputs all integrates agent Each . ) ob bet eov hstmsae ecos h numerical the choose we timescale, this resolve to able be To 1). j θ nerduigtelgsi ersinmdldpce nFg 3. Fig. in depicted model regression logistic the using inferred , i i Here, . 10 eevsfo natv neighbor active an from receives rtmeg h a lnkScey n h F etrof Center DFG the and Society, Planck Max the urttemberg, ¨ miia netgto fsaln ok:Abnhaksuyin study benchmark A flocks: starling of investigation Empirical al., et –5(2003). 1–75 32, 3 olciesae,mlitblt n rniinlbhvo in behavior transitional and multistability states, Collective al., et LSCmu.Biol. Comput. PLoS hD s −1 θ ¯ i d i rdcn naeaetrsodof threshold average an producing , K ∆t a estteatvto dose activation the set we , = i iigi Groups in Living τ tarate a at stei ereo h oa niiul uhta the that such individual, focal the of degree in the is act d D h ciainsga eevdfo individual from received signal activation the , d ij etakteCui aoaoyfrhlfldis- helpful for Laboratory Couzin the thank We a i i ciae niiul rniinit h recovered the into transition individuals activated , (t ∆t (t ρ epnsadi h rtrsodrt ninitial an to responder first the is and responds ih2psil values, possible 2 with ) max ) nm Behav. Anim. = = w K s(ρ ms 1 1 ij i i r 1095(2013). e1002915 9, τ ihnismmr ieecesisinternal its exceeds time memory its within ij X act = τ j d Ofr nvriyPes xod K 2002). UK, Oxford, Press, University (Oxford act ecos h weights the choose We . a ρ w Z ρ max max max t = 4 ij −τ 0–1 (2008). 201–215 76, t = needn uswr performed were runs independent ,mthn h experimentally the matching s, 0.5 w = m = .Temxmlatvto aeis rate activation maximal The 1. ij 1/∆t ∆t with , d .Tu,bsdo h maximal the on based Thus, 1. ij rdeFrcugo h State the of Forschung die ur (t ¨ j j and NSLts Articles Latest PNAS (K 0 tcatcdsso activat- of doses stochastic ) ). dt d i ρ = a w d 0 max = )oe h activation the over 1) ij a hD 10 IAppendix (SI n ,weeythe whereby 0, and en h maximal the being θ ¯ i −3 i hsacut for accounts This . n h weights the and θ hslae us leaves This . ¯ ρ w hc efit we which , max ij ob equal be to = τ 10 | m .With- ). 3 = f6 of 5 ∆ j s Adv. s. 2 sa is −1 t [1] is ,

ECOLOGY 10. I. Couzin, Collective minds. Nature 445, 715 (2007). 35. W. Pfeiffer, The fright reaction of fish. Biol. Rev. 37, 495–511 (1962). 11. A. Berdahl, C. Torney, C. Ioannou, J. Faria, I. Couzin, Emergent sensing of complex 36. W. Pfeiffer, The distribution of fright reaction and alarm substance cells in fishes. environments by mobile animal groups. Science 339, 574–576 (2013). Copeia 1977, 653–665 (1977). 12. E. Brush, D. Krakauer, J. Flack, Conflicts of interest improve collective computation of 37. R. Smith, Alarm signals in fishes. Rev. Fish Biol. Fish. 2, 33–63 (1992). adaptive social structures. Sci. Adv. 4, e1603311 (2018). 38. E. Heczko, B. Seghers, Effects of alarm substance on schooling in the common shiner 13. T. Caraco, S. Martindale, H. Pulliam, Avian flocking in the presence of a predator. (Notropis cornutus, cyprinidae). Environ. Biol. Fish. 6, 25–29 (1981). Nature 285, 400–401 (1980). 39. J. Krause, Transmission of fright reaction between different species of fish. Behaviour 14. A. Fox, A. Green, B. Hughes, G. Hilton, Rafting as an antipredator response of 127, 37–48 (1993). wintering white-headed duck Oxyura leucocephala. Wildfowl 45, 232–241 (1994). 40. J. Krause, The effect of ‘schreckstoff’ on the shoaling behaviour of the minnow: A 15. S. Lingle, Anti-predator strategies and grouping patterns in white-tailed deer and test of Hamilton’s selfish herd theory. Anim. Behav. 45, 1019–1024 (1993). mule deer. Ethology 107, 295–314 (2001). 41. M. Ferrari, C. Elvidge, C. Jackson, D. Chivers, G. Brown, The responses of prey fish to 16. D. Hoare, I. Couzin, J. Godin, J. Krause, Context-dependent group size choice in fish. temporal variation in predation risk: Sensory habituation or risk assessment? Behav. Anim. Behav. 67, 155–164 (2004). Ecol. 21, 532–536 (2010). 17. S. Creel, W. Winnie Jr, Responses of elk herd size to fine-scale spatial and temporal 42. C. Breder, Studies on social groupings in fishes. Bull. Am. Mus. Nat. Hist. 117, 393–482 variation in risk of predation by wolves. Anim. Behav. 69, 1181–1189 (2005). (1959). 18. S. Creel, P. Schuette, D. Christianson, Effects of predation risk on group size, vigilance, 43. G. Brown, J. Adrian Jr, M. Shih, Behavioural responses of fathead minnows and foraging behavior in an African ungulate community. Behav. Ecol. 25, 773–784 to hypoxanthine-3-n-oxide at varying concentrations. J. Fish Biol. 58, 1465–1470 (2014). (2001). 19. T. Schaerf, P. Dillingham, A. Ward, The effects of external cues on individual and 44. S. Viscido, D. Wethey, Quantitative analysis of fiddler crab flock movement: Evidence collective behavior of shoaling fish. Sci. Adv. 3, e1603201 (2017). for ‘selfish herd’ behaviour. Anim. Behav. 63, 735–741 (2002). 20. W. Hamilton, Geometry for the selfish herd. J. Theor. Biol. 31, 295–311 (1971). 45. J. Burgess, E. Shaw, Effects of Acoustico-Lateralis denervation in a facultative 21. W. Foster, J. Treherne, Evidence for the dilution effect in the selfish herd from fish schooling fish: A nearest-neighbor matrix analysis. Behav. Neural. Biol. 33, 488–497 predation on a marine insect. Nature 293, 466–467 (1981). (1981). 22. R. Xavier, N. Omar, L. de Castro, “Bacterial colony: Information processing and com- 46. A. Strandburg-Peshkin et al., Visual sensory networks and effective information putational behavior” in Third World Congress on Nature and Biologically Inspired transfer in animal groups. Curr. Biol. 23, R709–R711 (2013). Computing (NaBIC) (IEEE, 2011). 47. B. Lawrence, R. Smith, Behavioral response of solitary fathead minnows, Pimephales 23. R. Pagliara, D. Gordon, N. Leonard, Regulation of harvester ant foraging as a closed- promelas, to alarm substance. J. Chem. Ecol. 15, 209–219 (1989). loop excitable system. PLoS Comput. Biol. 14, e1006200 (2018). 48. M. Park, T. Hastie, L1-regularization path algorithm for generalized linear models. J. 24. M. Keenleyside, Some aspects of the schooling behaviour of fish. Behaviour 8, 183– R. Stat. Soc. B 69, 659–677 (2007). 247 (1955). 49. J. Schelldorfer, L. Meier, P. Buhlmann,¨ Glmmlasso: An algorithm for high-dimensional 25. M. Litvak, Response of shoaling fish to the threat of aerial predation. Environ. Biol. generalized linear mixed models using l1-penalization. J. Comput. Graph. Stat. 23, Fish. 36, 183–192 (1993). 460–477 (2014). 26. M. Johannes, D. McQueen, T. Stewart, J. Post, Golden shiner (Notemigonus crysoleu- 50. P. Dodds, D. Watts, Universal behavior in a generalized model of contagion. Phys. cas) population abundance: Correlations with food and predators. Can. J. Fish. Aquat. Rev. Lett. 92, 218701 (2004). Sci. 46, 810–817 (1989). 51. M. Rabinovich, P. Varona, A. Selverston, H. Abarbanel, Dynamical principles in 27. P. Domenici, R. Blake, The kinematics and performance of fish fast-start swimming. J. neuroscience. Rev. Mod. Phys. 78, 1213–1266 (2006). Exp. Biol. 200, 1165–1178 (1997). 52. A. Levina, J. Herrmann, T. Geisel, Dynamical synapses causing self-organized criticality 28. S. Rosenthal, C. Twomey, A. Hartnett, H. Wu, I. Couzin, Revealing the hidden net- in neural networks. Nat. Phys. 3, 857–860 (2007). works of interaction in mobile animal groups allows prediction of complex behavioral 53. D. Sumpter, J. Buhl, D. Biro, I. Couzin, Information transfer in moving animal groups. contagion. Proc. Natl. Acad. Sci. U.S.A. 112, 4690–4695 (2015). Theor. Biosci. 127, 177–186 (2008). 29. W. Cresswell, G. Hilton, G. Ruxton, Evidence for a rule governing the avoidance of 54. T. Mora, W. Bialek, Are biological systems poised at criticality? J. Stat. Phys. 144, 268– superfluous escape flights. Proc. R. Soc. B 267, 733–737 (2000). 302 (2011). 30. D. Blumstein, L. Verneyre, J. Daniel, Reliability and the adaptive utility of 55. A. Hein et al., The evolution of distributed sensing and collective computation in discrimination among alarm callers. Proc. R. Soc. B 271, 1851–1857 (2004). animal populations. eLife 4, e10955 (2015). 31. J. Kahlert, Factors affecting escape behaviour in moulting greylag geese Anser 56. B. Daniels, D. Krakauer, J. Flack, Control of finite critical behaviour in a small-scale answer. J. Ornithol. 147, 569–577 (2006). social system. Nat. Commun. 8, 14301 (2017). 32. G. Beauchamp, Determinants of false alarms in staging flocks of semipalmated 57. J. Pruitt et al., Social tipping points in animal societies. Proc. R. Soc. Biol. Sci. 285, sandpipers. Behav. Ecol. 21, 584–587 (2010). 20181282 (2018). 33. L. Giraldeau, T. Valone, J. Templeton, Potential disadvantages of using socially 58. P. Dodds, D. Watts, A generalized model of social and biological contagion. J. Theor. acquired information. Philos. Trans. R. Soc. Biol. Sci. 357, 1559–1566 (2002). Biol. 232, 587–604 (2005). 34. A. Mathuru et al., Chondroitin fragments are odorants that trigger fear behavior in 59. H. Korn, D. Faber, The Mauthner cell half a century later: A neurobiological model fish. Curr. Biol. 22, 538–544 (2012). for decision-making? Neuron 47, 13–28 (2005).

6 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1905585116 Sosna et al. Downloaded by guest on September 27, 2021