Individual and collective encoding of risk in animal groups

Abstract

The need to make fast decisions under risky and uncertain conditions is a widespread problem in the natural world. While there has been extensive work on how individual organisms dynamically modify their behavior to respond appropriately to changing environmental conditions (and how this is encoded in the brain), we know remarkably little about the corresponding aspects of collective information processing in animal groups. For example, many groups appear to show increased "sensitivity" in the presence of perceived threat, as evidenced by the increased frequency and magnitude of repeated cascading waves of behavioral change often observed in fish schools and bird flocks under such circumstances. How such context-dependent changes in collective sensitivity are mediated, however, is unknown. Here we address this question using schooling fish as a model system, focusing on 2 nonexclusive hypotheses: 1) that changes in collective responsiveness result from changes in how individuals respond to social cues (i.e., changes to the properties of the "nodes" in the social network), and 2) that they result from changes made to the structural connectivity of the network itself (i.e., the computation is encoded in the "edges" of the network). We find that despite the fact that perceived risk increases the probability for individuals to initiate an alarm, the context-dependent change in collective sensitivity predominantly results not from changes in how individuals respond to social cues, but instead from how individuals modify the spatial structure, and correspondingly the topology of the network of interactions, within the group. Risk is thus encoded as a collective property, emphasizing that in group-living species individual fitness can depend strongly on coupling between scales of behavioral organization.

Keywords: antipredator behavior; group structure; social contagion.

Fig. 1.

Effect of perceived predation risk on group structure. (A) A subset of the school prior to Schreckstoff. Rays (purple) represent a visualization of the field of view of the focal individual (colored white). (B) The entire school after receiving Schreckstoff. (C) Median nearest-neighbor distance upon exposure to Schreckstoff or water (dashed lines). Shaded regions indicate mean of the group medians $\pm$ 1 SE. (D) Distributions of number of visible 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 Schreckstoff, respectively. Dashed lines demonstrate difference in medians. (E) Distributions of the proportion of individuals’ visual field occupied by other fish.

Fig. 2.

Perceived predation risk changes alarm propagation. (A) Schreckstoff increases the intrinsic frequency of alarms: The number of startle cascades increased upon first and third exposure. Raw data are plotted alongside the mean $\pm$ 1 SE. (B) Schreckstoff increases average cascade size following first exposure, but not upon third exposure. Exposure to water does not increase frequency of alarms or average cascade size. (C) Distribution of cascade sizes before and after the first exposure to Schreckstoff. Lines represent contagion model fits to data, with shaded regions representing 95% confidence intervals. Model is described in main text. (D) Cascade size distributions before and after the third exposure to Schreckstoff.

Fig. 3.

Probability of an individual startling in response to an initiator as a function of the top 2 predictors, log metric distance (Left) and ranked angular area (Right), holding the other predictor constant at its mean value. Gray corresponds to the first-exposure data prior to receiving Schreckstoff; red corresponds to after receiving Schreckstoff. Solid lines are the fit of the model with the top 2 predictors to the first-responder data; shaded regions represent 95% confidence intervals. Top and Bottom histograms correspond to first responders and nonresponders, respectively.

Fig. 4.

SIR-type behavioral contagion model explains alarm propagation and indicates that changes in spatial positioning are necessary to explain increased cascade sizes. (A) Model schematic. The focal individual in the susceptible state (S, white) receives doses from active individuals (I, “infected,” magenta) that it integrates over timescale ${\tau }_m$. When the cumulative dose reaches the individual’s threshold, it startles and remains in the active state for time ${\tau }_{act}$, after which it enters the recovered state (R, gray). (B) The model is simulated starting with the observed initial startler and dose rates that correspond to the first-responder probability functions for first and third exposure to Schreckstoff. The relative log-likelihood of the model producing the observed cascade sizes is plotted as a function of the single free parameter that modulates individual responsiveness, the average dose threshold $\overline{\theta }$. (C) Best-fit parameter values controlling responsiveness are similar pre- and postexposure, with overlapping 95% credible intervals. (D) Comparing average cascade sizes after modulating responsiveness and spatial positioning separately reveals that a change in spatial positioning is essential for the increase of group responsiveness post-Schreckstoff.