Fish evacuate smoothly respecting a social bubble

Abstract

Crowd movements are observed among different species and on different scales, from insects to mammals, as well as in non-cognitive systems, such as motile cells. When forced to escape through a narrow opening, most terrestrial animals behave like granular materials and clogging events decrease the efficiency of the evacuation. Here, we explore the evacuation behavior of macroscopic, aquatic agents, neon fish, and challenge their gregarious behavior by forcing the school through a constricted passage. Using a statistical analysis method developed for granular matter and applied to crowd evacuation, our results clearly show that, unlike crowds of people or herds of sheep, no clogging occurs at the bottleneck. The fish do not collide and wait for a minimum waiting time between two successive exits, while respecting a social distance. When the constriction becomes similar to or smaller than their social distance, the individual domains defined by this cognitive distance are deformed and fish density increases. We show that the current of escaping fish behaves like a set of deformable 2D-bubbles, their 2D domain, passing through a constriction. Schools of fish show that, by respecting social rules, a crowd of individuals can evacuate without clogging, even in an emergency situation.

Figure 1

(a) The biological model is Paracheirodon innesi, a small and common freshwater species. (b) Photograph of the experimental setup as imaged for data analysis. The tank is divided into two equal spaces by a wall with a circular opening of different sizes. The fish are forced to move toward the door by a net. The red dashed box is the area where the fish density is measured. (c) Number of evacuated fish as a function of time for three realizations with different opening diameters. (d) Averaged passage of 30 fish for different diameters (15 realizations for each diameter).

Figure 2

(a) Fish current, determined by the fit of every evacuation trials, as a function of the opening diameter. (b) Average fish density in a virtual box (8×5$c{m}^2$, drawn on Fig. 1b) just before the opening as a function of the number of evacuated fish for the different opening diameters. (c) Average fish density over the first 15 fish as a function of the opening diameter. The density is stable for all diameters larger than 2 cm. A critical length $L_C$ is calculated from this averaged fish density (dashed grey line).

Figure 3

Statistical analysis of the fish evacuation. (a) Complementary of the cumulative distribution function of the time lapses between two fish exits, $q(\tau )$ for several opening diameters D, logarithmic scale on the y axis. (b) Zoom in the previous plot overlaid with the corresponding single-parameter fits for each diameter. The fitting function is an interpolation between a short-time inhibition at short timescales and an exponential decay with characteristic time ${\tau }_0$ at longer timescales. In the inset are plotted the same data with respect to the rescaled time ${\tau }_0$ to show that the proposed model fits well the data for the whole range of diameters. c. The measured averaged time lapses for each diameter, $<\mathrm{\Delta }t>$ are plotted together with the averaged time lapses obtained from the fit, ${\tau }_0(e-1)$. The two are in good agreement thereby validating the model. The dashed grey line shows $D_{\mathit{stop}}$, the diameter at which the flow vanishes and the time lapses diverge. The red line corresponds to Eq. (8) with the parameters obtained from the fit of the fish current.

Figure 4

Fish as cognitive bubbles. (a) The modified Beverloo’s law fits well the fish current when the cognitive length $L_C$ is taken as the characteristic size of the deformable particles. (b) Fish current plotted versus the fitted function to evaluate the goodness of the fit. The red line is $y=x$ as a reference. (c) Schematics of the model of cognitive bubbles dictating the fish behaviour.