Quorum decision-making facilitates information transfer in fish shoals

Abstract

Despite the growing interest in collective phenomena such as "swarm intelligence" and "wisdom of the crowds," little is known about the mechanisms underlying decision-making in vertebrate animal groups. How do animals use the behavior of others to make more accurate decisions, especially when it is not possible to identify which individuals possess pertinent information? One plausible answer is that individuals respond only when they see a threshold number of individuals perform a particular behavior. Here, we investigate the role of such "quorum responses" in the movement decisions of fish (three-spine stickleback, Gasterosteus aculeatus). We show that a quorum response to conspecifics can explain how sticklebacks make collective movement decisions, both in the absence and presence of a potential predation risk. Importantly our experimental work shows that a quorum response can reduce the likelihood of amplification of nonadaptive following behavior. Whereas the traveling direction of solitary fish was strongly influenced by a single replica conspecific, the replica was largely ignored by larger groups of four or eight sticklebacks under risk, and the addition of a second replica was required to exert influence on the movement decisions of such groups. Model simulations further predict that quorum responses by fish improve the accuracy and speed of their decision-making over that of independent decision-makers or those using a weak linear response. This study shows that effective and accurate information transfer in groups may be gained only through nonlinear responses of group members to each other, thus highlighting the importance of quorum decision-making.

Fig. 1.

Experimental set-up.

Fig. 2.

Comparison of the best fit of the model with experimental data when no predator was present. The conspecific replicas going left:right are, respectively, 1:1 (a), 2:2 (b), 0:1 (c), 0:2 (d), 0:3 (e), 1:2 (f), and 1:3 (g). Data are shown as histograms, and model outcomes are represented by a solid line.

Fig. 3.

Accuracy and speed of individual decision-making of model simulations for different group sizes (a and e) n = 2; (b and f) n = 4; (c and g) n = 8; and (d and h) n = 16. Simulations were run 5,000 times for different combinations of spontaneous accept rates, a, and the threshold steepness, k. (a–d) The average proportion of fish making “errors”: the darkest blue indicates that on average 0.2 fish have made an error; darkest red indicates that on average 0.35 have made an error. (e and f) Log₁₀ (mean number of time steps over all individuals) until an individual moves left or right. Dark red indicates slow decisions, and blue indicates fast decisions. The black × on each panel represents the best fit parameter values for the fish in the absence of the predator, and the circle represents those values in the presence of the predator.

Fig. 4.

Comparison of best fit of the model with experimental data when a replica predator was present. We assume that the predator is on the right and the number of conspecific replicas going left:right are, respectively, 0:0 (a), 0:1 (b), 0:2 (c), and 0:3 (d). Data are shown in the histograms, and model outcome is represented by the solid line.