A common rule for decision making in animal collectives across species

Abstract

A diversity of decision-making systems has been observed in animal collectives. In some species, choices depend on the differences of the numbers of animals that have chosen each of the available options, whereas in other species on the relative differences (a behavior known as Weber's law), or follow more complex rules. We here show that this diversity of decision systems corresponds to a single rule of decision making in collectives. We first obtained a decision rule based on Bayesian estimation that uses the information provided by the behaviors of the other individuals to improve the estimation of the structure of the world. We then tested this rule in decision experiments using zebrafish (Danio rerio), and in existing rich datasets of argentine ants (Linepithema humile) and sticklebacks (Gasterosteus aculeatus), showing that a unified model across species can quantitatively explain the diversity of decision systems. Further, these results show that the different counting systems used by animals, including humans, can emerge from the common principle of using social information to make good decisions.

Fig. 1.

A general decision-making rule in animal collectives. (A) Decision making between two sites when n_x and n_y animals have already chosen sites x and y, respectively. (B) The probability of choosing x in the general rule (Eq. 3), plotted as a function of the animals that have already chosen between the two sites, n_x and n_y. The theory predicts very different structure in the probability for the case of low and high numbers of animals, separated by point . The rate of change of P_x in the transition regions depends on the reliability parameter s, with the width of these regions proportional to . (C) Same as B but for three different values of parameter k: k = 0 (Left), 0 < k < 1 (Center), and k = 1 (Right).

Fig. 2.

Zebrafish choices correspond to the general rule of decisions in collectives. (A) Focal fish choosing between two sites with different number of zebrafish, separated from the focal fish by glass. (B) Probability of choosing option x for different numbers of zebrafish at sites x and y, n_x and n_y. Theoretical probabilities for a = 11.2 and s = 5, and k = 0 in Eq. 3 represented as a surface and experimental data represented as dots indicating the mean value of typically 15 animals at each configuration. Different dot colors correspond to different values of n_y and bars are SEM. (C) Same as B but plotted only as a function of n_x and different colors representing the value of n_y.

Fig. 3.

Ant choices correspond to the general rule of decisions in collectives. (A) Probability of choosing option x as a function of how many ants have previously been at locations x and y, n_x and n_y, for theory (Left) using Eq. 4 with a = 2.5, s = 1.07, k = 0.53, p_rand = 0.39, and experiments (Right) from Perna et al. (24). (B) Detail of A. (C) Same as A but represented as a function of and . (D) Slope of the probability of choosing x in A as obtained from a linear fit along the lines depicted in Inset. Experimental values (blue dots; error bars are 95% confidence interval), theory (red line), and Weber’s law (black line).

Fig. 4.

Stickleback choices correspond to the general rule of decisions in collectives. (A) Probability of finding a final proportion of sticklebacks choosing option x (blue histograms are experimental results from refs. and and theoretical values as lines for k = 1, k = 0.5, and k = 0) for different group sizes (two, four, and eight fish) and for three types of setups: a symmetric setup with different numbers of replica fish going to x and y (Top), a setup with a replica predator at x and different replica fish going to x (Middle), and a symmetric setup with modified replica fish (Bottom). See model parameters and 68 additional experiments with fits in Fig. S7. (B) Theoretical P_x for k = 1, a = 1 (Left), k = 0.5, a = 5 (Center), and k = 0, a = 224 (Right), and s = 2.5 in the three cases. All models require an effective ΔN rule to compare with data for the number of animals used in experiments (triangle).