How perceived threat increases synchronization in collectively moving animal groups

Abstract

Nature is rich with many different examples of the cohesive motion of animals. Previous attempts to model collective motion have primarily focused on group behaviours of identical individuals. In contrast, we put our emphasis on modelling the contributions of different individual-level characteristics within such groups by using stochastic asynchronous updating of individual positions and orientations. Our model predicts that higher updating frequency, which we relate to perceived threat, leads to more synchronized group movement, with speed and nearest-neighbour distributions becoming more uniform. Experiments with three-spined sticklebacks (Gasterosteus aculeatus) that were exposed to different threat levels provide strong empirical support for our predictions. Our results suggest that the behaviour of fish (at different states of agitation) can be explained by a single parameter in our model: the updating frequency. We postulate a mechanism for collective behavioural changes in different environment-induced contexts, and explain our findings with reference to confusion and oddity effects.

Figure 1.

In (a) and (b) we show empirical speed distributions for two different shoals of eight fish over 10 min in identical experimental conditions (treatment 1 in table 1). Note how the shape of the speed distributions varies between groups. In (c) and (d) we show simulated speed distributions for different values of Δt, which illustrate the model's capability to produce qualitatively similar speed distributions to those observed in the empirical data. To facilitate comparison, we have ensured that all histograms in this figure have area 1. Summary statistics are given for comparison: (a) mean = 13.3 ± 6.2 (s.d.) cm s⁻¹, skewness = 0.1; (b) mean = 9.1 ± 4.8 (s.d.) cm s⁻¹, skewness = 0.3; (c) mean = 12.7 ± 7.3 (s.d.) cm s⁻¹, skewness = 0.6; (d) mean = 12.7 ± 2.8 (s.d.) cm s⁻¹, skewness = 0.2. See text for details of the data analysis and the model simulations.

Figure 2.

Summary statistics for a shoal of eight fish for model simulations (a–c; five replicates) and empirical data (d–f; eight replicates) for varying Δt and different treatments, respectively. The model simulations are not fitted to the data. Error bars show 1 standard deviation from the mean; in (a) and (b), the error bars are smaller than the symbols. In (a) and (b) we show the mean of the standard deviations and skewness of normalized speed distributions (to account for varying group speeds). Both these statistics, as well as (c) the mean of the median nearest-neighbour distances, increase with increasing values of Δt (note the log scale on the x-axis, Δt, is measured in seconds). This trend is qualitatively replicated in the empirical data for decreasing perceived agitation levels (d–f). The effect of the treatments is analysed using a GLMM with predicting factors (categorical) treatment ID + sequential treatment order and random factor (categorical) replicate ID (see also electronic supplementary material). Significant differences between treatment 1 and other treatments are indicated by asterisks above the brackets (*p < 0.05, **p < 0.001).