Detailed quantifications of how predators and their grouping prey interact in three dimensions (3D) remain rare. Here we record the structure and dynamics of fish shoals (Pseudomugil signifer) in 3D both with and without live predators (Philypnodon grandiceps) under controlled laboratory conditions. Shoals adopted two distinct types of shoal structure: “sphere-like” geometries at depth and flat “carpet-like” structures at the water’s surface, with shoals becoming more compact in both horizontal and vertical planes in the presence of a predator. The predators actively stalked and attacked the prey, with attacks being initiated when the shoals were not in their usual configurations. These attacks caused the shoals to break apart, but shoal reformation was rapid and involved individuals adjusting their positions in both horizontal and vertical dimensions. Our analyses revealed that targeted prey were more isolated from other conspecifics, and were closer in terms of distance and direction to the predator compared to non-targeted prey. Moreover, which prey were targeted could largely be identified based on individuals’ positions from a single plane. This highlights that previously proposed 2D theoretical models and their assumptions appear valid when considering how predators target groups in 3D. Our work provides experimental, and not just anecdotal, support for classic theoretical predictions and also lends new insights into predatory–prey interactions in three-dimensional environments.

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle $$\alpha${}$ are ignored. The collective dynamics of this system is studied by agent-based simulations and kinetic mean-field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent $\frac{3}{2}$ for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point with different scaling laws is identified and calculated analytically. We investigate the shifting and vanishing of this point due to the formation of density bands as the system size is increased. Agent-based simulations in small systems with large particle velocities show excellent agreement with the kinetic theory predictions. We also find that at very small interaction angles, the polar ordered phase becomes unstable with respect to the apolar phase. We derive analytical expressions for the dependence of the threshold noise on the restriction angle. We show that the mean-field kinetic theory also permits stationary nematic states below a restriction angle of $0.681\phantom{\rule{0.16em}{0ex}}$\pi${}$. We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle, the transition is discontinuous but continuous at intermediate $$\alpha${}$. We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented. This method is shown to give excellent agreement with agent-based simulations, even in strongly ordered systems at noise values close to zero.

Collective motion occurs when individuals use social interaction rules to respond to the movements and positions of their neighbors. How readily these social decisions are shaped by selection remains unknown. Through artificial selection on fish (guppies, Poecilia reticulata) for increased group polarization, we demonstrate rapid evolution in how individuals use social interaction rules. Within only three generations, groups of polarization-selected females showed a 15% increase in polarization, coupled with increased cohesiveness, compared to fish from control lines. Although lines did not differ in their physical swimming ability or exploratory behavior, polarization-selected fish adopted faster speeds, particularly in social contexts, and showed stronger alignment and attraction responses to multiple neighbors. Our results reveal the social interaction rules that change when collective behavior evolves.

We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with an internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbors. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the character of individual motion in our model differ from those in the well-studied Vicsek model, it demonstrates identical statistical properties and phase behavior.

While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible enough to capture changes in the collective behaviour of animal groups at their different developmental stages and group sizes. Here, we analyse the statistical properties of schooling fish ( Pseudomugil signifer ) through a combination of experiments and simulations. We make novel use of a Boltzmann inversion method, usually applied in molecular dynamics, to identify the effective potential of the mean force of fish interactions. Specifically, we show that larger fish have a larger repulsion zone, but stronger attraction, resulting in greater alignment in their collective motion. We model the collective dynamics of schools using a self-propelled particle model, modified to include varying particle speed and a local repulsion rule. We demonstrate that the statistical properties of the fish schools are reproduced by our model, thereby capturing a number of features of the behaviour and development of schooling fish.