Emergence and repeatability of leadership and coordinated motion in fish shoals

Abstract

Studies of self-organizing groups like schools of fish or flocks of birds have sought to uncover the behavioral rules individuals use (local-level interactions) to coordinate their motion (global-level patterns). However, empirical studies tend to focus on short-term or one-off observations where coordination has already been established or describe transitions between different coordinated states. As a result, we have a poor understanding of how behavioral rules develop and are maintained in groups. Here, we study the emergence and repeatability of coordinated motion in shoals of stickleback fish (Gasterosteus aculeatus). Shoals were introduced to a simple environment, where their spatio-temporal position was deduced via video analysis. Using directional correlation between fish velocities and wavelet analysis of fish positions, we demonstrate how shoals that are initially uncoordinated in their motion quickly transition to a coordinated state with defined individual leader-follower roles. The identities of leaders and followers were repeatable across two trials, and coordination was reached more quickly during the second trial and by groups of fish with higher activity levels (tested before trials). The rapid emergence of coordinated motion and repeatability of social roles in stickleback fish shoals may act to reduce uncertainty of social interactions in the wild, where individuals live in a system with high fission-fusion dynamics and non-random patterns of association.

Keywords: collective behavior; coordination; emergence; leadership; phase transition; shoaling; time-depth.

Figure 1

(a) The test arena (730 mm x 425 mm). Pictured is a group of fish in their start boxes (7.5 cm x 7.5 cm box for each fish); fish stayed in the start boxes for 5 min prior to being released into the full test arena. (b) A schematic representation of the transparent start boxes, fish and their colored identity tags. The red rectangle provides an example of the area used to determine fish motion in that box in the 5 min before free-swimming. (c) A schematic representation of the grid points that were used to detect fish motion in the start boxes. In this example the fish with the blue tag was identified as most active.

Figure 2

Examples of the number of leadership events for fish in Group A (each fish is represented by a different shade) during Trial 1 (a) and Trial 2 (b), as a function of different CV* thresholds and where CV* = 1 indicates perfect correlation in the directions of fish i and fish j delayed in time τ; (c) and (d) show the variance in frequency of leadership between group individuals is maximized at values CV* > 0.5 for the data shown in (a) and (b); (e) and (f) show leadership within and across trials. Here, the number of occasions each fish led was divided by the sum of all leadership events within a group to provide as normalized leadership score for each fish. Fish ID is presented according to the leadership score in trial 1 and the order is maintained independent of leadership score in trial 2 for comparisons. Group A is highlighted by dashed lines and associated leadership data are given in Figures (a)-(d).

Figure 3

(a) Emergence of coordination identified by mean maximum directional correlation (CV*, line) and min/max CV* range (shaded area) across all studied fish groups over time. Mean CV* change point time = 40.6 secs and is indicated by a change in color from blue to red); (b) and (c) show mean CV* over time for Group A trial 1 and trial 2 and identified change points (dashed vertical line). The same plot for all groups and trials are given in Supplementary Figure S5; (d) and (e) provide continuous wavelet transform scalograms for Group A in trial 1 and trial 2. The different colors represent the correlation between the scaled/translated Morlet wavelets and the mean position of the group (expressed as the mean distance of the fish from a fixed tank point) in time. Warmer colors (yellow) indicate higher correlation. The yellow pattern shows the dominant frequency of this oscillatory motion which is around 0.035 Hz and indicates the emergence of oscillatory movement around the tank with period of 25–30 s confirming video observations (Supplementary Movies S1–S5 provide examples). The same plots for all groups and trials are provided in Supplementary Figure S6. (f) Box plot showing mean (vertical lines) quartiles (box) and 95% range (whiskers) for detected change points in during trial 1 and trial 2. Change point for Group B trial 2 was >300 s and not shown.

Figure 4

Relationship between individual fish leadership scores in trial 1 and trial 2, for all groups, during (a) disordered, non-shoaling states, and (b) ordered, shoaling states. The line in (b) represents the effect predicted by LMM2 (see methods). Figure 3 provides further information on defining the two states.