Self-organization and information transfer in Antarctic krill swarms

Abstract

Antarctic krill swarms are one of the largest known animal aggregations, and yet, despite being the keystone species of the Southern Ocean, little is known about how swarms are formed and maintained. Understanding the local interactions between individuals that provide the basis for these swarms is fundamental to knowing how swarms arise in nature, and what potential factors might lead to their breakdown. Here, we analysed the trajectories of captive, wild-caught krill in 3D to determine individual-level interaction rules and quantify patterns of information flow. Our results demonstrate that krill align with near neighbours and that they regulate both their direction and speed relative to the positions of groupmates. These results suggest that social factors are vital to the formation and maintenance of swarms. Furthermore, krill operate a novel form of collective organization, with measures of information flow and individual movement adjustments expressed most strongly in the vertical dimension, a finding not seen in other swarming species. This research represents a vital step in understanding the fundamentally important swarming behaviour of krill.

1. Introduction

The Antarctic krill, Euphausia superba (hereafter krill), is one of the world's most abundant species and is the keystone species of the Southern Ocean ecosystem. The aggregation of krill into swarms is thought to be a major part of their success, providing safety in numbers [1], the ability to track nutrient gradients, and an increase in swimming efficiency, leading to vital energy savings [2]. Given the crucial importance of swarming to the survival of krill, a number of studies have examined the structure and function of krill groups in both the laboratory and the field [3–5]. Nonetheless, we currently lack a detailed understanding of how these swarms are formed and maintained.

Previous work on grouping animals, mostly studied in 2D, has shown that group-level patterns of collective motion emerge through the repeated interactions that occur between individual animals within the group [6]. These interactions can often be distilled to a simple set of heuristics, including mechanisms for one or more of the following: close-range repulsion, long-range attraction and localized alignment. Together, such interactions are known as rules of interaction, or rules of motion. These rules generally describe how individuals adjust their behaviour based on the relative locations and actions of groupmates, providing insight into the global structuring of animal collectives. Similarly, information transfer arises in interactions between near neighbours relating to changes in speed or heading direction, resulting in individuals sequentially adapting their trajectories in time. Efficient information transfer among group members is critical to the effectiveness of collective behaviour. Information-theoretic measures, in particular transfer entropy, are now increasingly being employed to quantify information transfer in biological systems [7–9].

Using tracking data collected from free-swimming, captive Antarctic krill, we provide the first analysis of the interactions and information flow between individuals in three dimensions. Describing the rules of motion employed by krill in swarms, and mapping patterns of information transfer, represents an essential first step in developing a quantitative understanding of swarming in this critically important species. We determined the average rules of interaction used by individual krill to adjust their speed and heading as a function of the relative location and speed of near neighbours, adapting methods first fully developed in Herbert-Read et al. [10] and Katz et al. [11] to the study of three-dimensional collective movement.

2. Materials and methods

(a) . Study species

Antarctic krill were collected by midwater trawl from the Southern Ocean during the 2016/17 Austral summer. The krill used in this study (average length approximately 40 mm) were kept at the Australian Antarctic Division's marine research aquarium at Kingston, Tasmania, in groups of 3000 to 4000 individuals contained within an 1860 l cylindrical tank (see §3).

(b) . Filming and camera calibration

Two Gopro Hero 6 cameras were used for filming krill within their home tanks at a rate of 30 frames per second for at least 30 min at a time. Cameras were fixed on an aluminium frame and submerged approximately 50 cm beneath the surface of the water. The tanks were covered with white corflute for the duration of filming to minimize any disturbance by light or people walking by. In order to facilitate tracking, Gopros were positioned to film against this white background (i.e. pointing vertically upwards).

In order to calibrate the cameras, a black and white-printed grid was moved through the field of view of both cameras while submerged in each tank. Videos were then calibrated using the Stereo Camera Calibrator application in MATLAB. Using this tool, we were able to determine the intrinsic and extrinsic parameters of each camera and the distortion coefficients which would allow us to convert our images to three dimensions. Calibration accuracy and reprojection error were set manually to less than 1 pixel, so that the images on each camera matched to within 1 pixel. The mean reprojection error was 0.53 pixels. See electronic supplementary material, figure S1 for images relating to the calibration process.

(c) . Tracking

Individual krill were tracked manually in ImageJ from 10 s clips, with these clips further subdivided into smaller duration sections. Clips were cut to 10 s or less as this was typically the length of time a single krill would spend in the field of view of both cameras. Coordinate data were then imported into MATLAB where matched pairs of (x, y) coordinates were first corrected to take into account effects of camera distortion using the undistortpoints function, and then converted to three dimensions with (x, y, z) coordinates given in millimetres using the triangulate function. In the (x, y, z) coordinate system, the z-coordinate corresponded to the direction perpendicular to the Earth's surface, with the x and y coordinates describing displacements in the horizontal. For this study, we focussed our analysis on data derived from 10 clips of durations from 50 to 788 frames. In each clip, we tracked all visible krill separately, obtaining tracks for between 20 and 55 krill per clip.

(d) . Transfer entropy

We used the Kraskov, Stögbauer and Grassberger estimator [12] from the Java Information Dynamics Toolkit (JIDT) open-source software [13] via the demos/octave/Flocking scripts, to quantify information flow. Using time-series data (x, y, z), we measured transfer entropy (TE; in nats) based on both changes in heading direction and speed, whereby greater levels of TE suggest greater potential information transfer from one individual to another. Specifically, transfer entropy measures the information held about the target variable (in this case the change in target krill heading direction or speed) by the source variable, or the heading direction or speed of a source krill relative to the heading direction or speed of a target krill. As per [14], all source–target pairs within range across every frame of all 10 clips were used to create samples for the whole dataset, meaning that the TE measured for a clip is an ensemble average of the representative pairwise source–target interaction for all krill pairs at every frame in the trial.

3. Results

There was a high probability of observing neighbours in close proximity to a focal individual (figure 1, left column), within an area of local alignment extending approximately 100–200 mm (between 2.5 and 5 krill body lengths) from the focal to its near neighbours (figure 1, right column). The peak occurrence of near neighbours occurs alongside the focal individual on the horizontal plane relative to both its direction of motion and the component of gravity perpendicular to the direction of motion.

Figure 1.

The statistical density of neighbouring krill relative to a focal individual (left column), and mean angular difference in travelling direction, α in degrees (right column), of neighbouring krill relative to a focal individual. In all panels, the focal individual is positioned at (0, 0, 0) travelling parallel to the positive x-axis, with the component of gravity perpendicular to the focal individual aligned with the negative z-axis. (a,b) Central slices through a cubic volume where x = 0, y = 0, and z = 0 (mm). (c,d) Top-down view, with the focal travelling left to right. (e,f) Front view, with the focal travelling out of the page. (g,h) Right-hand side, with the focal travelling left to right. The left column shows peak occurrence of near neighbours to the left and right alongside the focal individual on the same horizontal plane. The right-hand column shows low angular differences out to front and left, as well as approximately 2–3 body lengths (BL) behind. Additionally, low angular differences in travelling direction with neighbours out to approximately 1–2 BL above and below. (Online version in colour.)

Focal individuals adjusted their speed in relation to the position of near neighbours, accelerating when near neighbours were in front, or behind them, and slowing when near neighbours were above or below (figure 2).

Figure 2.

The mean speed, s (left column), and change in speed, Δs/Δt (right column), of krill as a function of the relative (x, y, z) coordinates of neighbours. Panel structure is as in figure 1. The krill tended to travel at greater speeds on average when their neighbours occupied coordinates where z ≥ 50 mm (redder regions in panels (a,e,g)). Individual krill tended to reduce their speed when neighbours occupied the region above, where z ≥ 50 mm (dark blue regions in panels (b,f,h)), and a smaller region below the focal individual (blue and green triangular region in panel (h)). Outside these regions, when partners occupied regions to the front and rear, and level with, or below the focal individual, then the focal individual tended to increase its speed (redder regions in panels (b,d,h)). (Online version in colour.)

Focal individuals also adapted their heading direction according to the position of near neighbours in both the horizontal (figure 3, left column) and the vertical (figure 3, right column) plane, relative to the plane of movement. Notably, when near neighbours were below and ahead, the focal turned towards them, while when near neighbours were above and in front, the focal turns upward but away from them. Broadly, focal krill exhibit little change in direction with respect to near neighbours on the same horizontal plane and within a radius of 2–3 body lengths.

Figure 3.

The angular components associated with the mean change in direction of krill as a function of the relative (x, y, z) coordinates of neighbours. Δθ/Δt represents the component of turning in the plane of motion of the focal individual where z = 0 (left column). Positive Δθ/Δt (redder regions) corresponds to leftward/anticlockwise turns, whereas negative Δθ/Δt (bluer regions) corresponds to rightward/clockwise turns. (a) Δθ/Δt in the planes where x = 0, y = 0, z = 0 (mm); (c) Δθ/Δt in the plane where z = 150 mm (above the focal individual); (e) Δθ/Δt in the plane z = 0 mm; (g) Δθ/Δt in the plane where z = −150 mm (below the focal individual). Individual krill tended to make turns with rightward components when their partners were above and to their front left, or when their partners were above and to their rear right (c). The krill tended to make turns with leftward components when their partners were above and to their front right or rear left (c). The pattern of leftward and rightward turns reversed when partners were below (panel (g), with z = −150 mm). Krill would enact turns with rightward components when partners were below and to the front right or rear left, or with leftward components when partners were below and to the front left or rear right. Δϕ/Δt represents the component of turning perpendicular to the plane of motion of the focal individual where z = 0 (right column). Positive Δϕ/Δt (redder regions) corresponds to upward turns, whereas negative Δϕ/Δt (bluer regions) corresponds to downward turns. (b) Δϕ/Δt in the planes where x = 0, y = 0 and z = 0 (mm); (d) Δϕ/Δt in the plane where y = 150 mm (to the left of the focal individual); (f) Δϕ/Δt in the plane where y = 0 mm; (h) Δϕ/Δt in the plane where y = −150 mm (to the right of the focal individual). The krill tended to make turns with upward components when their neighbours were above and to the front, or below and to the rear, and turns with downward components when their partners were below and to the front or above and to the rear, irrespective of the relative left to right positions of neighbours. (Online version in colour.)

Information flow, inferred from measurements of mean pairwise transfer entropy (TE), differed according to whether it was calculated from changes in heading direction, or changes in speed (see figure 4). For both measures, information flow could be observed between focal individuals and near neighbours at all positions in the horizontal plane of movement. However, in the vertical plane of movement, information flow based on heading direction was strongest from near neighbours above and below the focal, while information flow based on speed was strongest between the focal and those near neighbours positioned in front of the focal. In general, values of transfer entropy computed on changes in heading direction were greater than that computed on changes in speed (mean speed TE = −0.001, mean heading TE = 0.061 nats). This, in addition to differences in the inferred interaction lag between source and target individuals for optimal TE (speed TE: lag = 3, heading TE: lag = 1), suggests a higher responsiveness and faster reactions to changes in heading direction from individuals above or below the focal, than changes in speed by those in front. For both TE computed on changes in heading direction and TE computed on changes in speed, information flow was statistically significant with reference to a null hypothesis of no directed interaction (p(surrogate > measured) less than 0.01 from 100 surrogates for both speed TE and heading TE).

Figure 4.

Mean pairwise transfer entropy calculated between a focal individual positioned at (0, 0) and travelling in a direction from negative to positive x, and a near neighbour. Transfer entropy calculated based on changes in heading direction is shown in (a) the horizontal and (b) the vertical plane, showing localized transfer entropy from near neighbours in the same horizontal plane and peak transfer entropy from near neighbours above and below in the vertical plane. Transfer entropy calculated on changes in speed is shown in (c) the horizontal and (d) the vertical plane, showing localized transfer entropy from near neighbours in the same horizontal plane and peak transfer entropy from near neighbours lying ahead of the focal in the vertical plane. Note differences in the scale for heading versus speed transfer entropy. (Online version in colour.)

4. Discussion

Antarctic krill respond strongly to the behaviour of near neighbours and employ clear interaction rules consistent with species that demonstrate social attraction [10,11]. This social attraction, coupled with the presence of information flow, concurrent with individual adjustments to velocity based on relative positions of neighbours, suggests that krill aggregations do not occur purely due to aggregation around food or advection by ocean currents, but do so as an active measure. When swarming in close proximity as here, near neighbours are positioned at a radius of two to three body lengths to the focal, the focal aligns with them to a large extent, which is consistent with similar observations made on shoals of fish or bird flocks moving in two dimensions [6,9,15]. Although focal krill tend to show little change in direction when near neighbours are travelling on the same horizontal plane, they do accelerate when those near neighbours are positioned ahead or behind. Previous work on the hydrodynamic properties of krill positioning has suggested a potential communication channel resulting from the propulsion jet of near neighbours [5], and indeed patterns of information transfer in the horizontal plane of movement suggest focal krill are regulating speed, and particularly heading direction, potentially as a means to align with near neighbours in this plane and maintain this channel of communication.

Interestingly, while there are some similarities between the interaction rules employed by krill and those employed by other group-living animals, there are several features that have so far not been documented, and indeed appear to be unique to krill. For instance, the ways in which krill respond to near neighbours, especially to those at a different vertical stratum, are qualitatively different to those reported in studies of the collective behaviour of other species, including those examining the movements of animals in three dimensions, such as midges and starlings [16,17]. Focal krill turned towards near neighbours who were ahead and below and up but away from those ahead and above. Accordingly, patterns of information transfer relating to heading direction in this vertical plane show strong interactions between focals and those above or below, but little information transfer from those directly ahead. Information transfer in respect of changes in speed in the vertical plane is primarily focused on those directly ahead. Taken together, this suggests that krill adapt their heading based on those ahead and above or below, and adapt their speed based on those near neighbours who are directly ahead of them. The net effect of this is a pattern of alignment with those ahead and below, and to some extent with those behind and above. One plausible explanation for the observed patterns is that the krill's responses are governed to some extent by the hydrodynamics of krill swarms. Near neighbours produce a flow field as they swim, pushing water downwards and behind them, which emphasizes the importance of avoiding near neighbours who are above and ahead in particular [18]. Decreasing speed and turning away when near neighbours are above may be an important part of this process. In addition, these strong responses in the vertical dimension may relate to krill predator-avoidance strategies or their mode of communication. For instance, many oceanic predators attack predominantly from above or below, rather from the side [19,20], while the positioning of bioluminescent photophores on the ventral surface mean that signalling between krill occurs predominantly in the vertical plane [21]. The suggestion that the photophores act to counter-illuminate krill and make them less conspicuous to predators attacking from below potentially means that these points are interrelated [21].

Our analysis of krill interactions in three dimensions represents an important first step in understanding the principles underlying krill swarming behaviour. While krill are a fundamentally important species both scientifically and commercially, there are still many fundamental aspects of their behaviour that are unknown and likely to be impacted in the near future. For instance, during the Austral winter, it is unknown if and where swarming might occur, and therefore how fundamental it is to their survival during this time. Likewise, krill are known to inhabit benthic habitats well below the euphotic zone, which, if visual cues are important in swarming, suggests other mechanisms might hold more important to the maintenance of swarms—mechanisms that are likely to be affected by changing ocean conditions.

Ultimately, data from free-ranging krill in the Southern Ocean are urgently required to ground truth the laboratory-based observations presented here. Future work should examine the context-dependency of krill interaction rules in relation to oceanic currents, ambient light, temperature, predator avoidance and food availability. In addition, it would be valuable to examine the adaptive significance of the responsiveness of krill to near neighbours in the vertical dimension.

Data accessibility

All data are freely available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.8gtht76qj [22].

The data are provided in electronic supplementary material [23].

Authors' contributions

A.L.B.: conceptualization, data curation, formal analysis, investigation, methodology, project administration, writing—original draft, writing—review and editing; T.M.S.: data curation, formal analysis, funding acquisition, investigation, methodology, project administration, software, writing—review and editing; J.L.: formal analysis, methodology, resources, software, visualization, writing—review and editing; S.K.: conceptualization, investigation, methodology, resources, supervision, writing—review and editing; M.C.: conceptualization, investigation, methodology, resources, writing—review and editing; R.K.: conceptualization, investigation, methodology, resources, writing—review and editing; J.K.: conceptualization, investigation, methodology, resources, writing—review and editing; A.J.W.W.: conceptualization, formal analysis, funding acquisition, investigation, methodology, project administration, resources, supervision, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Competing interests

The authors declare no competing interests.

Funding

This work was supported by funding from the Australian Research Council under project DP190100660.