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 analyzed 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 neighbors and that they regulate both their direction and speed relative to the positions of groupmates. These results suggest social factors are vital to the formation and maintenance of swarms. Further, 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 behavior of krill.
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 ~40mm) were kept at the Australian Antarctic Division’s marine research aquarium at Kingston, Tasmania, in an 1860L cylindrical tank (see 3).
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 minutes at a time. Cameras were fixed on an aluminium frame and submerged approximately 50cm 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 Figure S1 for images relating to the calibration process.
Tracking
Individual krill were tracked manually in ImageJ from 10-second clips, with these clips further subdivided into smaller duration sections. Clips were cut to 10 seconds 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, with tracks obtained for 20 to 55 krill for each of these clips.
Transfer entropy
We used the Kraskov, Stögbauer and Grassberger estimator (19) from the Java Information Dynamics Toolkit (JIDT) open-source software (20) via the demos/octave/Flocking scripts, to quantify information flow. Using time-series data (x,y,z), we measured transfer entropy (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 (21), 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.
The data set contains coordinates in three dimensions (x,y,z) of mobile Antarctic krill.
