Inferring the structure and dynamics of interactions in schooling fish

Abstract

Determining individual-level interactions that govern highly coordinated motion in animal groups or cellular aggregates has been a long-standing challenge, central to understanding the mechanisms and evolution of collective behavior. Numerous models have been proposed, many of which display realistic-looking dynamics, but nonetheless rely on untested assumptions about how individuals integrate information to guide movement. Here we infer behavioral rules directly from experimental data. We begin by analyzing trajectories of golden shiners (Notemigonus crysoleucas) swimming in two-fish and three-fish shoals to map the mean effective forces as a function of fish positions and velocities. Speeding and turning responses are dynamically modulated and clearly delineated. Speed regulation is a dominant component of how fish interact, and changes in speed are transmitted to those both behind and ahead. Alignment emerges from attraction and repulsion, and fish tend to copy directional changes made by those ahead. We find no evidence for explicit matching of body orientation. By comparing data from two-fish and three-fish shoals, we challenge the standard assumption, ubiquitous in physics-inspired models of collective behavior, that individual motion results from averaging responses to each neighbor considered separately; three-body interactions make a substantial contribution to fish dynamics. However, pairwise interactions qualitatively capture the correct spatial interaction structure in small groups, and this structure persists in larger groups of 10 and 30 fish. The interactions revealed here may help account for the rapid changes in speed and direction that enable real animal groups to stay cohesive and amplify important social information.A fundamental problem in a wide range of biological disciplines is understanding how functional complexity at a macroscopic scale (such as the functioning of a biological tissue) results from the actions and interactions among the individual components (such as the cells forming the tissue). Animal groups such as bird flocks, fish schools, and insect swarms frequently exhibit complex and coordinated collective behaviors and present unrivaled opportunities to link the behavior of individuals with dynamic group-level properties. With the advent of tracking technologies such as computer vision and global positioning systems, group behavior can be reduced to a set of trajectories in space and time. Consequently, in principle, it is possible to deduce the individual interaction rules starting from the observed kinematics. However, calculating interindividual interactions from trajectories means solving a fundamental inverse problem that appears universally in many-body systems. In general, such problems are very hard to solve and, even if they can be solved, their solution is often not unique.To avoid solving these inverse problems (and because detailed kinematic data were not available until recently), many attempts have been made to replicate the patterns observed in animal groups by...

Automated image-based tracking and its application in ecology

“…Recent break throughs in remote quantification of physical landscapes [58 60] and 3D imaging [29] should be especially helpful for these questions. Second, collective behavior in animal groups [1,26,33,38,40,43,45,62,82,83], including understanding how information about the physical and biological environment transfers between individuals. Generally, this research centers on intraspecific groups comprising large numbers of similar sized individuals.…”

“…Therefore, many tracking systems are limited to simple 2D arenas and either involve organisms that naturally move in 2D or quasi-2D, or work by constraining normally 3D individuals to only move in 2D. This latter method can be achieved by modifying organisms directly, such as by wing clipping [27), or by using physical boundaries to constrain behavior to near 2D [1,20,27,32,33) (Movie S1, Movie S4, Movie S5, and Movie S10 in the supplementary material online). In nature, however, most organisms incorporate at least some degree of movement in 3D, which influences ecological interactions [3) .…”

“…To prevent identity switch errors, the researcher must manually review uncertain events in the tracking data and make appropriate corrections (see above) [27,28,33,62] (Movie S1, Movie S10, and Movie S11 in the supplementary material online).…”

“…Knowledge about the spatiotemporal position of organisms relative to the environmental landscape, or to each other, is sufficient for many questions in ecology [1,3,4,33,53] (Box 1). For other questions, such as those about the mechanics of locomotion or ecological interactions, it is necessary to know about the positioning of appendages or other specific points along an individual's body [8,17,19,28,29,69] (Movie S2, Movie S11, Movie S14, and Movie S22 in the supplementary material online) (Box 1).…”

Optimal cooperative searching using purely repulsive interactions

“…This correlation is mainly due to the chemical signaling that is taking place, since dicty tries to avoid searching areas that were previously covered by avoiding the chemo-repellent areas left by other dicty cells, as well as moving toward chemo-attractive signals, where there may be a high local concentration of nutrients. Previous studies of short range interacting Brownian particles have been used to model biological systems such as transcription proteins sliding along DNA [18] and the swarming behaviors observed in birds and fishes [19][20][21].…”