Abstract
Groups of animals coordinate remarkable, coherent, movement patterns during periods of collective motion. Such movement patterns include the toroidal mills seen in fish shoals, highly aligned parallel motion like that of flocks of migrating birds, and the swarming of insects. Since the 1970's a wide range of collective motion models have been studied that prescribe rules of interaction between individuals, and that are capable of generating emergent patterns that are visually similar to those seen in real animal group. This does not necessarily mean that real animals apply exactly the same interactions as those prescribed in models. In more recent work, researchers have sought to infer the rules of interaction of real animals directly from tracking data, by using a number of techniques, including averaging methods. In one of the simplest formulations, the averaging methods determine the mean changes in the components of the velocity of an individual over time as a function of the relative coordinates of group mates. The averaging methods can also be used to estimate other closely related quantities including the mean relative direction of motion of group mates as a function of their relative coordinates. Since these methods for extracting interaction rules and related quantities from trajectory data are relatively new, the accuracy of these methods has had limited inspection. In this paper, we examine the ability of an averaging method to reveal prescribed rules of interaction from data generated by two individual based models for collective motion. Our work suggests that an averaging method can capture the qualitative features of underlying interactions from trajectory data alone, including repulsion and attraction effects evident in changes in speed and direction of motion, and the presence of a blind zone. However, our work also illustrates that the output from a simple averaging method can be affected by emergent group level patterns of movement, and the sizes of the regions over which repulsion and attraction effects are apparent can be distorted depending on how individuals combine interactions with multiple group mates.
Highlights
There are many perceived advantages for animals to stay and move in groups, including: reduced individual probability of becoming a victim of predation in the event of an attack on the group; the enhanced ability of many eyes to monitor the environment for potential threats at group level [4]; and enhanced decision-making ability during foraging [5], and finding and establishing a new home [6, 7]
Animal groups undergoing collective motion often form striking group level patterns of movement, including the complex swirls of starling murmurations, toroidal milling patterns produced by shoals of fish, the chaotic but guided motion of honey bee swarms, and directed parallel motion seen in groups of many species [9, 10]
With such broad rules in action, collective motion models are capable of generating emergent patterns that are visually similar to those seen in real animal groups, including coordinated parallel motion, milling and swarming [13, 22]
Summary
There are many perceived advantages for animals to stay and move in groups, including: reduced individual probability of becoming a victim of predation in the event of an attack on the group (via a dilution effect [1] and a confusion effect [2, 3]); the enhanced ability of many eyes to monitor the environment for potential threats at group level [4]; and enhanced decision-making ability during foraging [5], and finding and establishing a new home [6, 7]. Attraction: to avoid group fragmentation, individuals adjust their velocity to move towards other group members that are somewhat removed from the individual’s current relative position in the group With such broad rules in action, collective motion models are capable of generating emergent patterns that are visually similar to those seen in real animal groups, including coordinated parallel motion, milling and swarming [13, 22]. It is possible to obtain some fundamental analytic results for these models that give an explicit form for pairwise interactions in terms of changes in speed and direction of motion We illustrate these results in S3 Section of the S1 File, to be used as a point of comparison to the interactions inferred from simulated data, we note that a priori we do not expect exact extraction of the pairwise interactions by the averaging methods that we use due to the way data is aggregated across multiple individuals
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