Abstract
Animal groups frequently move in a highly organized manner, as represented by flocks of birds and schools of fish. Despite being an everyday occurrence, we do not fully understand how this works. In particular, what social interactions between animals give rise to the flock structures we observe? This question is often investigated using self-propelled particle models where particles represent the individual animals. These models differ in the social interactions used, individual particle properties, and various technical assumptions. One particular technical assumption relates to whether all particles update their headings and positions at exactly the same time (synchronous update) or not (asynchronous update). Here, we investigate the causal effects of this assumption in an attraction-only model and find that it has a dramatic impact. Polarized groups do not form when synchronous update is used, but are produced with asynchronous update, and this phenomenon is robust with respect to variation in particle displacements and inclusion of noise. Given that many important models have been implemented with synchronous update only, we speculate that our understanding of the social interactions on which they are based may be incomplete. Perhaps previously unobserved phenomena will emerge if other potentially more realistic update schemes are used.
Highlights
Moving animal groups such as schools of fish and flocks of birds often move in a highly coordinated fashion
In a typical self-propelled particle (SPP) model, a number of particles move in the plane, or space, and update their headings at each time step according to a specified local interaction rule operating on the position, and/or the heading, of nearby particles
We compare the effect of implementing the synchronous and a particular asynchronous update scheme in the simplest SPP model known to produce the three standard groups, the local attraction model (LAM) [34]. If this choice has an effect on this model, it is likely to have an effect on more sophisticated models, and as much of our current understanding of collective motion in moving animal groups is based on SPP models, this would be a valuable insight
Summary
Moving animal groups such as schools of fish and flocks of birds often move in a highly coordinated fashion. Direct comparisons of this type are largely absent from the SPP model literature, and in most models, it is assumed that all particles calculate and update their headings synchronously This assumption has been questioned by several authors and some have chosen to implement asynchronous update schemes [32,33,34,35,36]. Speed distributions in fish schools [32], interactions of a topological nature consistent with those observed in starling flocks [33], and collective motion in locusts [35] and soldier crabs [36] Despite these particular empirically motivated findings, systematic direct comparisons of various update schemes in standard SPP models have not been conducted, and it is still largely unknown what effects the choice of update scheme may have on models of this type. If this choice has an effect on this model, it is likely to have an effect on more sophisticated models, and as much of our current understanding of collective motion in moving animal groups is based on SPP models, this would be a valuable insight
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