Schools of fish and flocks of birds: their shape and internal structure by self-organization

Abstract

Models of self-organization have proved useful in revealing what processes may underlie characteristics of swarms. In this study, we review model-based explanations for aspects of the shape and internal structure of groups of fish and of birds travelling undisturbed (without predator threat). Our models attribute specific collective traits to locomotory properties. Fish slow down to avoid collisions and swim at a constant depth, whereas birds fly at low variability of speed and lose altitude during turning. In both the models of fish and birds, the 'bearing angle' to the nearest neighbour emerges as a side-effect of the 'blind angle' behind individuals and when group size becomes larger, temporary subgroups may increase the complexity of group shape and internal structure. We discuss evidence for model-based predictions and provide a list of new predictions to be tested empirically.

Short-range interactions versus long-range correlations in bird flocks

“…Understanding how interactions between flight directions are related to the spatial structure of the group is a complex problem. There could be positional attraction-repulsion forces between birds, which we did not consider in our ME analysis, and that can influence the spatial arrangement of individuals (see [15,53] for a discussion in numerical models). Recent analysis [41] however suggest that in systems with topological interactions velocity alignment has an important role in the structure, which is why our result can help to understand this issue.…”

“…Models of self-propelled particles [3,[11][12][13][14][15] and hydrodynamic flocking theories [10,16] have shown numerically and analytically that in active systems also short-range interactions can produce global ordering and long-range correlations. Indeed, there now seems to be some consensus in the field of collective animal behavior that interactions are short-ranged [18].…”

Collective motion in biological systems

“…Couzin et al [14] have shown that a change in the radius of orientation caused sudden transitions at the school level in terms of collective behaviours (swarming, milling and schooling) characterized by different levels of polarization and structure. In their paper, Hemelrijk & Hildenbrandt [15] extend these zone models to account for speed variability and they review how these models have contributed to our understanding of the shape and the internal structure of travelling groups of fish and birds. In most existing zone models, individuals respond to instantaneous positions of neighbours.…”

Flow-Mediated Interactions between Two Self-Propelled Flapping Filaments in Tandem Configuration

“…Although numerous studies on fish schools [7], bird flocks [8], and systems containing bacteria or active particles [9,10] can be found in the literature, the mechanism by which stable aggregations are formed remains unclear. The hydrodynamic characteristics of two coupled flapping (or traveling wavy) foils have been studied in some previous works [11][12][13].…”