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Hemelrijk, C. K., & Hildenbrandt, H. (2008). Self-Organized Shape and Frontal Density of Fish Schools. Ethology, 114(3), 245–254.
Abstract: Abstract Models of swarming (based on avoidance, alignment and attraction) produce patterns of behaviour also seen in schools of fish. However, the significance of such similarities has been questioned, because some model assumptions are unrealistic [e.g. speed in most models is constant with random error, the perception is global and the size of the schools that have been studied is small (up to 128 individuals)]. This criticism also applies to our former model, in which we demonstrated the emergence of two patterns of spatial organization, i.e. oblong school form and high frontal density, which are supposed to function as protection against predators. In our new model we respond to this criticism by making the following improvements: individuals have a preferred ‘cruise speed’ from which they can deviate in order to avoid others or to catch up with them. Their range of perception is inversely related to density, with which we take into account that high density limits the perception of others that are further away. Swarm sizes range from 10 to 2000 individuals. The model is three-dimensional. Further, we show that the two spatial patterns (oblong shape and high frontal density) emerge by self-organization as a side-effect of coordination at two speeds (of two or four body lengths per second) for schools of sizes above 20. Our analysis of the model leads to the development of a new set of hypotheses. If empirical data confirm these hypotheses, then in a school of real fish these patterns may arise as a side-effect of their coordination in the same way as in the model.
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Hildenbrandt, H., Carere, C., & Hemelrijk, C. K. (2010). Self-organized aerial displays of thousands of starlings: a model. Behav. Ecol., 21(6), 1349–1359.
Abstract: Through combining theoretical models and empirical data, complexity science has increased our understanding of social behavior of animals, in particular of social insects, primates, and fish. What are missing are studies of collective behavior of huge swarms of birds. Recently detailed empirical data have been collected of the swarming maneuvers of large flocks of thousands of starlings (Sturnus vulgaris) at their communal sleeping site (roost). Their flocking maneuvers are of dazzling complexity in their changes in density and flock shape, but the processes underlying them are still a mystery. Recent models show that flocking may arise by self-organization from rules of co-ordination with nearby neighbors, but patterns in these models come nowhere near the complexity of those of the real starlings. The question of this paper, therefore, is whether such complex patterns can emerge by self-organization. In our computer model, called StarDisplay, we combine the usual rules of co-ordination based on separation, attraction, and alignment with specifics of starling behavior: 1) simplified aerodynamics of flight, especially rolling during turning, 2) movement above a “roosting area” (sleeping site), and 3) the low fixed number of interaction neighbors (i.e., the topological range). Our model generates patterns that resemble remarkably not only qualitative but also quantitative empirical data collected in Rome through video recordings and position measurements by stereo photography. Our results provide new insights into the mechanisms underlying complex flocking maneuvers of starlings and other birds.
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Puga-Gonzalez, I., Hildenbrandt, H., & Hemelrijk, C. K. (2009). Emergent Patterns of Social Affiliation in Primates, a Model. PLoS Comput Biol, 5(12), e1000630.
Abstract: Author Summary
<p>Individual primates distribute their affiliative behaviour (such as grooming) in complex patterns among their group members. For instance, they reciprocate grooming, direct it more to partners the higher the partner's rank, use it to reconcile fights and do so in particular with partners that are more valuable. For several types of patterns (such as reconciliation and exchange), a separate theory based on specific cognitive processes has been developed (such as individual recordkeeping, a tendency to exchange, selective attraction to the former opponent, and estimation of the value of a relationship). It is difficult to imagine how these separate theories can all be integrated scientifically and how these processes can be combined in the animal's mind. To solve this problem, we first surveyed the empirical patterns and then we developed an individual-based model (called GrooFiWorld) in which individuals group, compete and groom. The grooming rule is based on grooming out of fear of defeat and on the anxiety reducing effects of grooming. We show that in this context this rule alone can explain many of the patterns of affiliation as well as the differences between egalitarian and despotic species. Our model can be used as a null model to increase our understanding of affiliative patterns of primates.</p>
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