Causes of variation of darkness in flocks of starlings, a computational model

The coordinated motion of large flocks of starlings is fascinating for both laymen and scientists. During their aerial displays, the darkness of flocks often changes, for instance dark bands propagate through the flock (so-called agitation waves) and small or large parts of the flock darken. The causes of dark bands in agitation waves have recently been shown to depend on changes in orientation of birds relative to the observer rather than changes in density of the flock, but what causes other changes in darkness need to be studied still and this is the aim of the present investigation. Because we cannot empirically relate changes in darkness in flocks to quantities, such as position and orientation of the flock and of its members relative to the observer, we study this in a computational model. We use StarDisplay, a model of collective motion of starlings, because its flocks resemble empirical data in many properties, such as their three-dimensional shape, their manner of turning, the correlation of heading of its group-members, and its internal structure regarding density and stability of neighbors. We show that the change in darkness in the flocks perceived by an observer on the ground mostly depends on the observer’s distance to the flock and on the degree of exposure of the wing surface of flock members to the observer, and that darkness appears to decrease when birds roll during sharp turns. Remarkably, the darkness of the flock perceived by the observer was neither affected by the orientation of the flock relative to the observer nor by the density of the flock. Further studies are needed to investigate changes in darkness for flocks under predation

Damping of waves of agitation in starling flocks

When a predator attacks a flock of starlings (Sturnus vulgaris), involving thousands of individuals, a typical collective escape response is the so-called agitation wave, consisting of one or more dark bands (pulses) propagating through the flock and moving away from the predator (usually a Peregrine falcon, Falco peregrinus). The mechanism underlying this collective behavior remains debated. A theoretical study has suggested that the individual motion underlying a pulse could be a skitter (in the form of a zigzag), that is copied by nearby neighbors, and causes us to temporarily observe a larger surface of the wing because the bird is banking during turning while zigzagging. It is not known, however, whether pulses during a wave event weaken over time. This is of interest, because whereas during the usual turning by an undisturbed flock the motion is copied completely without weakening, we may expect that pulses dampen during a wave event because individuals that are further away from a predator react less because of reduced fear. In the present paper, we show in empirical data that pulses during a wave event weaken over time. Our computational model, StarDisplay, reveals that this is most likely a consequence of a reduction of the maximum banking angle during the zigzag escape maneuver rather than by a reduced tendency to copy this maneuver with time. The response seems adaptive because of lowered danger at a larger distance to the location of attack

The evolution of social philopatry in female primates

The transition from solitary life to sociality is considered one of the major transitions in evolution. In primates, this transition is currently not well understood. Traditional verbal models appear insufficient to unravel the complex interplay of environmental and demographic factors involved in the evolution of primate sociality, and recent phylogenetic reconstructions have produced conflicting results. We therefore analyze a theoretical model for the evolution of female social philopatry that sheds new light on the question why most primates live in groups. In individual-based simulations, we study the evolution of dispersal strategies of both resident females and their offspring. The model reveals that social philopatry can evolve through kin selection, even if retention of offspring is costly in terms of within-group resource competition and provides no direct benefits. Our model supports the role of predator avoidance as a selective pressure for group-living in primates, but it also suggests that a second benefit of group-living, communal resource defense, might be required to trigger the evolution of sizable groups. Lastly, our model reveals that seemingly small differences in demographic parameters can have profound effects on primate social evolution

Some Causes of the Variable Shape of Flocks of Birds

Flocks of birds are highly variable in shape in all contexts (while travelling, avoiding predation, wheeling above the roost). Particularly amazing in this respect are the aerial displays of huge flocks of starlings (Sturnus vulgaris) above the sleeping site at dawn. The causes of this variability are hardly known, however. Here we hypothesise that variability of shape increases when there are larger local differences in movement behaviour in the flock. We investigate this hypothesis with the help of a model of the self-organisation of travelling groups, called StarDisplay, since such a model has also increased our understanding of what causes the oblong shape of schools of fish. The flocking patterns in the model prove to resemble those of real birds, in particular of starlings and rock doves. As to shape, we measure the relative proportions of the flock in several ways, which either depend on the direction of movement or do not. We confirm that flock shape is usually more variable when local differences in movement in the flock are larger. This happens when a) flock size is larger, b) interacting partners are fewer, c) the flock turnings are stronger, and d) individuals roll into the turn. In contrast to our expectations, when variability of speed in the flock is higher, flock shape and the positions of members in the flock are more static. We explain this and indicate the adaptive value of low variability of speed and spatial restriction of interaction and develop testable hypotheses

Non-local kinetic and macroscopic models for self-organised animal aggregations

The last two decades have seen a surge in kinetic and macroscopic models derived to investigate the multi-scale aspects of self-organised biological aggregations. Because the individual-level details incorporated into the kinetic models (e.g., individual speeds and turning rates) make them somewhat difficult to investigate, one is interested in transforming these models into simpler macroscopic models, by using various scaling techniques that are imposed by the biological assumptions of the models. However, not many studies investigate how the dynamics of the initial models are preserved via these scalings. Here, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local 1D and 2D models for biological aggregations to simpler models existent in the literature. Then, we investigate how some of the spatio-temporal patterns exhibited by the original kinetic models are preserved via these scalings. To this end, we focus on the parabolic scaling for non-local 1D models and apply asymptotic preserving numerical methods, which allow us to analyse changes in the patterns as the scaling coefficient ϵ is varied from ϵ=1 (for 1D transport models) to ϵ=0 (for 1D parabolic models). We show that some patterns (describing stationary aggregations) are preserved in the limit ϵ→0, while other patterns (describing moving aggregations) are lost. To understand the loss of these patterns, we construct bifurcation diagrams

Fluctuation-Driven Flocking Movement in Three Dimensions and Scale-Free Correlation

Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of “topological distances” and “scale-free correlations” are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the “metric distance”). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations

The effect of male incubation feeding on female nest attendance and reproductive performance in a socially monogamous bird

The incubation of eggs plays a key role in avian parental care. To ensure embryo development, incubating parents have to keep their eggs within the appropriate temperature limits. To do so, incubating individuals allocate substantial energy to the thermal demands of their eggs, but they face a trade-off with self-maintenance (own metabolism) because they usually cannot forage while incubating eggs. In species with female-only incubation, males can help their partners by providing them with food on the nest, a behavior which may enable females to spend more time incubating and could, consequently, lead to improved reproductive performance. In the study reported here, we first investigated whether incubation feeding by males affects nest attendance by females in Blue Tits (Cyanistes caeruleus) and subsequently determined how this incubation feeding affects reproductive performance. We found that the female nest attendance tended to increase with increasing amounts of food supplied by their male partner. Thus, males may enable females to incubate more when needed, as suggested by our observation that male incubation feeding was more frequent when the ambient temperature was lower, and especially so when females incubated later in the breeding season (during the study period the ambient temperature decreased rapidly over the breeding season, which is exceptional). Although female nest attendance did not result in a shorter time until the eggs hatched or in higher hatching success, females that attended the nest more produced heavier nestlings. We suggest that the trade-off between self-maintenance and meeting the demands of egg incubation likely tends to be less when females received more assistance from their partner during the egg incubation period, resulting in a higher investment in offspring