Reciprocal relationships in collective flights of homing pigeons

Inferring causal relationship in coordinated flight of pigeon flocks

Collective phenomenon of natural animal groups will be attributed to individual intelligence and interagent interactions, where a long-standing challenge is to reveal the causal relationship among individuals. In this study, we propose a causal inference method based on information theory. More precisely, we calculate mutual information by using a data mining algorithm named "k-nearest neighbor" and subsequently induce the transfer entropy to obtain the causality entropy quantifying the causal dependence of one individual on another subject to a condition set consisting of other neighboring ones. Accordingly, we analyze the high-resolution GPS data of three pigeon flocks to extract the hidden interaction mechanism governing the coordinated free flight. The comparison of spatial distribution between causal neighbors and all other remainders validates that no bias exists for the causal inference. We identify the causal relationships to establish the interaction network and observe that the revealed causal relationship follows a local interaction mode. Interestingly, the individuals closer to the mass center and the average velocity direction are more influential than others.

Misinformed leaders lose influence over pigeon flocks

In animal groups where certain individuals have disproportionate influence over collective decisions, the whole group's performance may suffer if these individuals possess inaccurate information. Whether in such situations leaders can be replaced in their roles by better-informed group mates represents an important question in understanding the adaptive consequences of collective decision-making. Here, we use a clock-shifting procedure to predictably manipulate the directional error in navigational information possessed by established leaders within hierarchically structured flocks of homing pigeons (Columba livia). We demonstrate that in the majority of cases when leaders hold inaccurate information they lose their influence over the flock. In these cases, inaccurate information is filtered out through the rearrangement of hierarchical positions, preventing errors by former leaders from propagating down the hierarchy. Our study demonstrates that flexible decision-making structures can be valuable in situations where 'bad' information is introduced by otherwise influential individuals.

Tracking a single pigeon using a shadowing filter algorithm

Miniature GPS devices now allow for measurement of the movement of animals in real time and provide high‐ quality and high‐resolution data. While these new data sets are a great improvement, one still encounters some measurement errors as well as device failures. Moreover, these devices only measure position and require further reconstruction techniques to extract the full dynamical state space with the velocity and acceleration. Direct differentiation of position is generally not adequate. We report on the successful implementation of a shadowing filter algorithm that (1) minimizes measurement errors and (2) reconstructs at the same time the full phase‐space from a position recording of a flying pigeon. This filter is based on a very simple assumption that the pigeon's dynamics are Newtonian. We explore not only how to choose the filter's parameters but also demonstrate its improvements over other techniques and give minimum data requirements. In contrast to competing filters, the shadowing filter's approach has not been widely implemented for practical problems. This article addresses these practicalities and provides a prototype for such application.

Route-dependent switch between hierarchical and egalitarian strategies in pigeon flocks

The mechanisms that underlie fascinating inter-individual interactions among animal groups have attracted increasing attention from biologists, physicists, and system scientists. There are two well-known types of interaction patterns: hierarchical and egalitarian. In the former type, individuals follow their leaders, whereas they follow their neighbors in the latter. Using high-resolution spatiotemporal data derived from the free flights of a flock of pigeons, we show that pigeon flocks actually adopt a mode that switches between the two aforementioned strategies. To determine its flight direction, each pigeon tends to follow the average of its neighbors while moving along a smooth trajectory, whereas it switches to follow its leaders when sudden turns or zigzags occur. By contrast, when deciding how fast to fly, each pigeon synthesizes the average velocity of its neighbors. This switching mechanism is promising for possible industrial applications in multi-robot system coordination, unmanned vehicle formation control, and other areas.

Temporal and contextual consistency of leadership in homing pigeon flocks

Organized flight of homing pigeons (Columba livia) was previously shown to rely on simple leadership rules between flock mates, yet the stability of this social structuring over time and across different contexts remains unclear. We quantified the repeatability of leadership-based flock structures within a flight and across multiple flights conducted with the same animals. We compared two contexts of flock composition: flocks of birds of the same age and flight experience; and, flocks of birds of different ages and flight experience. All flocks displayed consistent leadership-based structures over time, showing that individuals have stable roles in the navigational decisions of the flock. However, flocks of balanced age and flight experience exhibited reduced leadership stability, indicating that these factors promote flock structuring. Our study empirically demonstrates that leadership and followership are consistent behaviours in homing pigeon flocks, but such consistency is affected by the heterogeneity of individual flight experiences and/or age. Similar evidence from other species suggests leadership as an important mechanism for coordinated motion in small groups of animals with strong social bonds.

Interaction rules underlying group decisions in homing pigeons

Travelling in groups gives animals opportunities to share route information by following cues from each other's movement. The outcome of group navigation will depend on how individuals respond to each other within a flock, school, swarm or herd. Despite the abundance of modelling studies, only recently have researchers developed techniques to determine the interaction rules among real animals. Here, we use high-resolution GPS (global positioning system) tracking to study these interactions in pairs of pigeons flying home from a familiar site. Momentary changes in velocity indicate alignment with the neighbour's direction, as well as attraction or avoidance depending on distance. Responses were stronger when the neighbour was in front. From the flocking behaviour, we develop a model to predict features of group navigation. Specifically, we show that the interactions between pigeons stabilize a side-by-side configuration, promoting bidirectional information transfer and reducing the risk of separation. However, if one bird gets in front it will lead directional choices. Our model further predicts, and observations confirm, that a faster bird (as measured from solo flights) will fly slightly in front and thus dominate the choice of homing route. Our results explain how group decisions emerge from individual differences in homing flight behaviour.

Context-dependent hierarchies in pigeons

Hierarchical organization is widespread in the societies of humans and other animals, both in social structure and in decision-making contexts. In the case of collective motion, the majority of case studies report that dominant individuals lead group movements, in agreement with the common conflation of the terms "dominance" and "leadership." From a theoretical perspective, if social relationships influence interactions during collective motion, then social structure could also affect leadership in large, swarm-like groups, such as fish shoals and bird flocks. Here we use computer-vision-based methods and miniature GPS tracking to study, respectively, social dominance and in-flight leader-follower relations in pigeons. In both types of behavior we find hierarchically structured networks of directed interactions. However, instead of being conflated, dominance and leadership hierarchies are completely independent of each other. Although dominance is an important aspect of variation among pigeons, correlated with aggression and access to food, our results imply that the stable leadership hierarchies in the air must be based on a different set of individual competences. In addition to confirming the existence of independent and context-specific hierarchies in pigeons, we succeed in setting out a robust, scalable method for the automated analysis of dominance relationships, and thus of social structure, applicable to many species. Our results, as well as our methods, will help to incorporate the broader context of animal social organization into the study of collective behavior.

Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred.

The construction of mathematical models from experimental time-series data has been considered with some success in many areas of science and engineering, using the power of computer algorithms to build model structures and suitably tuning their parameters. When considering complex systems with nonlinear or collective behavior, computational models built from real data are the alternative to emulating the system as best as possible, since classic modeling approaches based on observation could prove difficult for complex dynamics. In this study, we provide a method to build models of collective dynamics from homing pigeon flight data. We show that our models follow the source dynamics well, and from them we are able to infer that significant collective behavior occurs in pigeon flights. Our results are consistent with the basic principles of previous hypotheses and models that have been proposed. Our approach serves as an initial outline towards the usage of experimental data to construct computational models to understand many complex phenomena with hypothesized collective behavior.