Self-organization of collective escape in pigeon flocks

Abstract

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.

Emergence of splits and collective turns in pigeon flocks under predation

“…We extended our agent-based model of collective escape of homing pigeons, HoPE (Homing Pigeons Escape) [ 47 ] to study the emergence of splits and collective turns. HoPE is based on empirical data of homing pigeons [ 47 ]: it resembles real flocks in both individual behaviour (specifics of flying motion, speed and coordination rules among flock-mates [ 31 , 46 , 61 , 70 ]) as well as collective patterns [ 46 , 47 ]. Its detailed description according to the ODD (Overview, Design concepts, Detail) protocol [ 71 ] is given as an appendix in our electronic supplementary material.…”

“…Coordination is controlled by the weighted sum of some social ‘ forces’ that represent these rules and has been adjusted to the specifics of flocking by pigeons [ 21 , 24 ]. Each pigeon-oid turns towards the centre of mass of its seven closest neighbours [ 30 , 33 , 47 ] and accelerates to stay close to them [ 31 ]. Alignment is represented by a force parallel to the average direction of all seven neighbours.…”

“…Complete trajectories of airborne birds in flocks under predation have only recently been collected with a newly developed, remotely controlled robotic-falcon (referred to as ‘RobotFalcon’ [ 45 ]) attacking flocks of homing pigeons ( Columba livia ) [ 46 ]. In the present study, we combine these quantitative data [ 46 ] with a species-specific computational model (HoPE—Homing Pigeons Escape, [ 47 ]) to investigate what behavioural rules underlie the patterns of collective escape in pigeons.…”

“…To understand how these patterns arise, we need a new computational model since neither early splits nor collective turns have been reported in previous models of collective escape. In most models, individuals have only a single rule of escape, usually a continuous tendency to turn away from the predator while coordinating with their neighbours [ 26 , 47 , 52 ]. Remarkably, this single rule has led to many patterns in a model of fish schools [ 26 ] ( figure 1 ), for instance the vacuole, the hourglass [ 9 ] and the split (in close vicinity to the predator).…”

“…To generate the early splits and collective turns (at large distance from the predator) that we see in pigeon flocks, we extend an agent-based model of pigeons' collective escape [ 31 , 47 , 61 ] with a new escape manoeuvre that is discrete, variable and uncoordinated. We give each individual a probability to turn away from the predator without coordinating with its neighbours.…”