Generating self-organizing collective behavior using separation dynamics from experimental data

Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena, and later tuned or verified to simulate desired dynamics. In contrast to this approach, we propose using a model that attempts to follow an averaged rule of the essential distance-dependent collective behavior of real pigeon flocks, which was abstracted from experimental data. By using a simple model to follow the behavioral tendencies of real data, we show that our model can exhibit emergent self-organizing dynamics such as flocking, pattern formation, and counter-rotating vortices. The range of behaviors observed in our simulations are richer than the standard models of collective dynamics, and should thereby give potential for new models of complex behavior.Comment: Submitted to Chao

Reciprocal relationships in collective flights of homing pigeons

Collective motion of bird flocks can be explained via the hypothesis of many wrongs, and/or, a structured leadership mechanism. In pigeons, previous studies have shown that there is a well-defined hierarchical structure and certain specific individuals occupy more dominant positions --- suggesting that leadership by the few individuals drives the behavior of the collective. Conversely, by analyzing the same data-sets, we uncover a more egalitarian mechanism. We show that both reciprocal relationships and a stratified hierarchical leadership are important and necessary in the collective movements of pigeon flocks. Rather than birds adopting either exclusive averaging or leadership strategies, our experimental results show that it is an integrated combination of both compromise and leadership which drives the group's movement decisions.Comment: 7 pages, 5 figure

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 predicting and 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

Simulations of high density instances () of the R2 model.

<p>Low and high initial speeds are considered. The simulation with high initial speed shows small groups dispersing in many directions. Plot (a) shows a snapshot after 100 s and (b) one after 500 s.</p

Comparison of separation measures between extreme cases of initial conditions for the R2 model.

<p>Statistics were averaged over 10 simulations for each case. Plot (a) shows that the initial speed plays an important part in the global separation of the system . In plot (b), the local separations tend to similar steady states regardless of the initial conditions.</p

Simulations of low density instances () of the R2 model.

<p>Low and high initial speeds are considered. The simulation with low initial speed shows a more aligned and cohesive flock. Plot (a) shows a snapshot after 100 s and (b) one after 500 s.</p

Homing flight 2: flock separation for models with different interaction structure.

<p>In (a), simulations consider initial conditions from the input data, while (b) averages over ten simulations of random initial conditions, and all time intervals. From the plots, a split occurs in the flock after (see (a)), while has the strongest collective component (see (b)).</p

Retrieved alignment rule by the “best” R1 model.

<p>Extracted rule representing alingment of an individual <i>i</i> at time : , as a function of the neighborhood alignments at time <i>t</i>: . In an ideal noiseless modified Vicsek model, these alignments are equal. This synchronization principle is the basis for the swarming behavior of the Vicsek model.</p

The “optimal” <i>M</i> value.

<p>Averaged mean absolute error (MAE) values between models and their source data for each homing flight. The MAEs from all the models of the same type (same <i>M</i>) were averaged in order to find which interaction followed best the separation dynamics. The models with show the least averaged MAE in all flights.)</p

Comparison of averaged separation measure for simulations of R2 model.

<p>Initial speeds and population radius (densities) for the R2 model were varied. Critical density values (highest cohesion) for each speed are marked for global separation in (a). Loosely invariant behavior for local separation is shown in (b). Statistics were averaged over 10 simulations for each parameter case.</p