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

Effects of anisotropic interactions on the structure of animal groups

This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the position of a limited number of close group mates. The proposed model is shown to produce clustered formations, as well as lines and V-like formations. The key factors which trigger the onset of different patterns are argued to be the relative strength of attraction and repulsion forces and, most important, the anisotropy in their application.Comment: 22 pages, 9 figures. Submitted. v1-v4: revised presentation; extended simulations; included technical results. v5: added a few clarification

On the duality between interaction responses and mutual positions in flocking and schooling.

Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we propose a complementary approach to the analysis of flocking phenomena, based on the idea that animals occupy preferential, anysotropic positions with respect to their neighbours, and devote a large amount of their interaction responses to maintaining their mutual positions. We test our approach by deriving the apparent alignment and attraction responses from simulated trajectories of animals moving side by side, or one in front of the other. We show that the anisotropic positioning of individuals, in combination with noise, is sufficient to reproduce several aspects of the movement responses observed in real animal groups. This anisotropy at the level of interactions should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, our work provides a frame to discriminate movement interactions that signal directional conflict from interactions underlying consensual group motion

Quantifying the interplay between environmental and social effects on aggregated-fish dynamics

Demonstrating and quantifying the respective roles of social interactions and external stimuli governing fish dynamics is key to understanding fish spatial distribution. If seminal studies have contributed to our understanding of fish spatial organization in schools, little experimental information is available on fish in their natural environment, where aggregations often occur in the presence of spatial heterogeneities. Here, we applied novel modeling approaches coupled to accurate acoustic tracking for studying the dynamics of a group of gregarious fish in a heterogeneous environment. To this purpose, we acoustically tracked with submeter resolution the positions of twelve small pelagic fish (Selar crumenophthalmus) in the presence of an anchored floating object, constituting a point of attraction for several fish species. We constructed a field-based model for aggregated-fish dynamics, deriving effective interactions for both social and external stimuli from experiments. We tuned the model parameters that best fit the experimental data and quantified the importance of social interactions in the aggregation, providing an explanation for the spatial structure of fish aggregations found around floating objects. Our results can be generalized to other gregarious species and contexts as long as it is possible to observe the fine-scale movements of a subset of individuals.Comment: 10 pages, 5 figures and 4 supplementary figure

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Bayesian Inference for Identifying Interaction Rules in Moving Animal Groups

The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of “universal” classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed

Trail formation based on directed pheromone deposition

We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromones and interact with them through alignment interaction. The directed pheromones intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant-pheromone interaction frequency is increased can be evidenced. Finally, we propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level