Inherent noise can facilitate coherence in collective swarm motion

Abstract

Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker-Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker-Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker-Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker-Planck equation coefficient estimation approach, can be implemented in the selfpropelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.collective behavior | locusts | density-dependent switching | coarse-graining | swarming W hile recent years have seen an explosion in the number of simulation models of moving animal groups, there is little detailed comparison between these models and experimental data (1, 2). The models usually produce motion that "looks like" that of a swarm of locusts, a school of fish, or a flock of birds, but the similarities are difficult to quantify (3). Furthermore, the simulation models themselves are often difficult to understand from a mathematical viewpoint since, by their nature, they resist simple mean-field descriptions. These complications make it difficult to use models to predict, for example, the rate at which groups change direction of travel or how spatial patterns evolve through time (4, 5). We are left with a multitude of models, all of which seem to relate to the available experimental data, but none of which provide clear predictive power.One approach to the problem of linking experimental data to model behavior is the detailed study of the local interactions between animals. This approach has yielded better understanding of the rules ...

From behavioural analyses to models of collective motion in fish schools

“…A typical feature of models of collective motion is a competition between a stochastic component and a tendency to order, although it is important to note that stochastic effects may also facilitate the instatement of collective motion [79]. However, there is a different way to implement stochasticity, which has been recently investigated by Bode et al [80].…”

Relation between cooperative molecular motors and active Brownian particles

“…Our method here is similar to the one used by Yates et al [14], who extracted the functions f (v) and g(v) by measuring the Kramers-Moyal coefficients and compared the resulting stationary probability density (see below) to the velocity's histogram. In contrast to this, we extract f (v) and g(v) from both kinds of statistics independently.…”

“…Besides the phenomenological description of experimental data, ABP models have been shown to reproduce qualitatively the statistics of more complicated multivariable stochastic models [14,15]. One such model proposed by Jülicher and Prost [16] describes the stochastic dynamics of a group of rigidly coupled molecular motors (CMMs) [15,17].…”

“…For an active Brownian particle (ABP), as considered in the following, the nonlinear dissipation term f (v) is negative for a range of velocities, which precludes thermodynamic equilibrium. Several authors have measured * Corresponding author: benji@pks.mpg.de the functions f (v) and g(v) (also in multidimensional setups) from experimental data of biological systems [6,[12][13][14].…”

“…In this paper we provide numerical versions of this mapping. We use two independent numerical approaches: one which is based on the stationary velocity distribution of the motor system and one which is based on the Kramers-Moyal coefficients of the velocity (the two approaches were used by Yates et al [14], who studied experimental data from locusts). The fact that both methods yield comparable results for the functions f (v) and g (v) underpins that the ABP model is a reasonable approximation of a system of many coupled motors.…”