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 ...

We consider the switching rate of a metastable reaction scheme, which includes reactions with arbitrary steps, e.g., kA<-->(k+r)A (both forward and reverse reaction steps are allowed to happen). Employing a WKB approximation, controlled by a large system size, we evaluate both the exponent and the preexponential factor for the rate. The results are illustrated on a number of examples.

Abstract. The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d ≥ 2, but all the solutions are regular in one dimension; a mathematical fact that crucially affects the patterns that can form in the biological system. One of the strongest assumptions of the KellerSegel model is the diffusive character of the cellular motion, known to be false in many situations. We extend this model to such situations in which the cellular dispersal is better modelled by a fractional operator. We analyze this fractional Keller-Segel model and find that all solutions are again globally bounded in time in one dimension. This fact shows the robustness of the main biological conclusions obtained from the Keller-Segel model. AMS classification scheme numbers: 35K45, 35K55, 92C15, 92C17