Examination of an averaging method for estimating repulsion and attraction interactions in moving groups

Collective order and group structure of shoaling fish subject to differing risk-level treatments with a sympatric predator

It is imperative for individuals to exhibit flexible behaviour according to ecological context, such as available resources or predation threat. Manipulative studies on responses to threat often focus on behaviour in the presence of a single indicator for the potential of predation, whereas in the wild perception of threat will probably be more nuanced. Here, we examine the collective behaviour of eastern mosquitofish (Gambusia holbrooki) subject to five differing threat scenarios relating to the presence and hunger state of a jade perch (Scortum barcoo). Across threat scenarios, groups exhibit unique behavioural profiles that differ in the durations that particular collective states are maintained, the probability of transitions between states, the size and duration of persistence of spatially defined subgroups, and the patterns of collective order of these subgroups. Under the greatest level of threat, subgroups of consistent membership persist for longer durations. Group-level behaviours, and their differences, are interconnected with differences in estimates of the underlying rules of interaction thought to govern collective motion. The responses of the group are shown to be specific to the details of a potential threat, rather than a binary response to the presence or absence of some form of threat.

Selective social interactions and speed-induced leadership in schooling fish

Animals moving together in groups are believed to interact among each other with effective social forces, such as attraction, repulsion, and alignment. Such forces can be inferred using "force maps," i.e., by analyzing the dependency of the acceleration of a focal individual on relevant variables. Here, we introduce a force map technique suitable for the analysis of the alignment forces experienced by individuals. After validating it using an agent-based model, we apply the force map to experimental data of schooling fish. We observe signatures of an effective alignment force with faster neighbors and an unexpected antialignment with slower neighbors. Instead of an explicit antialignment behavior, we suggest that the observed pattern is the result of a selective attention mechanism, where fish pay less attention to slower neighbors. This mechanism implies the existence of temporal leadership interactions based on relative speeds between neighbors. We present support for this hypothesis both from agent-based modeling as well as from exploring leader-follower relationships in the experimental data.

Applying collective motion models to study discordant individual behaviours within a school of fish

Computational models of collective motion successfully reproduce the most common behaviours of a school of fish, using only a few elementary interactions between individuals. However, their ability to also reproduce individual behaviours that are discordant from those of the group has not yet been adequately investigated. In this paper, a self-propelled particle model using three interaction zones is considered in relation to the counter-rotation of an individual: a phenomenon observable in real schools of fish milling in a torus, when an individual moves in the same torus but in the opposite direction for a certain period of time. This study shows that the interactions of repulsion, orientation and attraction between individuals moving at constant speed in a three-dimensional space, with asynchronous updating, can generate temporary counter-rotations. The analysis of such events sheds light on the mechanisms that start the counter-rotation and those that end it. Although the contribution of the repulsion interaction is often significant to start and terminate the counter-rotation, it does not prove to be decisive. Indeed, it is observed that even when interactions between individuals are limited to attraction alone, temporary counter-rotations of individuals occur, provided the fish density along the circumference is not uniform. Some of these conclusions, deduced from the simulations performed, are visually consistent with what is observed in some underwater video recordings of milling schools of fish.

An examination of force maps targeted at orientation interactions in moving groups

Force mapping is an established method for inferring the underlying interaction rules thought to govern collective motion from trajectory data. Here we examine the ability of force maps to reconstruct interactions that govern individual's tendency to orient, or align, their heading within a moving group, one of the primary factors thought to drive collective motion, using data from three established general collective motion models. Specifically, our force maps extract how individuals adjust their direction of motion on average as a function of the distance to neighbours and relative alignment in heading with these neighbours, or in more detail as a function of the relative coordinates and relative headings of neighbours. We also examine the association between plots of local alignment and underlying alignment rules. We find that the simpler force maps that examined changes in heading as a function of neighbour distances and differences in heading can qualitatively reconstruct the form of orientation interactions, but also overestimate the spatial range over which these interactions apply. More complex force maps that examine heading changes as a function of the relative coordinates of neighbours (in two spatial dimensions), can also reveal underlying orientation interactions in some cases, but are relatively harder to interpret. Responses to neighbours in both the simpler and more complex force maps are affected by group-level patterns of motion. We also find a correlation between the sizes of regions of high alignment in local alignment plots and the size of the region over which alignment rules apply when only an alignment interaction rule is in action. However, when data derived from more complex models is analysed, the shapes of regions of high alignment are clearly influenced by emergent patterns of motion, and these regions of high alignment can appear even when there is no explicit direct mechanism that governs alignment.

Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging to infer the interaction rules directly from data. In the field of equation discovery, the weak-form sparse identification of nonlinear dynamics (WSINDy) methodology has been shown to be computationally efficient for identifying the governing equations of complex systems from noisy data. Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for the second-order IPS to learn equations for communities of cells. Our approach learns the directional interaction rules for each individual cell that in aggregate govern the dynamics of a heterogeneous population of migrating cells. To sort a cell according to the active classes present in its model, we also develop a novel ad hoc classification scheme (which accounts for the fact that some cells do not have enough evidence to accurately infer a model). Aggregated models are then constructed hierarchically to simultaneously identify different species of cells present in the population and determine best-fit models for each species. We demonstrate the efficiency and proficiency of the method on several test scenarios, motivated by common cell migration experiments.

Systematic Analysis of Emergent Collective Motion Produced by a 3D Hybrid Zonal Model

Emergent patterns of collective motion are thought to arise from local rules of interaction that govern how individuals adjust their velocity in response to the relative locations and velocities of near neighbours. Many models of collective motion apply rules of interaction over a metric scale, based on the distances to neighbouring group members. However, empirical work suggests that some species apply interactions over a topological scale, based on distance determined neighbour rank. Here, we modify an important metric model of collective motion (Couzin et al. in J Theor Biol 218(1):1-11, 2002), so that interactions relating to orienting movements with neighbours and attraction towards more distant neighbours operate over topological scales. We examine the emergent group movement patterns generated by the model as the numbers of neighbours that contribute to orientation- and attraction-based velocity adjustments vary. Like the metric form of the model, simulated groups can fragment (when interactions are influenced by less than 10-15% of the group), swarm and move in parallel, but milling does not occur. The model also generates other cohesive group movements including cases where groups exhibit directed motion without strong overall alignment of individuals. Multiple emergent states are possible for the same set of underlying model parameters in some cases, suggesting sensitivity to initial conditions, and there is evidence that emergent states of the system depend on the history of the system. Groups that do not fragment tend to stay relatively compact in terms of neighbour distances. Even if a group does fragment, individuals remain relatively close to near neighbours, avoiding complete isolation.

A statistical method for identifying different rules of interaction between individuals in moving animal groups

The emergent patterns of collective motion are thought to arise from application of individual-level rules that govern how individuals adjust their velocity as a function of the relative position and behaviours of their neighbours. Empirical studies have sought to determine such rules of interaction applied by 'average' individuals by aggregating data from multiple individuals across multiple trajectory sets. In reality, some individuals within a group may interact differently from others, and such individual differences can have an effect on overall group movement. However, comparisons of rules of interaction used by individuals in different contexts have been largely qualitative. Here we introduce a set of randomization methods designed to determine statistical differences in the rules of interaction between individuals. We apply these methods to a case study of leaders and followers in pairs of freely exploring eastern mosquitofish (Gambusia holbrooki). We find that each of the randomization methods is reliable in terms of: repeatability of p-values, consistency in identification of significant differences and similarity between distributions of randomization-based test statistics. We observe convergence of the distributions of randomization-based test statistics across repeat calculations, and resolution of any ambiguities regarding significant differences as the number of randomization iterations increases.