Analysis of Pairwise Interactions in a Maximum Likelihood Sense to Identify Leaders in a Group

Collective motion in animal groups manifests itself in the form of highly coordinated maneuvers determined by local interactions among individuals. A particularly critical question in understanding the mechanisms behind such interactions is to detect and classify leader–follower relationships within the group. In the technical literature of coupled dynamical systems, several methods have been proposed to reconstruct interaction networks, including linear correlation analysis, transfer entropy, and event synchronization. While these analyses have been helpful in reconstructing network models from neuroscience to public health, rules on the most appropriate method to use for a specific dataset are lacking. Here, we demonstrate the possibility of detecting leaders in a group from raw positional data in a model-free approach that combines multiple methods in a maximum likelihood sense. We test our framework on synthetic data of groups of self-propelled Vicsek particles, where a single agent acts as a leader and both the size of the interaction region and the level of inherent noise are systematically varied. To assess the feasibility of detecting leaders in real-world applications, we study a synthetic dataset of fish shoaling, generated by using a recent data-driven model for social behavior, and an experimental dataset of pharmacologically treated zebrafish. Not only does our approach offer a robust strategy to detect leaders in synthetic data but it also allows for exploring the role of psychoactive compounds on leader–follower relationships

Detecting intermittent switching leadership in coupled dynamical systems

Leader-follower relationships are commonly hypothesized as a fundamental mechanism underlying collective behaviour in many biological and physical systems. Understanding the emergence of such behaviour is relevant in science and engineering to control the dynamics of complex systems toward a desired state. In prior works, due in part to the limitations of existing methods for dissecting intermittent causal relationships, leadership is assumed to be consistent in time and space. This assumption has been contradicted by recent progress in the study of animal behaviour. In this work, we leverage information theory and time series analysis to propose a novel and simple method for dissecting changes in causal influence. Our approach computes the cumulative influence function of a given individual on the rest of the group in consecutive time intervals and identify change in the monotonicity of the function as a change in its leadership status. We demonstrate the effectiveness of our approach to dissect potential changes in leadership on self-propelled particles where the emergence of leader-follower relationship can be controlled and on tandem flights of birds recorded in their natural environment. Our method is expected to provide a novel methodological tool to further our understanding of collective behaviour

Inferring causal relationships in zebrafish-robot interactions through transfer entropy: a small lure to catch a big fish

In the field of animal behavior, effective methods to apprehend causal relationships that underlie the interactions between animals are in dire need. How to identify a leader in a group of social animals or quantify the mutual response of predator and prey are exemplary questions that would benefit from an improved understanding of causality. Information theory offers a potent framework to objectively infer cause-and-effect relationships from raw experimental data, in the form of behavioral observations or individual trajectory tracks. In this targeted review, we summarize recent advances in the application of the information-theoretic concept of transfer entropy to animal interactions. First, we offer an introduction to the theory of transfer entropy, keeping a balance between fundamentals and practical implementation. Then, we focus on animal-robot experiments as a means for the validation of the use of transfer entropy to measure causal relationships. We explore a test battery of robotics-based protocols designed for studying zebrafish social behavior and fear response. Grounded in experimental evidence, we demonstrate the potential of transfer entropy to assist in the detection and quantification of causal relationships in animal interactions. The proposed robotics-based platforms offer versatile, controllable, and customizable stimuli to generate a priori known cause-and-effect relationships, which would not be feasible with live stimuli. We conclude the paper with an outlook on possible applications of transfer entropy to study group behavior and clarify the determinants of leadership in social animals