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

Abstract

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 selfpropelled 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.

Decoding collective communications using information theory tools

“…To determine whether one random variable is actually influenced by another, rather than merely correlated with it, one can instead use an IT metric called transfer entropy (TE) [49]. This metric has been used to measure how movement information cascades through simulated [25,58] and real [27,59] systems, to study interactions between animals and robots [29,60,61], and to establish hierarchy in leader-follower experiments [23,44].…”

“…Specifically, while many studies are able to infer interactions among group members (e.g. [6,[18][19][20][21][22][23]) it remains challenging to synthesize these lessons across bodies of work as approaches and conclusions can vary on a case-by-case basis.…”

Reducing the Number of Individuals to Monitor Shoaling Fish Systems – Application of the Shannon Entropy to Construct a Biological Warning System Model

“…Fish cognition and behavior is a well-established research field ( Vila Pouca and Brown, 2017 and references therein), and the characterisation of fish model systems’ behavior, using behavioral measurable changes, has found several practical applications, such as the detection of leaders in a group ( Mwaffo et al, 2017 ), the identification of information flows within a school of fish ( Crosato et al, 2018 ), the presence in the aquatic environment of contaminants including caffeine ( Ladu et al, 2015 ), drugs ( Liu et al, 2011 ), hypochlorite ( Magalhães et al, 2007 ; Nimkerdphol and Nakagawa, 2008 ; Teles et al, 2015 ), methyl-mercury ( Eguiraun et al, 2014 , 2016 ), the Se:Hg molar ratio in their feeds ( Eguiraun et al, 2018 ) and alterations in environmental parameters such as hypoxia, feeding regime ( Polonschii et al, 2013 ), and high fish density ( Papoutsoglou et al, 1998 ; Di Marco et al, 2008 ).…”

Detecting intermittent switching leadership in coupled dynamical systems

“…To address the limitations inherent to individual methods in dissecting between leader and follower, we have demonstrated in 43 , that a combination of individual methods yields more robust and consistent results. Yet, identifying leadership based on current approaches poses several challenges.…”