Fish use visual cues to coordinate behavior during schooling motion, search and find food sources, and spread information about predation threats through the group. Previous work has demonstrated the efficacy of visual networks in predicting the spread of information cascades through the group \cite{Strandburg_Peshkin_2013,Rosenthal_2015}. However, the time-dependent structure of how individuals exchange information within a group, and how this affects motion and decision making abilities, are not well understood. We use time-dependent interaction and response networks in schools of fish to examine hierarchy within the group and to determine the relationship between structural networks, which are obtained via visual field reconstruction and metric quantities, to functional networks, which are obtained by correlations in movements.  Laboratory experiments with small schooling fish (three-spined stickleback, Gasterosteus aculeatus and sunbleak, Leucaspius delineatus) in different sized groups are used to construct time-dependent visual, distance, and correlation networks, and these results are compared to model simulations of collective motion.  This analysis reveals general features of information flow in an actively moving animal group, and provides a framework to analyse such networks in other contexts of collective behavior.
Interactions in animal groups are often represented by proximity networks.  However, depending on species and context, this may be a poor approximation of information exchange \cite{Farine_2015}.  A more accurate representation of inter-individual connections can be obtained via visual field reconstruction \cite{Strandburg_Peshkin_2013,Rosenthal_2015}.  This approach reveals the 'structural' network, i.e. what communication routes may exist between individuals.  The 'functional' network, which represents the actual exchange of information, is constrained by structure, but may have different patterns of connectivity.  We use cross-correlation techniques inspired by statistical physics to infer functional connections between animals \cite{Nagy_2010}.   Comparing functional networks to the structural networks reveals how individuals use visual cues to communicate and coordinate their behavior.
Many ecological systems can be represented by temporal networks \cite{Blonder_2012}, but few studies have analyzed group movement using this framework (e.g. \cite{Rubenstein_2015}). We use a temporal network representation and community detection methods  \cite{Ahn_2010,Berger_Wolf_2010} to examine hierarchy and structure within an actively moving group.  Both sticklebacks and sunbleaks live in fission-fusion groups, often breaking into smaller groups and subsequently merging and re-forming.  We apply community detection methods to test if fission events can be predicted.  We also ask whether groups have consistent internal structures that reflect active sorting; for example, if faster fish consistently group together at the front of the group and act as leaders \cite{Jolles_2017}.  
By combining visual field reconstruction and movement correlation methods, this work provides a framework to compare structural-functional networks during other behavioral tasks.  For example, active perturbations can target only a few individuals who are trained to a specific cue \cite{Strandburg_Peshkin_2013}.  General features from the temporal communication networks can be used with theoretical models of coupled decision-making \cite{Torney_2014,Srivastava_2014}, to ask how different structures affect the group's ability to spread information or reach consensus.  Future work will use this framework to compare and analyse communication networks in different species and during different tasks, and to understand how coupled decision-makers can remain robust to changes in structure while being sensitive to important incoming information.