Abstract
From fish schools and bird flocks to biofilms and neural networks, collective systems in nature are made up of many mutually influencing individuals that interact locally to produce large-scale coordinated behavior. Although coordination is central to what it means to behave collectively, measures of large-scale coordination in these systems are ad hoc and system specific. The lack of a common quantitative scale makes broad cross-system comparisons difficult. Here we identify a system-independent measure of coordination based on an information-theoretic measure of multivariate dependence and show it can be used in practice to give a new view of even classic, well-studied collective systems. Moreover, we use this measure to derive a novel method for finding the most coordinated components within a system and demonstrate how this can be used in practice to reveal intrasystem organizational structure.
Highlights
In the absence of a quantitative definition, papers on collective behavior often begin by listing well-known examples of collective systems, like fish schools or bird flocks
In the context of a fish school or a bird flock, this could be the set of all the velocity vectors of the individuals in the group; for neurons, this could be the state of each neuron
One of the foundational results from information theory is that no lossless description of a random variable can be shorter on average than the tight lower bound given by its entropy (Shannon 1948)
Summary
In the absence of a quantitative definition, papers on collective behavior (including this one) often begin by listing well-known examples of collective systems, like fish schools or bird flocks. This gives a useful reference point for the reader, but offers little guidance on what to consider “collective” in other systems and behaviors. Even a canonical example of collective behavior like a fish school may vary in the degree of coordinated movement over time and transition between periods of ordered movement and disordered aggregation (Tunstrøm et al 2013). Schools can vary widely in size across and within species and environments. Millions of sardines moving together may be clearly collective, but a school of two is less clear
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