Quantifying collectivity

•The collectivity of aggregate behavior can be quantified using information theory.•Amplification quantifies information flow from small to large scales and hence system-level sensitivity to perturbations at the small-scale.•Measures of decomposability tell us whether the aggregate-level behavior is reducible and hence can reveal the basic causal units in the system.

In biological function emerges from the interactions of components with only partially aligned interests. An example is the brain - a large aggregation of neurons capable of producing unitary, coherent output. A theory for how such aggregations produce coherent output remains elusive. A first question we might ask is how collective is the behavior of the components? Here we introduce two properties of collectivity and illustrate how these properties can be quantified using approaches from information theory and statistical physics. First, amplification quantifies the sensitivity of the large scale to information at the small scale and is related to the notion of criticality in statistical physics. Second, decomposability reveals the extent to which aggregate behavior is reducible to individual contributions or is the result of synergistic interactions among components forming larger subgroups. These measures facilitate identification of causally important components and subgroups that might be experimentally manipulated to study the evolution and controllability of biological circuits and their outputs.