Information-theoretic individuality and multilevel individuals

Verworn described a community of ants as a single individual, a unitary whole whose parts work together like the parts of an organism, though it consists of many single individuals¹. Verworn proposed calling the more comprehensive form an individual of a higher order and its components individuals of a lower order. The coral stem and its polyps stand in the same relation as the ant community and its ants¹. Verworn added a qualification. Constituents of a higher individual are not always real individuals. Some are only virtual, because they cannot preserve themselves when separated from their fellows².

Child (1915) fixed a vocabulary for the problem. Child called the individual that starts a developmental, reproductive or life-history the primary individual³. Rádl (1930) surveyed the older discussion of the question. Rádl listed persons formed by the loose union of similar individuals, as in corals, or by the closer union of structurally different ones, as in Siphonophora⁴. Rádl also reported that Tönnies separated communities, whose members descend from the same parents, from societies, where this is not so⁴. Lichens served as a case of two organisms, an alga and a fungus, each able to live independently⁴.

Information theory later supplied a quantitative tool. Wolf and colleagues (2008) estimated memory as the mutual information between cell history and cell behavior⁵. Sengupta, Stemmler and Friston (2013) set out a limit. Information theory can quantify the transmission of information, but it has no notion of semantics⁶. Flack (2017) used the measure for a social system. A DSP will be a reliable predictor of interaction cost if it has mutual information with the hidden distribution of fighting abilities and changes slowly⁷.

Krakauer, Bertschinger, Olbrich, Flack and Ay (2020) argued that there is little agreement on what individuals are. They proposed that individuals are aggregates that preserve temporal integrity by propagating information from past to future⁸. Their formulation yields three forms, organismal, colonial and driven, which differ in environmental dependence and inherited information⁸. It admits adaptive aggregations that are multi-scale and distributed and do not necessarily have physical boundaries such as cell walls or clonal somatic tissue⁸. Blackiston and colleagues (2025) built networks of cells in aneural tissue, with edges given by the Gaussian mutual information between the signal time series of each pair⁹.