D64 Characterization of information flows

Topic

This characterization of information flows within a colony employs Shannon's information theory—part of the framework established here—to quantify both how individuals communicate with one another and how information propagates throughout the colony.

Shannon entropy in this context measures the diversity of behavioral states: a colony where all individuals perform the same task exhibits low entropy, whereas a colony with a balanced distribution of tasks among individuals exhibits high entropy.

Mutual information between two individuals quantifies the extent to which knowing the state of one individual reduces uncertainty regarding the state of the other; a pair of individuals sharing high mutual information is thus strongly coordinated within the colony.

Entropy transfer between two individuals is both asymmetric and causal: it measures whether the past state of one individual reduces uncertainty about the future state of the other—beyond the reduction achieved by the second individual's own past state—in accordance with Granger causality expressed in terms of entropy. A higher rate of entropy transfer from one individual to another implies a greater influence of the first individual upon the second within the colony. Conversely, the contact network within this colony shapes its ultimate social structure: an individual with a significant number of contacts within the colony becomes critical to the spread of information throughout it. If such an individual accumulates even more contacts, their importance to the information's propagation increases further.

Thus, the model—based on the flow of information through a colony—uses the network's efficiency to measure how quickly a signal travels from any one individual to another within that colony; a "small-world" network achieves remarkably high efficiency despite having a relatively small number of contacts. As the colony's contact network moves closer to this small-world structure, the efficiency of the information flow across the colony increases even more.

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