Cluster formation by allelomimesis in real-world complex adaptive systems.

Animal and human clusters are complex adaptive systems and many organize in cluster sizes s that obey the frequency distribution D (s) proportional to s(-tau). The exponent tau describes the relative abundance of the cluster sizes in a given system. Data analyses reveal that real-world clusters exhibit a broad spectrum of tau values, 0.7 (tuna fish schools) <or=tau<or=4.61 (T4 bacteriophage gene family sizes). Allelomimesis is proposed as an underlying mechanism for adaptation that explains the observed broad tau spectrum. Allelomimesis is the tendency of an individual to imitate the actions of others and two cluster systems have different tau values when their component agents display unequal degrees of allelomimetic tendencies. Cluster formation by allelomimesis is shown to be of three general types: namely, blind copying, information-use copying, and noncopying. Allelomimetic adaptation also reveals that the most stable cluster size is formed by three strongly allelomimetic individuals. Our finding is consistent with available field data taken from killer whales and marmots.

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