Reed's Law

Biological Parallel

Reed's Law: network value scales exponentially with possible subgroups (2^N - N - 1), not just connections. Bottlenose dolphins in Shark Bay form three nested alliance levels—pairs or trios herd females, 4-14 males form second-order alliances lasting decades, and second-order groups ally into third-order coalitions. Recent analysis of 121 adult males (2023) reveals the largest nonhuman alliance network known: 14 dolphins create 16,369 possible subgroup combinations. Baboons form shifting coalitions for mating access, resource defense, and rank challenges—pairs, trios, temporary super-groups all activated situationally. Mycorrhizal networks connect trees in combinatorial resource-sharing: a single fungi species links dozens of tree species, creating thousands of potential nutrient-exchange subgroups that shift seasonally. Chimpanzee politics run on Reed's Law: the 200-member Ngogo community forms patrol parties (3-8 individuals), hunting coalitions (2-5 individuals, preceding 50% of hunts), border defense groups (5-12), and alpha-coalition alliances (2-4)—overlapping memberships create exponential strategic options. The power isn't in N nodes—it's in 2^N possible groups.