Conflict-Mediated Group Size Regulation: A Theory of Supraoptimal and Suboptimal Group Size

Abstract

Observed group sizes rarely match the size that would maximize what each member gets from belonging. We propose a two-part theory in which group size is regulated by two related conflicts: insider-outsider conflict over admission, and within-group conflict as crowding, competition, and social tensions intensify with size. Three strategies are available within a group of interchangeable members: admission, exclusion, and fission. The models hold each member's standing and resource exploitation strategy constant. While both vary and determine a member's own game and its payoffs, explaining this complexity and its consequences is beyond our scope. The theory's first part shows that even when exclusion is unavailable, fission dynamics alone drive group size away from the optimum in both directions, with the pattern set by how prospective joiners encounter groups and by the geometry of fission. When joiners compare groups across a shared landscape and fission is asymmetric, the standing distribution is bimodal: supra-optimal large groups coexisting with a sub-optimal mode of small groups, the pattern characteristic of fission-fusion societies. The second part promotes exclusion and fission to active decisions: incumbents weigh the per-capita cost of accommodating entry ({beta}) against the costs of coordinated exclusion (c +{gamma} N) and fissioning (F). A single inequality, {beta} > c +{gamma} N, partitions populations into two regimes: where it holds, exclusion is viable and groups lock at the optimum size; where it fails, groups grow past the optimum and cycle through recurrent fission. > {varphi} then fixes the geometry of that fission, separating splits in which members leave independently, which strand small daughters and give the bimodal distribution, from splits in which several members depart at once. Modal group size, fission frequency, and exclusion behavior together identify which regime governs a population -- a set of predictions applicable across fishes, social insects, birds, and mammals including primates and human foragers.