Two key features of human sociality are anatomically complex brains with neuron-dense cerebral cortices, and the propensity to form complex social networks with non-kin. Complex brains and complex social networks facilitate flows of fitness-enhancing energy and information at multiple scales of social organization. Here, we consider how these flows interact to shape the emergence of macroscopic regularities in hunter-gatherer macroecology relative to other mammals and non-human primates. Collective computation is the processing of information by complex adaptive systems to generate inferences in order to solve adaptive problems. In hunter-gatherer societies the adaptive problem is to resolve uncertainty in generative models used to predict complex environments in order to maximize inclusive fitness. The macroecological solution is to link complex brains in social networks to form collective brains that perform collective computations. By developing theory and analyzing data, the author shows hunter-gatherers bands of ~16 people, or ~4 co-residing families, form the largest collective brains of any social mammal. Moreover, because individuals, families, and bands interact at multiple time scales, these fission-fusion dynamics lead to the emergence of the macroscopic regularities in hunter-gatherer macroecology we observe in cross-cultural data. These results show how computation is distributed across spatially-extended social networks forming decentralized knowledge systems characteristic of hunter-gatherer societies. The flow of information at scales far beyond daily interactions leads to the emergence of small-worlds where highly clustered local interactions are embedded within much larger, but sparsely connected multilevel metapopulations.