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The biogeographic expansion of modern humans out of Africa began ≈50,000 years ago. This expansion resulted in the colonization of most of the land area and habitats throughout the globe and in the replacement of preexisting hominid species. However, such rapid population growth and geographic spread is somewhat unexpected for a large primate with a slow, density-dependent life history. Here, we suggest a mechanism for these outcomes by modifying a simple density-dependent population model to allow varying levels of intra-specific competition for finite resources. Reducing intra-specific competition increases carrying capacities, growth rates, and stability, including persistence times and speed of recovery from perturbations. Our model suggests that the energetic benefits of cooperation in modern humans may have outweighed the slow rate of human population growth, effectively ensuring that once modern humans colonized a region long-term population persistence was near inevitable. Our model also provides insight into the interplay of structural complexity and stability in social species. [ABSTRACT FROM AUTHOR]