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Archaeologists now routinely use summed radiocarbon dates as a measure of past population size, yet few have coupled these measures to theoretical expectations about social organization. To help move the 'dates as data' approach from description to explanation, this paper proposes a new integrative theory and method for quantitative analyses of radiocarbon summed probability distributions (SPDs) in space. We present this new approach to 'SPDs in space' with a case study of 3571 geo-referenced radiocarbon dates from Wyoming, USA. We develop a SPD for the Holocene in Wyoming, then analyze the spatial distribution of the SPD as a function of time using a standard nearest-neighbor statistic. We compare population growth and decline throughout the Holocene with expectations for different Ideal Distribution Models from population ecology that predict the relationship between habitat quality and population density. Results suggest that populations in Wyoming were initially clustered and then became increasingly dispersed through the course of the Holocene. These results suggest that Allee-like benefits to aggregation, rather than ideal free-driven dispersion patterns, explain settlement decisions in response to growing populations. Our approach is a first step in constructing a method and theory for describing relationships between social organization and population growth trends derived from archaeological radiocarbon time-series.