Cities are increasingly the fundamental socio-economic units of human societies worldwide, but we still lack a unified characterization of urbanization that captures the social processes realized by cities across time and space. This is especially important for understanding the role of cities in the history of human civilization and for determining whether studies of ancient cities are relevant for contemporary science and policy. As a step in this direction, we develop a theory of settlement scaling in archaeology, deriving the relationship between population and settled area from a consideration of the interplay between social and infrastructural networks. We then test these models on settlement data from the Pre-Hispanic Basin of Mexico to show that this ancient settlement system displays spatial scaling properties analogous to those observed in modern cities. Our data derive from over 1,500 settlements occupied over two millennia and spanning four major cultural periods characterized by different levels of agricultural productivity, political centralization and market development. We show that, in agreement with theory, total settlement area increases with population size, on average, according to a scale invariant relation with an exponent in the range . As a consequence, we are able to infer aggregate socio-economic properties of ancient societies from archaeological measures of settlement organization. Our findings, from an urban settlement system that evolved independently from its old-world counterparts, suggest that principles of settlement organization are very general and may apply to the entire range of human history.

Ancient Mesoamerican settlements obey the same scaling laws as modern cities despite vast differences in economy, technology and political organization.

Empirical studies of ancient cities must break down communities into their component parts, but frequently encounter difficulty with the scarcity of excavated domestic structures (e.g., Kramer, 1982, p. 673). I introduce to the archaeological literature the entropy estimating statistical bootstrap (EESB), a tool developed in information theory and computational social science by DeDeo et al. (2013) which provides a way to assess how representative a small dataset is of a parent population, categorized according to some useful typology. This method can be used to decide when small datasets can add further detail to our quantitative studies of archaeological settlements or when they need to be rejected as too small. I then illustrate its uses within the context of urban demography by examining the distribution of house forms to calculate household characteristics specific to Metapontum, an ancient Greek city. Future applications will include building larger urban datasets that are empirically grounded in the specific evidence for each community, facilitating the work of research programs such as urban scaling.