Settlement scaling and increasing returns in an ancient society

Abstract

A key property of modern cities is increasing returns to scale-the finding that many socioeconomic outputs increase more rapidly than their population size. Recent theoretical work proposes that this phenomenon is the result of general network effects typical of human social networks embedded in space and, thus, is not necessarily limited to modern settlements. We examine the extent to which increasing returns are apparent in archaeological settlement data from the pre-Hispanic Basin of Mexico. We review previous work on the quantitative relationship between population size and average settled area in this society and then present a general analysis of their patterns of monument construction and house sizes. Estimated scaling parameter values and residual statistics support the hypothesis that increasing returns to scale characterized various forms of socioeconomic production available in the archaeological record and are found to be consistent with key expectations from settlement scaling theory. As a consequence, these results provide evidence that the essential processes that lead to increasing returns in contemporary cities may have characterized human settlements throughout history, and demonstrate that increasing returns do not require modern forms of political or economic organization.

Keywords: Basin of Mexico; Mesoamerica; Networks; Productivity; Scaling; Settlement Patterns; Urbanization; archaeology.

Fig. 1. The BOM.

(A) Location within Mexico. (B) Settlements dating to the Formative period (outline shows surveyed area; circle size is proportional to population; colors denote elevation; gray area shows the extent of Mexico City in 1964). Today, settlement covers the entire basin, and the lake has been drained. See the Supplementary Materials for imagery sources.

Fig. 2. Super-linear scaling of socioeconomic rates with population.

(A) Political unit population versus public monument construction rates. (B) Settlement population versus total domestic mound area. Symbols denote time periods, solid lines show power law fits from ordinary least-squares (OLS) regression of the log-transformed data, and dashed lines represent proportionate (linear) scaling. Inset shows the independence of average G on N, where G = A/N * (mean domestic mound area) (see also Table 2).

Fig. 3. Histograms of domestic-mound areas.

(A) Distribution of log-transformed domestic mound areas across all sites. (B) Distribution of residuals from OLS regression of log [settlement population] versus log [mean house area]. Note that both distributions are approximately normal [Kolmogorov-Smirnov (Lilliefors) test results are P < 0.001 for (A) and P = 0.2 for (B)].