K. Blake Vernon and Scott Ortman

2024-04-20

- A site that functions as either a large residential center or as a place for social interaction, often both.
- Identified archaeologically by the presence of civic architecture or more households than can be reasonably related by reckoned kinship (e.g., great houses and great kivas).

Is it because it’s more productive at those locations (like C1) or more central (like C2)?

Locations of community centers ▲ and farms ●

Outcome of interest is a Poisson-distributed random variable \(N\) of centers per unit area.

\[ N_{i} \sim Poisson(\lambda_{i})\\ E(N_{i}) = \lambda_{i}\\ log(\lambda_{i}) = \beta X_{i} + \epsilon_{i} \]

- covariates \(X\) include gravity-weigted BC, precipitation, and maize GDD
- \(\epsilon_{i}\) is the random error
- model also includes fixed effects for study area and time period

Fitting an approximation of this model with **down-sampled random forest**.

For graph \(G(V,E)\) with vertices \(V\) and edges \(E\), the **gravity-weighted betweenness centrality** of vertex \(v \in V\) is given by:

\[gBC(v) = \sum_{s,t \in V; s\neq v\neq t}^{N} I_{s,t}(v)\cdot G_{s,t}\]

where

- \(I_{s,t}(v)\) is the indicator function that is 1 if on shortest path between \(s\) and \(t\), 0 otherwise and
- \(G_{s,t}\) is the gravitational attraction between \(s\) and \(t\)

**But…**

… in a highly structured spatial grid graph, gBC is just a wordy synonym for **population density**.

Gravity breakdown

Using precipitation and temperature as proxies.

Probability of centers as a function of the density of farms over time.

Center niche in **ecological space** averaged over **1200-1300 CE**

Center niche in **geographic space** averaged over **1200-1300 CE**

This analysis is more exploratory than final, but tentatively…

- You should always prefer the simpler model.
- Community centers positively co-vary with the density and distribution of farms.
- The relationship between farms and centers varies by region.

Next step is to model the co-occurrence of farms and centers directly.

- Matt Peeples
- Simon Brewer
- Brian Codding
- Weston McCool
- Josh Watts