The network ecology of settlement persistence

K. Blake Vernon

Center for Collaborative Synthesis in Archaeology (CU)

Simon Brewer

School of Environment, Society, and Sustainability (UU)

Brian Codding

Department of Anthropology (UU)

Scott Ortman

Center for Collaborative Synthesis in Archaeology (CU)

2024-08-30

kbvernon/eaa-2024_settlement-persistence

A pueblo in front of a city in the desert.

Why do some human settlements last longer than others?

Inspiration

Figure 1

Is persistence an inherent good?

No, its value derives from the contribution it makes to human life.

Figure 2

The Lord Baron model

Figure 3

The Lord Baron model

Goal is to maximize individual utility, \(F\):

\[F(R) = P(R) + S(R)\]

where

\(P\) = Primary production function
\(S\) = Social production function
\(R\) = Transport costs or “distance”

Figure 4

This anticipates many of the ideas that have come to be known as settlement scaling theory (Ortman et al 2014).

Settlement dynamics

Lord Baron assumes that settlement is a dynamic system with multiple, discontinuous equilibrium states.

Figure 5

Scaling effects

\(R\) is the per capita contribution of an individual to the “public good.”

Figure 6

Collective Action Problem

If you can’t get buy-in, the whole system unravels.

Figure 7

But, what about persistence?!

Read it from left to right, starting with the village equilibrium state.

Figure 8

“Agglomerations, once established, are usually able to survive even under conditions that would not cause them to form in the first place” (Fujita, Krugman, Venables 1999).

Expectations

  1. Agglomerated systems should persist longer than dispersed systems.
  2. Everyone should be “better off” in an agglomeration system, whether they are
    • profiting off that system or
    • trapped in it, having no viable alternative.

Unit of analysis

Figure 9

Population

Estimated for each grid cell using UPDA (Ortman 2016).

Figure 10

Duration

Derived by applying threshold to population reconstruction.

Figure 11

Agglomeration

Based on population distribution within travel time \(t\) of a focal grid cell.

Figure 12

Climate

Reconstructed using paleoCAR (Bocinsky and Kohler 2014).

Figure 13

Survival analysis

What explains the amount of time \(T\) that passes before a settlement is abandoned?

\[ \begin{aligned} T &\sim f(t)\\ S(t) &= Pr(T > t) = \int_{t}^{\infty} f(u)du\\ h(t) &= \frac{f(t)}{S(t)} \end{aligned} \]

with

  • \(S(t)\) being the survival function and
  • \(h(t)\) the hazard rate: the number of settlements you can expect to be abandoned at \(t\) given that they persisted up to \(t\).

Discrete-time proportional hazards

Can’t assume that \(T\) is continuous, so we use discrete time and model the hazard rate using ordinary logistic regression.

\[ \begin{aligned} E(T) &= h(t)\\ logit(h(t)) &= \alpha + \beta X + \epsilon \end{aligned} \]

\(X\): maximum agglomeration, maximum population, Maize GDD per time step, PPT per time step, initial start date, and region.

To handle spatial autocorrelation, the model also includes Moran Eigenvector Maps (MEMs).

Hazard rate

For illustration purposes.

Figure 14

Lingering issues

Probably in order of importance…

  1. Need to build population reconstruction using deep learning (Reese 2021).
  2. A better way of measuring agglomeration.
  3. Need a climate reconstruction that is better able to capture spatial variance.
  4. Might need to include lags.

Acknowledgments

  • Matt Peeples
  • Peter Yaworsky
  • Weston McCool
  • Josh Watts
  • The {extendr} crew
Figure 15