2024-08-30

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

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”

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

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

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

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

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

“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).

- Agglomerated systems should persist longer than dispersed systems.

- Everyone should be “better off” in an agglomeration system, whether they are
- profiting off that system or

- trapped in it, having no viable alternative.

- profiting off that system or

Study area

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

Derived by applying threshold to population reconstruction.

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

Reconstructed using paleoCAR (Bocinsky and Kohler 2014).

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*\(t\).

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).

For illustration purposes.

Probably in order of importance…

- Need to build population reconstruction using deep learning (Reese 2021).

- A better way of measuring agglomeration.

- Need a climate reconstruction that is better able to capture spatial variance.

- Might need to include lags.

- Matt Peeples
- Peter Yaworsky
- Weston McCool
- Josh Watts
- The
`{extendr}`

crew