# Selection and the Roy Model in the Neolithic Transition

## Introduction

Technological and climate shift

direct effect: incentives and decisions

**indirect effect**: population distribution

### This paper

Climate shift and adoption of agriculture over the past 14,000 years

Link selection to economic activity choice (farming vs foraging)

Evolution in population distribution

**Impact**: current choices depend on actions of past generations

## Contributions

**Polygenic selection**: Berg and Coop (2014); Racimo, Berg, and Pickrell (2018); Guo, Yang, and Visscher (2018); Cox et al. (2019); S. Mathieson and Mathieson (2018); Uricchio (2020); I. Mathieson (2021); Song et al. (2021); Stern et al. (2021); Yair and Coop (2022)

### Link to economic model of activity choice

**Economics of farming spread:** Bowles (2011); Bowles and Choi (2013); Robson (2010); Rowthorn (2011); Rowthorn and Seabright (2010)

### Emphasise the role of genotype distribution

## Climate and agriculture

Holocene (\(\approx\) 11,000 years ago - present)

Agriculture

- begins to spread \(\approx\) 11,000 years ago
- higher marginal productivity thanks to climate change
- evolutionary advantages: higher fertility, lower mortality (Shennan 2018)

### Selection of farming-friendly genotypes

## Model of genotype evolution

Based on Wright-Fisher model

- finite, constant population \(N\)
- \(K\) causal loci
- unit of analysis - haplotype pairs \(\mathbf{H} = (l, r) = \left(\{0, 1\}^K, \{0, 1\}^K\right)\)
- mutation, recombination,
**selection**

## Selection and technology

- \(z(g)\) is a polygenic score

\[ z(g) = \sum_{k = 1}^K \beta(k) g(k) \] - two technologies: HG - foraging and AG - farming
- technology-specific fitness function

\[f(z, \tau) = R_\tau \exp\left(\omega_\tau z\right), \forall \tau \in \{HG, AG\}\] **fitness-maximising technology choice**: \(\hat{f}(z) \equiv \max_\tau f(z, \tau)\)

## Technology choice

### Roy model

. . .

### Adapted to fitness

## Data

### Genotypes

### GWAS estimates

- Educational attainment (Lee et al. 2018)

## Descriptive evidence

### Education PGS in aDNA

### Edge and Coop (2019) Waiting-time estimator

## Estimation

Parameter of interest: technology-specific selection gradient \(\omega_\tau\)

- Assume distribution before climate shift is at steady state: \(\omega_{HG} = 0\)
- Estimate \(\omega_{AG}\) by maximising simulated likelihood
Draw initial haplotype matrix consistent with allele frequencies in WHG

Simulate independent histories from the model over \(T\) generations

Compute simulated likelihood of phenotypes in modern EUR

## Results

## Results

### Full sample

. . .

### Truncated sample

## Conclusion

- Study genetic evolution in European populations over the last 14,000 years
- Extend Wright-Fisher model with activity choice in the spirit of Roy model
- Estimate using ancient and modern genotypes

Future extensions:

- Migration
- Estimation with path