Reproduction and Social Mobility

This project aims to replicate the social mobility theory by Alan Rogers ^{1 2}. See here for an abstract.

There are three sets of code that constitute this replication:

1. Leslie Matrix Model

First, I reproduce the Leslie matrix model in R. See file leslie_matrix_model.R and its supporting functions in leslie_matrix_functions.R. The matrix model is the backbone of the social mobility model. It basically shows that the growth rates for a population and its age/wealth classes, the age/wealth class distribution in the population, and the proportions of long-term fitness can be captured by the dominant eigenvalue, the corresponding eigenvector, and the corresponding left eigenvector, respectively. See visualizations in the figures folder.

For the certain leslie matrices I have tried, we see that for individuals in the third class, they reproduce less offspring, but in the long-run, they have a higher fitness (genetic representation) in the population.

2. Social Mobility Model

The second part attempts to replicate the core of the social mobility model, in which parents maximize long-term growth rates by choosing a best reproductive strategy --- an optimized fertility allocation as a proportion of their wealth. See social_mobility_model.py as the start. It makes use of the optimization algorithm social_mobility_optimization.py and its supporting functions in social_mobility_functions.py. Input desired parameters in the PARAMETERS part of social_mobility_model.py and get your data in the data folder.

3. Data Analysis

The data produced by the model is analyzed in the third part: analyze_data.R, which makes use of read_data.R. The preliminary analysis shows no clear pattern as said in the abstract. Further analysis will be added.

Footnotes

1. Rogers, A. R. (1990). Evolutionary economics of human reproduction. Ethology and Sociobiology, 11(6), 479-495. ↩

2. Harpending, H., & Rogers, A. (1990). Fitness in stratified societies. Ethology and sociobiology, 11(6), 497-509. ↩