Asymmetric Demographic Hysteresis in a Spatial Agent-Based Urban System (1.0.0)
This paper develops a spatial agent-based model to examine how fertility regime shifts reshape population concentration and wealth distribution in an abstract urban system. Migration decisions combine population preference, cultural homophily, expected net income, and resource endowment through a standardised softmax utility. The design is deliberately stylised: it is not calibrated to a particular country or city system, but is intended to isolate the feedbacks linking migration, fertility, urban scaling, and accumulated wealth.
The simulations reveal robust directional asymmetry. When fertility shifts from low to high, population concentration responds rapidly; when fertility shifts from high to low, concentration declines only after a detectable delay and may temporarily continue in the previous direction. Wealth adds a second layer of hysteresis: cell total-wealth concentration follows population concentration with delay, cell mean-wealth inequality and system-level wealth indicators are slower still, and phase-space trajectories form loops rather than collapsing onto a single population–wealth curve. Robustness experiments indicate that longer fertility cycles, wider mobility neighbourhoods, and smoother resource landscapes change the magnitude of delay and overshoot, but do not remove the qualitative asymmetry. The paper argues that demographic decline should be understood not as the mirror image of demographic expansion, but as a path-dependent transition mediated by fast migration-income feedbacks and slower fertility, cohort, culture, and wealth mechanisms.
Release Notes
Initial review release associated with the manuscript “Asymmetric Demographic Hysteresis in a Spatial Agent-Based Model of Urban Population and Wealth Dynamics”.
This release contains the model code, input data, and ODD documentation used to reproduce the simulation experiments reported in the manuscript. The code implements the spatial agent-based model, including local migration choice, resource and income effects, evolving cell culture, density-dependent fertility propensity, age-dependent mortality, and wealth accumulation. It also includes scripts/notebooks for generating the main simulation outputs and summary statistics used in the figures and tables.
This release is intended for peer review and replication. Access is currently restricted for reviewers. The model may be made public after publication.
Main contents:
- Model implementation notebook.
- External input data used by the model.
- ODD appendix describing entities, state variables, process overview, submodels, and parameter settings.
- Reproducibility information including baseline and robustness experiment settings.
Associated Publications
Asymmetric Demographic Hysteresis in a Spatial Agent-Based Urban System 1.0.0
Submitted by
Chen Shen
Published Jul 24, 2026
Last modified Jul 24, 2026
This paper develops a spatial agent-based model to examine how fertility regime shifts reshape population concentration and wealth distribution in an abstract urban system. Migration decisions combine population preference, cultural homophily, expected net income, and resource endowment through a standardised softmax utility. The design is deliberately stylised: it is not calibrated to a particular country or city system, but is intended to isolate the feedbacks linking migration, fertility, urban scaling, and accumulated wealth.
The simulations reveal robust directional asymmetry. When fertility shifts from low to high, population concentration responds rapidly; when fertility shifts from high to low, concentration declines only after a detectable delay and may temporarily continue in the previous direction. Wealth adds a second layer of hysteresis: cell total-wealth concentration follows population concentration with delay, cell mean-wealth inequality and system-level wealth indicators are slower still, and phase-space trajectories form loops rather than collapsing onto a single population–wealth curve. Robustness experiments indicate that longer fertility cycles, wider mobility neighbourhoods, and smoother resource landscapes change the magnitude of delay and overshoot, but do not remove the qualitative asymmetry. The paper argues that demographic decline should be understood not as the mirror image of demographic expansion, but as a path-dependent transition mediated by fast migration-income feedbacks and slower fertility, cohort, culture, and wealth mechanisms.
Release Notes
Initial review release associated with the manuscript “Asymmetric Demographic Hysteresis in a Spatial Agent-Based Model of Urban Population and Wealth Dynamics”.
This release contains the model code, input data, and ODD documentation used to reproduce the simulation experiments reported in the manuscript. The code implements the spatial agent-based model, including local migration choice, resource and income effects, evolving cell culture, density-dependent fertility propensity, age-dependent mortality, and wealth accumulation. It also includes scripts/notebooks for generating the main simulation outputs and summary statistics used in the figures and tables.
This release is intended for peer review and replication. Access is currently restricted for reviewers. The model may be made public after publication.
Main contents:
- Model implementation notebook.
- External input data used by the model.
- ODD appendix describing entities, state variables, process overview, submodels, and parameter settings.
- Reproducibility information including baseline and robustness experiment settings.