Spatial Altruism

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World State

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Population Balance

Altruist, selfish, and empty patch counts

Model

Research Basis

This implementation follows the steady-state variable-density Mitteldorf-Wilson model. Altruists pay cost c, distribute benefit b across a five-site von Neumann neighborhood, and each site is reoccupied through a local weighted lottery among altruist, selfish, and empty competitors.

In the code, harshness is the void fitness eta and disease is the extra void lottery mass xi. The repository now covers the full paper-level variant set, including periodic uniform-culling and compact-swath disturbance modes, but this replay stays on the frozen steady-state configuration.

Observable mechanics prove an equation-level match to the steady-state Mitteldorf-Wilson model shown here. They do not, by themselves, prove whether this Python implementation was historically derived directly from the paper or through an intermediate implementation.

Experiment

Culling Results

A first culling-only sweep compared uniform_culling and compact_swath across b from 0.00 to 1.00, c from 0.00 to 0.35, fixed harshness = 0.96, disturbance interval 50, and disturbance fractions 0.25 and 0.50.

In that sweep, both culling variants produced coexistence regions, but uniform_culling was more robust: its mean coexistence probability was about 0.089 versus 0.057 for compact_swath, and it retained higher mean occupancy as well.

The sharpest difference appeared at disturbance fraction 0.50: uniform_culling still reached coexistence probability 1.0 in some cells, while compact_swath peaked at 0.8 and showed a much stronger occupancy collapse. That suggests contiguous swath clearing creates a harsher recolonization bottleneck than scattered clearing under the same nominal disturbance level.

World State

Population Balance

Static Culling Heatmaps