Each band starts from a single origin population (top-left star) with maximum genetic and cultural diversity (H₀ = 1.0). As a band's population grows past the carrying capacity, it splits — a small group founds a new settlement further along the migration front. Every such founding event carries only a subset of the parent's diversity, so diversity falls with each generation of splits:
H(n) = H0 * (1 - k)^n
where n is the number of founder events between a band and the origin, and k is the founder-effect strength. This is a simplified, discrete stand-in for the "serial founder effect" documented in real human population genetics (Ramachandran et al., PNAS 2005), where heterozygosity decreases roughly linearly with migration distance from East Africa — the model here reproduces the same qualitative pattern: diversity fades the further, and the more splits, a lineage is from home.
- Migration speed — how fast bands drift across the plane once founded.
- Carrying capacity — population a territory can sustain before it fissions into a new band.
- Founder-effect strength (k) — fraction of diversity lost by the founding group at each split.
- Time scale — overall simulation speed (generations per second).
Colour encodes diversity: bright teal near H≈1 fading toward grey as H→0. Marker size scales with each band's current population. Faint dots mark past founding sites — the "archaeological record" of the migration.