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The Boyd & Richerson (2009) Culture Replication

GitHub code

1. The question the paper asks​

Ordinary group-selection theory has a well-known problem: migration between groups usually erases the between-group variation that selection needs something to act on. Boyd & Richerson (2009), "Culture and the Evolution of Human Cooperation" (Phil. Trans. R. Soc. B), ask why human societies nonetheless differ from each other far more than other primate groups do, and answer with a single ratio: culture can sustain a much lower migration/selection ratio than genetics ever could, preserving exactly the standing variation between groups that group selection requires as its raw material.

2. The mechanism: a tug-of-war between two forces​

The model is a 256-subpopulation torus, each site holding a value on 3 frequency-dependent cultural traits. Two forces pull in opposite directions every generation:

  • Selection (s) — each trait is frequency-dependent: whichever variant a subpopulation already has more of gets pulled further toward that side. This force creates and preserves differences between neighboring subpopulations.
  • Migration (m) — a fraction of each subpopulation is replaced by immigrants from its 4 nearest neighbors each generation, pulling each subpopulation toward whatever its neighbors have. This force erases those differences.

Which force wins is decided entirely by the ratio m/s: high m/s homogenizes the whole population into one shared culture; low m/s preserves a lasting patchwork of different local norms. Genetics is stuck near m/s ≈ 25 (fast dispersal, weak selection) — enough to homogenize primate groups before real differences can build up. Culture, the paper argues, gets both a faster effective s (rapid social learning) and a lower effective m (migrants tend to assimilate to local norms rather than diluting them), letting it sustain a far lower ratio.

3. This site's replication​

A from-scratch, independently reviewed reproduction of the paper's illustrative Section 3(b)-(c) model, with no author-released code to check against, is available in the BoydRicherson2009 repository's culture_human_cooperation/ module.

4. Result: reproduces, plus an independently confirmed refinement​

The three qualitative panels reproduce as the paper describes: m/s = 5 (migration-dominant) converges to a single trait combination everywhere; m/s = 0.1 (selection-dominant, the paper's own literal ratio) produces visibly more spatial clustering, though a real, disclosed gap remains — the best of 30 seeds tried at this ratio still clusters somewhat less tightly than the paper's own published figure; m/s = 0.5 (balanced) shows the same "mostly homogeneous, one clean domain boundary" structure as the paper's middle panel, though the boundary's shape and orientation aren't claimed to match exactly.

Beyond reproducing the published panels, a full sweep across the m/s range turned up a refinement the paper doesn't report: m/s = 1 does not fully homogenize even after 300,000 generations — 15× more generations than were used to produce the illustrative figure — and repeated runs confirm this isn't a fluke. The paper's own dividing line between "homogenizes" and "doesn't" needs a longer time horizon to state precisely than the illustrative figure alone suggests.

References​

  • Boyd, R., & Richerson, P. J. (2009). "Culture and the Evolution of Human Cooperation." Philosophical Transactions of the Royal Society B, 364, 3281–3288. https://doi.org/10.1098/rstb.2009.0134